UNIVERSITEIT GENT

FACULTEIT ECONOMIE EN BEDRIJFSKUNDE

ACADEMIEJAAR 2014 – 2015

Combinatorische Veilingen in de Supply

Chain

Masterproef voorgedragen tot het bekomen van de graad van

Master of Science in de Toegepaste Economische Wetenschappen: Handelsingenieur

Leander Catthoor

onder leiding van

Prof. Dries Goossens

UNIVERSITEIT GENT

FACULTEIT ECONOMIE EN BEDRIJFSKUNDE

ACADEMIEJAAR 2014 – 2015

Combinatorische Veilingen in de Supply

Chain

Masterproef voorgedragen tot het bekomen van de graad van

Master of Science in de Toegepaste Economische Wetenschappen: Handelsingenieur

Leander Catthoor

onder leiding van

Prof. Dries Goossens

PERMISSION

Ondergetekende verklaart dat de inhoud van deze masterproef mag geraadpleegd en/of

gereproduceerd worden, mits bronvermelding.

Catthoor Leander

SAMENVATTING

Tegenwoordig worden veilingen wereldwijd gebruikt door bedrijven voor de aan- en verkoop van

goederen en diensten. Combinatorische veilingen zijn complexer dan de alom bekende klassieke

veilingen (bv. de veilingen op eBay), waar de hoogste bieder het individuele product wint.

Deelnemers kunnen op dit soort veilingen bieden op een bundel of pakket van meerdere producten

in plaats van op een afzonderlijk product. De bieder wint achteraf ofwel het hele pakket ofwel niets.

Dit laat hen toe om hun voorkeur voor de beschikbare producten beter uit te drukken en synergiën

(het geheel is meer dan de som van de verschillende delen) tussen de producten te benutten. Een

transportbedrijf kan bijvoorbeeld bieden om goederen te verplaatsen van locatie A naar locatie B, in

combinatie met een transport van B naar A. Dit zorgt ervoor dat hij niet van locatie B naar locatie A

moet terugkeren met een lege vrachtwagen. De mogelijkheid om te bieden op pakketten van

goederen verhoogt de complexiteit in de verdeling van de producten over de verschillende bieders

wel aanzienlijk en maakt het kiezen voor de winnende bieders niet eenvoudig.

Combinatorische veilingen werden geïntroduceerd in 1982 door Rassenti, Smith, & Bulfin (1982)

voor de toewijzing van landingstijdstippen op een luchthaven. Tegenwoordig zijn deze soort

veilingen een opkomend fenomeen en hebben ze veel toepassingsgebieden. In de productieketen

worden ze het vaakst gebruikt door bedrijven voor de inkoop van goederen en de toewijzing van

vrachtwagenvervoer over verschillende trajecten. Dat komt omdat de producten in deze

toepassingen grote kans op synergiën bevatten. Als men combinatorische veilingen op de juiste

manier toepast, is het mogelijk om van deze positieve effecten gebruik te maken en zorgt het voor

een hogere efficiëntie in de toewijzing van de producten. Hierdoor zijn ze een effectieve methode

voor bedrijven om hun productieketen te verbeteren. De vele beschikbare softwareleveranciers van

combinatorische veilingen illustreren het potentieel in deze toepassingsgebieden.

Bedrijven hebben vandaag de dag meer en meer nood aan uitbestedingsstrategieën en

samenwerkende productienetwerken om hun eigen productieketen op een effectieve manier te

beheren. Dit vraagt om een verhoogde automatisatie en flexibiliteit in hun keuze naar de juiste

productiepartners. Via combinatorische veilingen kunnen bedrijven niet alleen bieden op de aan- en

verkoop van goederen maar ook op transformaties van goederen in het productieproces. Hierdoor

kunnen bedrijven uit de verschillende schakels in de productieketen aan elkaar worden gelinkt. Op

deze manier staan ze bedrijven bij in de vorming en automatisatie van hun productieketen.

Een goed gekozen combinatorische veiling, kan vele voordelen bieden aan de verschillende

bedrijven in een productieketen. Naast de verhoogde efficiëntie, laat het ook een snellere

informatie-uitwisseling tussen de deelnemers toe en kan het hen veel kosten besparen, zoals lagere

aankoopprijzen en transactiekosten. Dit zorgt ervoor dat combinatorische veilingen, in bepaalde

toepassingen van de productieketen, een tijdbesparend en efficiënt onderhandelingsproces kunnen

zijn in vergelijking met traditionele onderhandelingsmethoden.

I

Acknowledgements

This thesis was the last hurdle in acquiring my degree of Master of Science in Business Engineering.

Although this was by far my most independent work, I couldn’t have established it without the help

and support of a few people. I therefore like to thank them for their contribution.

In the first place I want to thank my promotor, Professor Dries Goossens, for the good support and

advice about the subject during my work. I also want to thank him for the critical evaluation of my

work approach and the helpful recommendations.

Further on special thanks goes out to my parents, not only for reviewing my work but also for their

moral support and advice.

Last but not least, I want to thank my friends and girlfriend for their support and the highly

appreciated relaxing moments.

II

Content

Acknowledgements .................................................................................................................................. I

Content ................................................................................................................................................... II

List of Abbreviations .............................................................................................................................. IV

List of Figures .......................................................................................................................................... V

Preface .................................................................................................................................................... 1

1. Introduction .................................................................................................................................... 3

1.1. Auction History ....................................................................................................................... 3

1.2. Basic Auction Theory ............................................................................................................... 6

1.3. Types of Auctions .................................................................................................................... 8

1.4. Combinatorial Auctions ........................................................................................................ 10

1.5. Auctions in the Supply Chain ................................................................................................ 12

1.6. Applications ........................................................................................................................... 14

2. Combinatorial Auctions................................................................................................................ 16

2.1. Dimensions Auction Space .................................................................................................... 16

2.1.1. Resources ...................................................................................................................... 17

2.1.2. Bidding Rules ................................................................................................................. 17

2.1.3. Information Revelation Policy ....................................................................................... 19

2.1.4. Clearing Policy ............................................................................................................... 20

2.2. Auction Classification ............................................................................................................ 23

2.2.1. Non-Iterative Combinatorial Auctions .......................................................................... 23

2.2.2. Iterative Combinatorial Auctions .................................................................................. 24

2.3. Bidding Languages ................................................................................................................ 25

2.3.1. Expressiveness versus Simplicity ................................................................................... 26

2.3.2. Types Bidding Languages .............................................................................................. 26

2.4. Winner Determination .......................................................................................................... 28

III

2.4.1. NP-hardness .................................................................................................................. 30

2.4.2. Approximation .............................................................................................................. 30

3. Auctions in the Supply Chain ....................................................................................................... 32

3.1. Supply Chain Formation ........................................................................................................ 32

3.2. Modelling Supply Chain Formation ....................................................................................... 35

3.2.1. Double Auctions ............................................................................................................ 35

3.2.2. Task Dependency Networks .......................................................................................... 37

3.2.3. Mixed Multi-Unit Combinatorial Auctions .................................................................... 40

3.3. (Online) Reverse Auctions ..................................................................................................... 43

3.3.1. How and When to Use Reverse Auctions ..................................................................... 45

3.3.2. Benefits of Reverse Auctions ........................................................................................ 46

3.3.3. Risks of Reverse Auctions.............................................................................................. 48

4. Practical Applications ................................................................................................................... 50

4.1. Industrial Procurement ......................................................................................................... 50

4.1.1. Current Practices ........................................................................................................... 51

4.1.2. Design Combinatorial Procurement Auctions ............................................................... 53

4.1.3. Examples ....................................................................................................................... 54

4.2. Truckload Transportation ..................................................................................................... 56

4.2.1. Current Practices ........................................................................................................... 56

4.2.2. Design Combinatorial Transportation Auctions ............................................................ 58

4.2.3. Examples ....................................................................................................................... 60

4.3. Higher Level Supply Chains ................................................................................................... 63

4.4. Software ................................................................................................................................ 64

4.4.1. Overview Software Providers ....................................................................................... 65

4.4.2. Mixed Multi-unit Combinatorial Auction Test Suite ..................................................... 70

5. Conclusions ................................................................................................................................... 73

References ............................................................................................................................................. VI

IV

List of Abbreviations

B2B Business-to-Business

CA Combinatorial Auctions

IP Integer Programming

MMUCA Mixed Multi-Unit Combinatorial Auctions

MMUCATS Mixed Multi-Unit Combinatorial Auction Test Suite

MUCRAtR Multiunit Combinatorial Reverse Auction with Transformability Relationships

among Goods

NP Non-deterministic Polynomial time

OR Additive-or

ORA Online Reverse Auction

RFQ Request For Quote

SCF Supply Chain Formation

TDN Task Dependency Network

WDP Winner Determination Problem

WTPN Weighted Transition Petri Nets

XOR Exclusive-or

V

List of Figures

Figure 1: Schematic of a generic supply chain ...................................................................................... 13

Figure 2: Parameter choices of three classic auctions .......................................................................... 22

Figure 3: Parameter choices of three online auctions .......................................................................... 22

Figure 4: Supply chain stages and flows ............................................................................................... 33

Figure 5: A TDN of an automotive supply chain ................................................................................... 38

Figure 6: Products purchased through ORAs ........................................................................................ 46

Figure 7: Gross versus net savings in an online reverse auction .......................................................... 49

Figure 8: Sourcing cycle for procurement ............................................................................................. 51

Figure 9: Estimates and data about CAs in procurement ..................................................................... 52

Figure 10: Results of the first CA of SLS ................................................................................................ 61

Figure 11: Statistics of the first CA at The Home Depot ....................................................................... 62

Figure 12: Bidder entry screen at Optimal Auctions ............................................................................. 68

Figure 13: A simple auction example in MMUCATS ............................................................................. 71

Figure 14: Optimal supply chain of the simple auction example in MMUCATS ................................... 72

1

Preface

Auctions are used worldwide by many companies and governments to buy and sell goods and

services. Combinatorial auctions or multi-item auctions are more complex than the widely known

classic auctions (for example the auctions on eBay) where the highest bidder wins the individual

product. Instead of bidding on a single product, participants can bid on bundles or packages of

multiple products. The bidder wins the full package or nothing. This enables them to better declare

their preferences for the available products and capture synergies between the products (the whole

is greater than the sum of its parts).

The strengths and benefits of package bidding are illustrated in the next examples. For instance, a

logistics provider can submit a package bid to transport goods from location A to location B

combined with transportation from B to A, which ensures he doesn’t need to drive back from

location B to location A with an empty truck. Another example is bidding on a car fleet together with

the needed insurances and the maintenance service for the cars in the future. Companies can also

use combinatorial auction to outsource parts of its production and increase integration with

suppliers. For example a company that needs packaging materials; instead of just bidding on the

delivery of the specific type of boxes, potential suppliers can include the design, validation,

manufacturing, and delivery of the boxes into its bids.

Because of the increased complexity due to package bidding, it is not always easy to allocate the

products across the bidders. Another important aspect in auctions is its mechanism or design. An

auction is characterized by many different design rules and changing such a rule can alter the

auction type. For this reason, many different types of (combinatorial) auctions exist.

Combinatorial auctions are introduced for the first time by Rassenti, Smith, & Bulfin (1982) for the

allocation of airport landing slots. Nowadays, they are a real upcoming phenomenon and have many

different application domains. In the supply chain, they are regularly used for industrial procurement

and the allocation of truckload transportation.

A lot of papers are available about the different aspects of combinatorial auctions. Also, many

papers exist with information regarding supply chain management and formation. However, little

information is available about the use of combinatorial auctions in the supply chain. Nearly all of the

2

auctions in a B2B environment, trade multiple items. However, most research about auction theory

is primarily based on single-item auctions (Elmaghraby & Keskinocak, 2004).

The goal of this thesis is therefore to fill this gap between the two subjects by giving an overarching

literature study about combinatorial auctions with a direct link to the supply chain. This literature

review bundles the most interesting aspects of combinatorial auctions and explains how they can be

applied in a supply chain setting. Three different methods are described how combinatorial auctions

can improve the automation of the supply chain formation. A few applications are detailed and

expanded with some real life case studies. Additionally, an overview of the available software

providers for its applications is given, something that didn’t exist yet in the available literature. This

enriches the thesis with a more practical insight so it doesn’t solely focus on the theoretical aspects.

This literature review starts with a general introduction to let the reader get familiar with the

subject. Next, the chapter about combinatorial auctions describes some of its most important

aspects (e.g. dimensions, classification, bidding languages, and winner determination). Afterwards,

the chapter about auctions in the supply chain explains how combinatorial auctions can be used in

the formation of supply chains. To conclude this thesis, a detailed description of the most interesting

practical applications of combinatorial auctions in the supply chain is given, combined with an

overview of some software providers.

This thesis doesn’t go too far into the technical details and mathematics behind the different kinds

of auctions. The reader doesn’t need to have studied the subject explicitly to understand the

content. Hence, it is ideal for laymen or experts in the field to acquire the needed knowledge about

combinatorial auctions in the supply chain.

3

1. Introduction

An auction is a process or mechanism to trade goods and services between buyers and sellers. An

auction is organized by taking bids from potential buyers and after analysing the bids, the items are

sold to the highest bidders. The word “auction” is originated from the Latin “auctus”, meaning “I

increase” or “I augment”. Therefore bids are increased until the highest price is found.

“Auctions are important market mechanisms, used since the earliest of times for the allocation of

goods and services. Public and private institutions generally prefer them over other common trading

processes (lotteries, price-posting, etc.) because they are open, quite fair, generally easy to

understand by participants, and often lead to economically efficient outcomes” (Abrache, Crainic,

Gendreau, & Rekik, 2007, p.132). Auctions are therefore widely used in situations in which fairness

or at least the appearance of fairness plays an important role because they make sure all potential

bidders have an equal chance of winning goods in the auction (Rothkopf & Park, 2001). Another

advantage of auctions is that a seller who finds himself in a relatively weak bargaining position can

do as well as a strong bargained seller (P. R. Milgrom, 1985).

We first go back to the roots of auctions in history and how they became more common in our lives

today. Afterwards some of the most basic auction types and theories are described before moving

on to combinatorial auctions (CA) and its applications in the supply chain.

1.1. Auction History

This section about auction history is primarily based on the paper of Doyle & Baska (2002) and is

expanded with several references from other authors.

As one of the oldest surviving classes of economic institutions, auctions have a rich history. The first

form of an auction is recorded in Greece by Herodotus 500 years before Christ. According to him,

annual auctions of women for marriage were held in Babylon and it was illegal to sell a daughter

outside this auction method (P. R. Milgrom, 1985). This auction used the descending method,

whereby the starting price was periodically lowered until the first bidder was willing to pay that

price. It was possible to set a minimum selling price for the bride. Returning (part of) the money was

also allowed if the marriage didn’t work out as planned. ‘Try-outs‘ in advance before the start of the

4

auction however, were not allowed. As expected, the highest prices were paid for the most beautiful

women. Sometimes extra monetary offers were added to the auction to ease the sale of lesser

attractive women.

Around the time of Christ, Romans used auctions to sell slaves and war trophies. Auctions were also

a popular means to sell family estates and possessions of debtors whose property has been

impounded, a technique still used in our modern days. In the Middle Ages, belongings of deceased

monks were also sold at auctions. Despite the explicit history of auctions, they lost favour in Europe

after the Roman Empire until the 17th century.

In 1674, Baron Claes Ralamb founded the Stockholm Auction House, the first known auction house

in the world1. That same year the well-known English auction (infra section 1.3) was executed at the

Summerset House for the first documented auction of a painting in England. In 1739, the first real

estate auction was held in the London Evening Post. Dutch auctions, which operated in a descending

order until someone submitted a bid, were also popular around that time. Auctioneers were looked

upon as charismatic entertainers of the crowd. Therefore coffee houses and inns were popular

places for English auctions. At the beginning of the 18th century, auctions changed from a small

event with only a few people to bigger meetings, which were promoted in daily advertisements.

Around this time, auctioneers also started to open up their own permanent place of residence to

hold auctions. The auction house Sotheby’s was founded by Samuel Baker in London in 1744 when

he wanted to dispose a collection of several hundred rare and valuable books and it is now the

second-largest auction house in the world. In 1766, James Christie started the auction house Christie

to sell art and is now the world’s largest. Currently, it offers around 450 auctions per year in more

than 80 different categories2. In 1886, The Auctioneers Institute of the United Kingdom was

founded, and it has more than 2.000 members nowadays.

Auctions in America started when the Pilgrims arrived on America’s Eastern Shores in the 1600s and

sustained their popularity during the colonization by selling furs, crops, livestock, tools and slaves. In

the 1860s Civil War Colonels auctioned the loots of war and in 1876 antique auctions began to

flourish. In 1883, Thomas Kirby opened the American Art Association in New York City, which was

the first auction house in Amerika to sell fine art. This association contributed towards the current

trend of art auctions being formal, black tie evening sales with theatrical presentations of the goods

1 <www.auktionsverket.com/about-us/about-stockholms-auktionsverk> (28-12-2014)

2 <www.christies.com/about-us/company/overview> (28-12-2014)

5

to be auctioned. Real estate auctions also grew fast in America and it was assessed that half of all

real estate in New York was sold at auctions in 1904. Many auction schools started at the beginning

of the 20th century, with the National School of Auctioneering and Oratory founded by Carey Jones in

1904 believed to be the first. The increasing popularity of auctions was demonstrated in the 1920s

when American companies started to incorporate images of auctions in their advertising. Scenes of

auctions were displayed in beer, insurance and Ford automobile advertisements. In the 1930s when

the depression hit most of the people hard, many auctioneers crossed the country to liquidate the

estates of bankrupt farmers and families. After World War II, many businessmen began to see

auctions as an alternative marketing tool because the sale of goods and real estate was strongly

increasing in the period after the war. Auctions increasingly became property of wealthy

businessmen in suits and tie and raised its reputation to a higher level. In 1949, the National

Auctioneers Association (NAA) was founded and is now the world’s largest professional association

devoted to professional auctioneers3.

It wasn’t an easy job for auctioneers to organize an auction in the past. Auctioneers had to travel by

horse and wagon and there were no amplifiers yet for the auctioneer’s voice. The weather often

determined when the auction could begin. It wasn’t always easy to communicate the upcoming

auction and find enough participants, so free lunches were frequently given to lure the crowd.

Auctioneers faced many challenges in those days which are now eliminated in our modern society.

As technology improved rapidly in the 1980s and 90s, auctioneers began to incorporate this

technology into auctions at a fast pace. Cell phones, microphones, screens, computers, etc. made it

much easier for the auctioneer to organise and carry out an auction. The most significant growth in

the usage of auctions was the development of the internet. The internet lifted the restriction of time

and space and auctioneers could take bids from a much broader range of buyers than before.

In the 1980s, Reynolds Metal Company was the first to use optimization for its winner determination

problem (infra section 2.4) in an auction for transportation services (Caplice & Sheffi, 2006). The first

use of combinatorial auctions was in 1982 for the allocation of airport landing slots. In 1993, Sears

Logistics Services was the first to use combinatorial auctions and package bidding in its freight

allocations. The FCC’s Nationwide Narrowband Auction of spectrum rights in 1994 was one of the

first examples of the use of CAs for selling spectrum rights. Currently, these types of auctions are still

frequently organized by governments for the distribution of spectrum rights. Since 1995, London

3 <http://www.auctioneers.org/about-us> (28-12-2014)

6

Transport also started using combinatorial auctions for allocating bus routes to the different bus

service providers (de Vries & Vohra, 2003).

In 1995, auctions approached the territory of cyberspace when the Japanese car company Aucnet

went online for the auction of automobiles. Also in 1995, Freemarkets Inc. opened a business, which

was one of the pioneers of the online reverse auctions at that time. Other firms like ITOI and

Commerce One added to the success (Kros, Nadler, & Chen, 2011). This was followed closely by a lot

of other companies with the launch of eBay, which is currently the market leader in online auctions,

as the best known example.

Other pioneering applications of combinatorial auctions were for the distribution of school meals in

Chile in 1999, the use of combinatorial auctions at The Home Depot for its transportation services in

2000 and for the procurement processes at the large chocolate manufacturer Mars Inc. in 2001

(Bichler, Davenport, Hohner, & Kalagnanam, 2006). Most of these cases are described in chapter 4.

This has led to a continuous growth in the use and presence of auctions in the supply chain

formation of companies all over the world. The National Auctioneers Association stated that the

gross revenue of the auction industry was around $268,4 billion in 2008.

1.2. Basic Auction Theory

Before moving on to the combinatorial auctions, the most important aspects about basic auction

theory are described shortly. As a first aspect, a brief evolution of the basic valuation models is

given. Three main theories exist:

1) The private value auction model introduced by Vickrey (1961). In this model, every bidder knows

his own value but not those of the other participants in the auction. This value depends on the

monetary worth he is willing to give for a specific package of items and is independent of the

information of others. The private value model is used as the benchmark environment and we

will assume this model when talking about auction environments further on.

2) Wilson (1969) introduced the common value auction model. In this model all bidders have the

same value for the items but this value depends on the private information of all bidders and is

therefore uncertain. An important phenomenon of common value auctions is the winner’s curse

which occurs because bidders can only estimate the value of a good. If the bidders, on average,

estimate the value correctly, the winning bidder is likely to have paid more for the item than it is

7

worth. An example is auctioning a jar with coins; this jar has the same value for all bidders but

the value is uncertain.

These two previously cited models are two extreme cases which are useful in deriving strong

theoretical results. In practice however, these models fall short because auction environments often

have both private and common value items. For this reason, Milgrom (1981) created a realistic

hybrid auction model in which both private and common value items exists.

3) This hybrid model led to the affiliated values model (P. Milgrom & Weber, 1982). In this model

the value of a bidder is derived directly from the private information of all the bidders. However

a critical aspect is that the signals of the bidders (the estimates of the value for an item) are

connected to each other, meaning it is expected that if one bidder has a high signal of value for

an item, the other bidders will also have high signals of value.

These three basic types contributed to the fast development of auction theory and the introduction

of many other models in later years. For example, Myerson (1981) created the revenue maximizing

auction by building on the private value model of Vickrey. In this auction the revenues of the seller

are maximized and bidders are assumed to behave risk neutral and generate their value for specific

bundles by independent private information (Cramton, Shoham, & Steinberg, 2007).

This leads us to our second aspect of auction theory, namely the objective or the allocation rule of

the auction. An objective can be revenue maximization, which is the maximum profit for a seller in

an auction. The goods in the auction are allocated to the bidders in such a way that the seller

receives the highest revenues. Besides this objective it is also possible to require the maximization of

economic efficiency. Economic efficiency is concerned with dividing the surplus (the difference

between the actual price of a good and the value of the good for a bidder) of an auction over the

bidders. This means that the buyer who has the highest value for a good (and therefore is often

willing to pay the highest price) receives the good. The primary goal of the seller is not to generate

the highest revenue for himself but to maximize the overall benefits or surplus for the participating

bidders. It is also possible goods are handed out for free but people who needs them the most will

receive them first. This method is often pursued by governments to increase the overall welfare of

its citizens (Abrache et al., 2007).

Another important aspect of auction theory is the pricing rule. This rule indicates how much a

winning bidder has to pay for a good. It can be a first-price rule, where winning bidders have to pay

the exact amount of their bid. Another option is the second-price rule, where the winning bidders

receive the goods but only have to pay the price of the second highest bid (Abrache et al., 2007).

8

In designing an auction mechanism, one has to consider four different subjects (Babaioff & Nisan,

2004):

Incentive Compatibility (IC): The auction mechanism encourages the self-interested participants

to bid truthfully and reveal their true costs by making sure this is the dominant strategy (infra

Vickrey auctions section 1.3).

Individual Rationality (IR): Bidders participate voluntarily in the auction and they don’t pay more

than their valuation for the received items.

Economic Efficiency: The outcome of the auction should maximize the total value for all the

participants.

Budget Balance (BB): The auction doesn’t lose money, otherwise there is little encouragement to

hold the auction. This is especially important in double auctions (infra section 3.2.1) meaning

that the total payments of the buyers must be greater or at least equal to the total amount

received by the sellers. Otherwise the market mechanism has to subsidize the auction.

Unfortunately in two-sided negotiations, it is not possible to apply these four conditions

simultaneously. Trade-offs therefore have to be made between conditions in designing the auction

mechanism (Babaioff & Walsh, 2003).

1.3. Types of Auctions

The wide range of situations for which auctions can be used is remarkable. They are applicable for

livestock, rare and unusual items (e.g. diamonds, art), durables, perishables, financial assets, land,

equipment, supplies and many more. Therefore auctions come in many different forms and varieties

(P. R. Milgrom, 1985). An important aspect in the type of auction is the market structure, which

corresponds to the roles the participants play in the auction. You can make a distinction between on

the one hand one-sided auctions and on the other hand two-sided auctions or double auctions. The

one-sided auctions can be further divided into two different types:

a) A forward auction where a single seller offers resources to multiple buyers. Some widely known

examples of this type of auction are (McAfee & McMillan, 1987):

The English auction, also known as the open ascending price auction, is the most common

type of auction in use today. In this form of auction, participants openly bid against each

other and have enough time to react to concurrent bids and make counteroffers. Prices are

announced by the bidders themselves or by an auctioneer who continuously raises the price

9

until no further bids are called out. The auction comes to an end when there are no bidders

willing to increase their bid and therefore the seller can take the last and highest price bid to

sell the good. It is possible for the seller to set a minimum sale price (reserve price) in

advance; the auction price must reach this minimum otherwise the good remains unsold.

This type of auction is frequently used for selling antique, artwork, second-hand goods, and

real estate. Online auction sites (e.g. eBay) often use English auctions formats to let

consumers sell goods.

The Dutch auction is similar to the English one; the only difference is that this is an open

descending price auction instead of ascending. In this auction the auctioneer starts with a

high asking price for a certain amount of goods. The price then decreases step by step until a

participant is willing to accept the offered price. As in the English auction, it is also possible

for the auctioneer to set a reserve price.

In the sealed first-price auction or the first-price sealed-bid auction, all bidders submit sealed

bids so the buyers don’t know the bids of other participants. The difference with the English

version is that bidders cannot adjust their bid to concurrent ones. This auction is commonly

used in the USA for selling mineral rights to government-owned land. These first three types

of auctions are all examples of the first-price type.

In Vickrey auctions or second-price sealed-bid auctions, participants hand in sealed bids for a

desired item and the winning bidders only pay the price of the second highest bid. In this

mechanism there is no reason for the bidder to incorrectly state his value because an

individual bidder cannot influence the price it ultimately pays for the winning item. In this

type of auction, the dominant strategy for bidders is to bid their valuations truthfully

because this is the only way for the bidder to win exactly what he wants at the price he is

willing to pay. In a forward Vickrey auction, the buyers receive a discount compared to the

winning price bid (Ausubel & Milgrom, 2006).

b) A reverse auction is an auction where a single buyer wants to buy resources or a contract from

multiple sellers. The roles of the buyer and seller are reversed, hence the name a reverse

auction. This type of auction is also called a procurement auction. Rather than just having

potential buyers bid on a good they want to acquire, a buyer often offers a contract for the

supply of a service or an amount of goods. Multiple suppliers then contend for winning the

contract by bidding descending prices until a final bid wins the contract and ends the auction

(Smart & Harrison, 2003). Suppliers have the possibility to submit more than one offer, as a

reaction to a concurrent bid. The main goal of this auction is to drive the buying price downward

10

and let the buyer find the lowest-price supplier. The objective in procurement auctions is in

general to minimize the procurement costs of the buyer. Other advantages are time savings,

faster and more effective information transmitting, a broader potential supplier pool, and

increased competition (Kros et al., 2011). This auction is commonly used in the different stages

of the supply chain and is therefore applied excessively by organizations, the state and local

governments. English, Dutch and Vickrey auctions can also be used as reverse auctions. In the

reverse Vickrey auction, sellers obtain a premium (equal to the 2nd lowest price minus the lowest

price) in comparison with the clearing price (Ausubel & Milgrom, 2006). More information about

reverse auctions can be found in section 3.3.

The other type of auctions are called double auctions or combinatorial exchanges in which multiple

buyers offer resources to multiple sellers (Kalagnanam & Parkes, 2004). In this case participants in

the auction can indicate bids to buy or sell, or both at the same time (Wurman, Wellman, & Walsh,

2001). With these auctions it is also possible to express the transformation of goods and is therefore

frequently used in the supply chain. This type is discussed in much more detail in section 3.2.1.

1.4. Combinatorial Auctions

“An auction is combinatorial when bidders can place bids on combinations of items, called packages,

rather than just individual items” (Cramton, Shoham, & Steinberg, 2007, p.3). The goods are traded

as a package if the package bid surpasses the total value of the separate bids for the items in the

bundle. Combinatorial auctions are valuable when bidders have preferences for sets of items or

bundles because of complementarities between the different goods. When a certain set of goods

has a higher utility than the sum of the individual utilities for the items, the goods are complements

(Cramton et al., 2007). Allowing potential buyers to bid directly on bundles of items instead of

individual items can improve the economic efficiency and/or auction revenues because of the

potential synergies between the goods in a bundle (de Vries & Vohra, 2003).

If a bidder has interest in two different goods at a combinatorial auction, he can directly make an

offer for the two goods in a single bid. This is not the case in regular auctions whereby the bidder has

to make two individual bids on the goods. If he only wins one of the goods, his intentions for the

other good are exposed. Another problem with single-item auctions is for example when a bidder

needs three goods to transform them into another good. If he fails to win one of the goods, he ends

up with two goods he can’t do anything with. The ability to bid on bundles alleviates this exposure

problem because it gives the bidders the possibility to bid their exact valuations and preferences for

11

any bundle of goods they aspire. Combinatorial auctions therefore eliminate the possibility of ending

up with unwanted goods (Abrache et al., 2007).

In combinatorial auctions, it is not always certain that a bidder with the highest individual bid for a

bundle of goods also wins the goods. Consider this example to illustrate: imagine an auction of a

table and 4 chairs. Bidder A offers €70 for 2 chairs and the table, bidder B is willing to give only €10

for 2 chairs, bidder C is prepared to pay €20 for 3 chairs and bidder D offers €65 for one chair and

the table. While bidder A has the highest individual bid and therefore outbids every other bidder, he

doesn’t win the bid because the combined bids of C and D generate higher revenue for the seller (70

+ 10 < 65 + 20) (de Vries & Vohra, 2003).

However, combinatorial auctions can introduce several difficulties. On the one hand, it is necessary

that bidders have enough flexibility in their bidding opportunities to capture the needed synergies

between goods and eliminate the exposure problem. On the other hand, too much flexibility can

lead to strategic behaviour and damages the efficiency and optimality of the auction. A form of

strategic behaviour occurs when bidders submit package bids and offer discounts even if there are

no synergies between the goods in the package. This bidder can hereby win goods even if he isn’t

the most cost efficient supplier. This form of strategic behaviour is called strategic bundling. Another

problem is that bidders can sometimes free ride on others to outbid a competitor for a bundle of

goods. Consider as an example, bidder 1 wants good A for €40 and bidder 2 wants good B for €30

but bidder 3 submits a package bid of €75 for both good A and B. Because bidder 3 offers a higher

price than the sum of the two individual bids, bidder 1 and/or bidder 2 have to increase their bids if

they want to win the good. Bidder 1 has two options: increase his bid to outbid the package bid of

bidder 3 or free ride in the hope that bidder 2 increases his bid. In this last option he doesn’t need to

pay a higher price for good A but risks not winning the good if bidder 2 thinks the same way. The two

first bidders must coordinate their bidding behaviour to make sure they both win the good but this

cooperation is not an easy task for smaller bidders. Big competitors therefore have an advantage

because they can bid on larger packages, an option often not desirable for the smaller bidders. This

can bias the outcome of the auction in favour of large bidders and possibly generate inefficiencies

and increase the cost of allocation. This is called the threshold problem because the smaller bidders

have to coordinate their bidding so that the sum of their bids overcomes the package bid (threshold)

of the larger bidder (Olivares, Weintraub, Epstein, & Yung, 2012).

12

Combinatorial auctions bring along an extra amount of decision making problems. Not only the

allocation of the goods to the bidders is important, also the design of the auction plays a significant

role. The amount of rounds, restrictions on the biddings, amount of information received by the

bidders during the auction, etc. are all important aspects (Spieksma, 2003).

The problem in a combinatorial auction with a specified set of bids is to find an allocation that

maximizes the economic efficiency or the auctioneer’s revenue, including the option that the seller

preserves some of the goods. It can be a complex process to define the winning bidders in a

combinatorial auction when the amount of items and bidders in the auction increases. The winner

determination problem (WDP) is in general NP-hard (non-deterministic polynomial-time hard),

meaning that there is no known polynomial-time algorithm to find the optimal allocation and it is

unlikely that one exists. Many models and algorithms have been introduced to discover an

approximated solution for the combinatorial auction problem, for example bounding techniques.

Most of the time, the type of auction and application determines which algorithm is the best.

Though if possible, it is advised to always search for an optimal solution instead of an approximated

one. This is because the losing bidders can claim the auction was not run fairly and can feel deceived

when an approximation method is used to determine the winners in the auction. Hence it is best to

only use approximated solutions when the problem becomes very complex and it is takes too long to

find an optimal solution (Abrache et al., 2007). This winner determination problem is further

elaborated in section 2.4.

Combinatorial auctions are described extensively in chapter 2.

1.5. Auctions in the Supply Chain

The supply chain of a product or service starts with raw materials and components and transforms it

into a finished product that is distributed to the end customer. The supply chain is a complex system

of resources, activities and organizations in which a product moves in many different stages from

supplier to end user. The different stages in a supply chain have interrelated exchange relationships

between the goods and the values for buying several inputs and producing outputs are jointly

reliant. Auctions in a supply chain therefore have to deal with strong complementarities between

the goods. A producer can risk producing unsold goods when there is no demand for the product

downstream and has the possibility to fail to produce the already sold products when he is unable to

retrieve the required inputs. This can damage his reputation (Giovannucci, Rodriguez-Aguilar,

Vinyals, Cerquides, & Endriss, 2007).

13

A schematic plan of a generic supply chain is showed in figure 1. A supply chain can consist of many

different stages with multiple companies in every stage.

Figure 1: Schematic of a generic supply chain (Thomas & Griffin, 1996)

Supply chain formation (SCF) brings together a network of agents that can transform basic raw

materials into end goods. It requires assembling complex production and exchange relationships

(Walsh, Wellman, & Ygge, 2000). The different production levels in the supply chain can present

difficult coordination problems for supply chain formation because precedencies and dependences

must be taken into account. In combinatorial auctions these complementarities can be characterized

as relationships amongst goods. Purchases of raw materials therefore have to be linked with sales of

finished goods. The difficulty in supply chain formation however is that the interdependencies not

only include products but also production or transformation relationships alongside the different

supply chain levels (Giovannucci, Rodriguez-Aguilar, Vinyals, et al., 2007). “In combinatorial auctions,

agents place all-or-nothing bids for bundles of goods. The auction computes a high-quality allocation

of bundles, ensuring that agents do not receive undesirable partial bundles” (Walsh et al., 2000,

p.260). This way, producers cannot lose profits by obtaining inputs and failing to sell the

productions.

One method for dealing with these interdependencies of markets is to handle the entire supply

chain as an individual complex huge market. This approach has the advantage of generating a

centralized solution. However, it also has the problem that it is necessary to concentrate all

communications, information and decision making at a single point and making the integration of all

markets into one huge market an extremely complex optimization problem (Babaioff & Nisan, 2004).

14

Another method for dealing with such complementarities is to handle the supply chain as a

sequence of individual markets that connects each other by using a certain procedure to generate a

distributed mechanism (Babaioff & Nisan, 2004). This approach is introduced by Walsh et al. (2000)

and is given the name task dependency network (TDN). These networks include consumers and

producers. Consumers wish to obtain goods from producers for a certain value. Producers fabricate

or assemble the required goods, provided that they receive all the necessary inputs.

According to Giovannucci et al. (2007) TDNs are valuable for modelling supply chain formations but

need additional requirements. They prescribe expressiveness requirements (dealing with

complementarities and transformations of goods by fully expressible bidding languages), formal

requirements (supporting the structural and behavioural characteristics of a supply chain) and last

but not least computational requirements (computational manageability while guarding optimality)

to bolster automated supply chain formation.

Mixed multi-unit combinatorial auctions (MMUCAs) are a generalisation of the typical model of

combinatorial auctions and are introduced by Cerquides, Endriss, Giovannucci, & Rodriguez-Aguilar

(2007). The auctioneer and bidders in MMUCAs bargain over transformations, which are

distinguished by a set of input and output goods, and not over simple goods. An extension of this

auction is the Multiunit Combinatorial Reverse Auction with Transformability Relationships among

Goods. This allows bidders to indicate both transformability relationships among goods and their

desires for bundles of goods (Giovannucci, Cerquides, & Rodríguez-Aguilar, 2010).

More information about auctions in the supply chain and methods to automate the supply chain

formation is found in chapter 3.

1.6. Applications

Combinatorial auctions come in many different forms and types and can be used for numerous

practical applications. The eldest application for CA’s was introduced by Rassenti et al. (1982) for

airport landing slots. Nowadays auctions are used for a wide variety of purposes, for example

industrial procurement, course registration, sale of spectrum rights, sale of online seats, allocation of

airport slots, truckload transportation, bus routes, network routing, etc. (Abrache et al., 2007). The

most interesting usage of combinatorial auctions in the supply chain is the distribution of truckload

transportation and industrial procurement.

15

Industrial procurement is especially interesting in the business to business (B2B) domain. “In a

reverse or procurement auction, a buyer puts out a request for quote (RFQ) for a service or a

product(s), and prices are determined by a competition among potential sellers” (Elmaghraby &

Keskinocak, 2002, p.246). Industrial procurement managers define specifications, select potential

suppliers and discuss price conditions; they are accountable for the complete sourcing process. This

iterative bargaining process can produce an achievable solution, given the constraints, while

maximizing the offers received from their portfolio of suppliers (Bichler et al., 2006).

The transportation market consists of shippers and carriers. Retailers, distributors and

manufacturers that need to transport cargo are seen as shippers and are the auctioneers in the

allocation of transport services. The companies that own the transportation resources (e.g. trucks,

trains) are the bidders in the auction. These auctions, often consists of one shipper which is the

auctioneer and multiple carriers which are the bidders in the process. The carriers aim to win

contracts to transport the shipper’s cargo (Caplice & Sheffi, 2006). Transportation auctions can also

be used for allocating bus routes.

These applications are discussed in more detail in chapter 4.

16

2. Combinatorial Auctions

After the introduction about auctions and the supply chain, a more detailed view on combinatorial

auctions is handled in this chapter. First, the dimensions of the auction space are described. Next, a

classification of the different auctions is given because auctions come in many different types and

forms. Afterwards the bidding languages are touched without going too much into the technical

details. This chapter is concluded by describing the winner determination problem.

2.1. Dimensions Auction Space

Before we can explain the dimensions of the auction’s design space, the first step is to identify three

fundamental activities common to auctions. According to Wurman, Wellman, & Walsh (2001) these

three activities are:

a) Receive bids: Agents send in bids to partake in the exchange of goods via an auction. The bids

must be according the specific bidding rules of the auction and are admitted as active bids if

they pass these rules.

b) Reveal intermediate information: These are termed as ‘quotes’ and give the agents an

intermediate status of the submitted bids. The revealed quotes give the bidders information

about the results of a conditional clear at that moment.

c) Clear: This is the end purpose of an auction and makes sure that, if possible, resources are

traded between sellers and buyers. It also ensures that corresponding payments are received

correctly. Clearing an auction means that the goods are conditionally or temporarily allocated

over the bidders according to the collected bids at that moment.

An auction must complete the first and last activity to achieve an end result in the auction. The

second activity is not a necessity but most auctions provide these intermediate information updates

to the agents participating in the auction. Conditional to the auction rules and type, these activities

may be repeated multiple times (Wurman et al., 2001).

17

A lot of different types of auctions exist and it is therefore not easy to make a complete

parameterization of all the dimensions of the auction space. Only the most important dimensions

are discussed here. This parameterization is based on the work of Wurman et al. (2001) and is

extended with findings of Abrache et al. (2007) and Kalagnanam & Parkes (2004).

2.1.1. Resources

The first step in defining an auction is to identify what types of resources are traded at the auction.

Multiple distinctions are possible:

The considered resource can be single-unit or multi-unit. A single-unit auction has numerous

different goods in the auction but each good only has one unit. A multi-unit auction means that

each good in the auction has multiple units to be sold (Kalagnanam & Parkes, 2004).

Another possible distinction is between a standard item and a multi-attribute item. For standard

items, participants can only reflect a single attribute, the price, in their bids. With multi-attribute

goods, agents need to stipulate attributes other than price (type, quality, etc.) with an inherent

scoring function between the different characteristics to make a trade-off (Kalagnanam &

Parkes, 2004).

We can also have a distinction between indivisible and divisible goods. An indivisible good is

something that cannot be physically cut into pieces and thus has to be sold as a whole. For

example a table can only be sold as a full table and not leg by leg. A divisible good can be sold in

different pieces to multiple buyers, e.g. capacity in telecommunications (Abrache et al., 2007).

A resource can be a pure commodity, which has no special structure, or it can be a network

commodity. The latter goods refer to capacity or services that pertain systems with network

structure (Abrache et al., 2007).

2.1.2. Bidding Rules

Bidding rules regulate when an agent can introduce, modify or withdraw his bid. They depend on the

current status of the bid, the agent’s identity and the auction history. When an incoming bid satisfies

the bidding rules, it enters into the set of existing bids. In case the bid doesn’t correspond to the

admission criteria, the agent receives a message that his offer is denied (Wurman et al., 2001).

Bidding rules are characterized by many different aspects:

18

Expressiveness

“An auction mechanism dictates a language for bids, defining their syntax as well as expressive

power” (Wurman et al., 2001, p.313). The auction determines the complexity of the participants’

bids. The bid structure regulates the flexibility of the agents to express their preferences and

requirements when placing a bid for resources. If a bid only consists of the composition (the

desired goods) with a conforming price, the bidders can use simple bids, which are unrelated to

each other. However if more complex bidding requirements are needed, participants can rely on

more complicated bidding languages (Abrache et al., 2007). These bidding languages are

discussed in more detail in section 2.3.

Dominance

Dominance rules limit the new offering of an agent’s bid. This means that an agent’s new bid

must hold some relationship with previous offers for the same good. We speak of an ascending

rule if new bids have to be superior to old bids and a descending rule if the new bids have to be

inferior regarding old offerings. Most of the time, new bids have to beat some sort of price

quote or a minimum incremental change in price. The main reason for these rules is to assure an

evolution of prices. The buying side of an offer often has an ascending rule and the selling side a

descending rule because this is instinctively the most natural way of bidding. However in some

occasions it may be worthwhile to have a descending rule while buying. This is because the

buyer can then lower his bid to a zero price to withdraw his bid from the auction. The same can

be said for retreating a selling bid by increasing it to infinity (Wurman et al., 2001).

Withdrawal and Expiration Rules

Auctions provide rules for withdrawing a bid. These rules stipulate if it is allowed to withdraw or

not. If it is allowed, it also states at what point of time in the auction the withdrawal can take

place. For example, a possible rule is that a bid can only be revoked when the auction undergoes

a clearing operation or if it provides intermediate information. Of course many other rules exist.

If the withdrawal is planned in advance at certain times it is called an expiration (Wurman et al.,

2001).

Activity Rules

The auction provides activity rules to make sure that everyone involved in the auction stays

active in the bidding process. These rules must make sure that bidders cannot benefit by staying

inactive and therefore withholding information while others expose their intentions and

19

information by actively participating. This avoids that some bidders steal the deal at the end by

handing in their bid when the bidding process converges towards an end result (Wurman et al.,

2001). An example of an activity rule is given by DeMartini, Kwasnica, Ledyard, & Porter (1999)

where bidders may only place a defined amount of bids in each round of a multi-round auction.

This amount is equal to the number of bids placed in the former round plus the number of

temporarily winning items in the auction. Hence, active bidders are rewarded with more

possible bids and inactivity will result in exclusion from the bidding process.

2.1.3. Information Revelation Policy

As already mentioned above, an auction has the possibility to reveal intermediate information

during the auction. The given information can be regarding a price signal or a conditional allocation

or both. In sealed bid auctions, the participants do not receive information or feedback as long as

the auction isn’t finished. This is a direct mechanism because the bidders cannot adjust their bids

once handed in. In an open auction, bidders receive feedback and signals about their position in the

auction. Hence, participants in the auction can refine their bids according to the received

information. For this reason, these auctions are indirect mechanisms (Kalagnanam & Parkes, 2004).

Other important aspects regarding information revelation are:

Price Quotes

A price quote gives an agent more information about the range of bids that are in the exchange

set. Obviously, it is best practice that all bidders receive the price quotes at the same time.

Otherwise, if there is a time period between delivering the same quotes to all the different

participants, the last agent in line may receive an outdated quote. The information captured in a

price quote can vary not only between different auctions but also between bidders in the same

auction. If all agents receive the same quote, it is anonymous. When each participant receives a

personalised price quote, they are discriminatory (Wurman et al., 2001).

Quote Timing

Price quotes can alter in quantity and frequency. These aspects determine the quote timing. The

most common timing polices are (Wurman et al., 2001):

Random Quotes: The quotes occur at randomly picked points in time generated according a

stochastic distribution.

Scheduled Quotes: The price quotes are released following a predetermined nominal

schedule.

20

Bidder Activity: Quotes are produced with every newly entered bid.

Bidder Inactivity: Quotes are produced after a specific period of inactivity.

Order Book and Transaction History

The order book of an auction captures the current set of active bids. It is up to the auctioneer to

decide if he reveals all or only some of the information to the bidders. Commonly used tactics

are to retain the order book closed for everybody, reveal only the temporarily winning bids, or

open the book entirely. Auctions can also announce certain information about the historical

exchanges. The auction can choose what to publicize, concerning the prices, the quantities and

the agents’ identities. Revealing this information helps countering the information asymmetry

that bidders encounter when they didn’t participate in previous auctions (Wurman et al., 2001).

2.1.4. Clearing Policy

As explained in the beginning of this part of the chapter, an auction clears when it calculates an

allocation based on the currently obtained offers from the bidders.

Matching Function

The clearing of an auction is calculated by the matching function. The operation of determining

the exchanges consists of two steps: first, it resolves the question of which agents will

participate in the trade; secondly, it determines the exact conditions of every exchange. The

surplus of an exchange is the difference in payments between what the buyer is maximally

willing to pay and what the seller minimally wants to receive. If this surplus is positive, the

exchange between the two participants is mutually beneficial (Wurman et al., 2001). Matching

supply and demand is also called the winner determination. An important decision is whether to

allow single- or multi-sourcing. In single-sourcing, the buyers and sellers in an auction are paired

against each other. While in multi-sourcing, it is possible to link numerous sellers with a single

buyer, or the other way around. This has an impact on the difficulty of solving the winner

determination problem and ranges from straightforward sorting problems to optimization

problems that are NP-hard (infra section 2.4) (Kalagnanam & Parkes, 2004).

21

Clear Timing

The timing when an auction clears is an important aspect of the clearing policy. Some frequently

used timing policies are given next (Wurman et al., 2001). Of course some sort of combination

between the policies is always possible.

Random: The clear happens at a randomly picked point in time generated by a random

distribution, e.g. the memoryless Poisson distribution. This policy prevents agents using

time-dependent tactics.

Scheduled: The auction clears after achieving a certain scheduled milestone. This could be

for example predefined nominal times or some implicit statement. Besides these examples

many other scheduled rules exist to clear an auction.

Bidder Activity: If the auction is continuous, it clears every time a participant submits a new

bid. A variation of this timing policy is used in a synchronized auction where the auction only

clears when it received a bid from each participant or after a predetermined amount of bids.

Bidder Inactivity: The auction clears after a certain period of inactivity by all the bidders.

Closing Conditions

The closing conditions regulate when a clear is the final clear by using a logical test. Examples

are: having the closing clear at a random or scheduled time, after a certain period of inactivity of

the bidders, at an external signal or when the agents’ bids are matched (Wurman et al., 2001).

Tie Breaking

When two agents bring out the same willingness (e.g. the same price) for some subset of

resources, a tie takes place between the participants. The auctioneer has to choose one of the

bids because it is impossible to let two bidders win the same resources. These tie breaking rules

affect the end result of the auction. The most common methods to determine a winner are: to

break ties arbitrarily, in favour of the earliest bidder or the largest quantity bid (Wurman et al.,

2001).

Auctioneer Fees

Payments don’t always go solely from buyer to seller. In some auctions, mostly commercial

auctions, it is common that the auctioneer charges a commission fee for himself in exchange for

organizing the auction. If this is a non-negligible amount, the auctioneers have to take these

charges into account when bidding. Examples of these transaction costs are an entrance fee

(fixed payment for the first bid), a bid fee (fixed payment for every bid placed during the

22

auction), ad valorem (percentage of the exchange price), or nonlinear (nonlinear function of the

exchange price) (Wurman et al., 2001). It is also possible for the bidders to receive fees from the

auctioneer. This can occur when bidders have to make a great amount of preparations or

investments before entering the auction. The auctioneer therefore subsidizes participation in

the auction. More information about these kinds of auctions is described by Anderson, Birgean,

& MacKie-Mason (1999).

As an example, some parameter choices of three classic auctions are showed in figure 2 and some

parameter choices of three online auctions in figure 3. CDA stands for continuous double auctions.

Figure 2: Parameter choices of three classic auctions (Wurman et al., 2001)

Figure 3: Parameter choices of three online auctions (Wurman et al., 2001)

23

2.2. Auction Classification

Combining all the dimensions discussed above, creates a matrix of the different auction types. The

dimensions characterize the type of auction. The decisions regarding the different dimensions

determine the complexity of the auction analysis. A lot of different types of auctions are available

because of the extensive amount of dimensions. The most important aspects are: the number of

buyers and sellers, the preferences of the participants, and the amount of traded items (Cramton et

al., 2007). In categorizing the different auctions types, a major distinction is made between iterative

and non-iterative or single-round auctions. This section is therefore further divided between these

two types.

2.2.1. Non-Iterative Combinatorial Auctions

In non-iterative auctions, participants in the auction can hand in multiple bids but can only do so

once. They don’t have the opportunity to adjust their bids to other rival bids. Bidders only have one

chance to win the bid and therefore have to analyse their bid before submitting. This is a direct

mechanism because once all bidders hand in their bid, the auction automatically clears and

calculates the winning bids. Next a few examples of single-round auctions are given.

In a sealed bid combinatorial auction, participants don’t receive any information or feedback about

the bids of other bidders. Although it is possible that these auctions are iterative, they mostly settle

in a single-round because participants don’t receive any extra information with an additional round.

In the original Vickrey mechanism for multiple units, each bidder is presumed to have non-increasing

marginal values for the goods. “The bidders simultaneously submit sealed bids comprising demand

curves. The seller combines the individual demand curves in the usual way to determine an

aggregate demand curve and a clearing price for 𝑆 units. Each bidder wins the quantity he

demanded at the clearing price. However, rather than paying the prices he bid or the clearing price

for his units, a winning bidder pays the opportunity cost for the units won” (Ausubel & Milgrom,

2006, p.59). The original Vickrey mechanism has been expanded with the Clarke-Groves design for

public goods problems to form the Vickrey-Clarke-Groves or the VCG mechanism. Participants state

their value for all the bundles and the auction afterwards assigns the items to the bidders so that the

total value is maximized. This expansion of the original mechanism can be applied for both

homogeneous and heterogeneous goods and it is no longer necessary for bidders to have non-

increasing marginal values. The VCG mechanism still allocates the items efficiently and charges the

winning bidders with the opportunity cost of the items. However, a difference with the original

24

mechanism of single-item auctions is that it is no longer possible to state the paid amounts as the

sum of the individual bids for the items. Important virtues of the VCG mechanism are that it allows

direct reporting of dominant strategies (truthful bidding) and generates efficient outcomes. It also

has a broad scope for available applications. However, the VCG mechanism can be vulnerable to

collaboration of the losing bidders and can have disappointingly low revenues for the seller. More

information about the VCG mechanism and its virtues and weaknesses can be found in Ausubel &

Milgrom (2006).

2.2.2. Iterative Combinatorial Auctions

In iterative auctions, it is possible for bidders to submit one or multiple bids and adjust their bids

continuously or after certain time frames, depending on the type of auction. Iterative auctions

provide feedback to the participants about the concurrent bids so that it is possible for the bidders

to adapt their strategy during the auction. Multi-round auctions have several advantages over single-

round auctions. It is more transparent because these types of auctions trade and give more

information to the bidders. Another advantage is that the dynamic nature of exchanging information

between the participants in the auction tends to enhance revenue and efficiency. However,

supporting incremental and focused bidding without jeopardizing the economic goals of efficiency or

optimality is one of the biggest challenges in iterative auctions (Parkes, 2006).

Iterative auctions can be continuous, in which the conditional allocation and corresponding prices

update continuously. Bidders can also adjust their bids at any moment in time, which stimulates the

faster propagation of feedback. However, a disadvantage of continuous auctions is that they need to

recalculate the winner determination problem every time a new bid enters the auction. This

increases the monitoring and participation costs of the bidders and can make the allocation

infeasible. Iterative auctions can also be discrete or round based. Discrete auctions solely give

periodic updates between the different rounds and only allows bidders to modify their bid between

these rounds (Parkes, 2006).

The multiple rounds in an iterative auction make the design space much bigger than in single-round

auctions. The most important aspect in iterative auctions is the information feedback. This is a

valuable instrument for the auctioneer to help and guide bidders in the bidding process. The

feedback can only include information about the concurrent bids or it can also include aggregate

information, for example the conditional allocation of the items or price feedback. Information

feedback can also be limited by rounding the auction or by discriminatory reporting of the

25

information. This reduces the potential of collusion, in the form of signalling and coordination

between bidders. The amount of given feedback therefore is a trade-off between the ability to guide

the bidding and the chance of collusion (Parkes, 2006).

Another important aspect in iterative auctions is the bid improvement rule which places a bound on

the allowable bid price, for example a minimal percentage improvement over current highest bid.

An iterative auction can have a fixed deadline as closing condition, which is useful when bidders are

impatient and don’t want auctions to stay open for a long time. Auctions with a fixed deadline

however need strong activity rules to make sure that bidders aren’t able to wait until the last round

to make a winning bid. Delaying bids to the last round reduces its iterative character to a single-

round auction. Another option is to have a rolling closure in which the auction is kept open while

losing bidders can carry on making competitive bids. This tends to promote early and honest bidding

(Parkes, 2006).

A special case of iterative combinatorial auctions is the combinatorial clock auction. A clock auction

starts with the auctioneer stating the prices for the different goods in the auction. Bidders can

afterwards indicate the amount of each good they want to buy at the stated prices. A clock auction

is iterative and follows an ascending price rule. If there is excess demand for a good (higher quantity

demanded to buy than available in the auction), the auctioneer increases the price for this good. A

new round then starts with new bids. This process keeps going until there is no more excess demand

for any good. In the combinatorial version of this auction, bidders can hand in package bids for the

different goods. If the auction finishes and there is no excess supply for any good, the determination

of the winning bidders is easy and doesn’t require any calculations. Otherwise in the case there is

excess supply, which can occur if the auctioneer increases the price for a good in a new round but no

bidder submits a new bid so the supply exceeds the demand, the auctioneer calculates a solution to

an IP problem to find the winning bids that maximize his revenues (Porter, Rassenti, Roopnarine, &

Smith, 2003). Governments often use these kinds of auctions for the sale of spectrum rights.

2.3. Bidding Languages

Every bidder must have the opportunity to reveal his intentions by bidding on the required bundles

of objects. Auctions need to specify how bidders can express and hand in their bids. The bidding

languages regulate the capability of bidders to indicate their preferences. The amount of available

bids is usually enormous in combinatorial auctions due to the complexity of bids. For example, if

there are n different items in an auction, specifying a bid would require providing a value for each of

26

the possible (2n − 1) not empty subsets and thus requires a huge amount of numbers to

characterize each potential bid. A bidding language translates this enormous amount of potential

bids into a much shorter string of characters and allows to hand in bids more concisely (Nisan, 2006).

First, the trade-off between expressiveness and simplicity is described. Secondly, some bidding

languages for direct single-unit combinatorial auctions are given, following the structure of Nisan

(2006).

2.3.1. Expressiveness versus Simplicity

The expressiveness of a bidding language is its capability to express any preferred set of bids. The

simplicity specifies how straightforward it is for the bidders and auctioneer to use and comprehend

the language. These objectives should both be achieved in a technical manner (short expression and

easy to compute the allocation of the bids) and in a human manner (easy to understand and express

bids in the language) (Nisan, 2000).

The purpose of a bidding language is to be able to express any desired bid and be easy to use.

However, in choosing between different bidding languages, a trade-off exists between

expressiveness and simplicity. This is because the more bids the language can express, the more

complex it becomes and thus tougher to operate. An appropriate bidding language must seek a good

balance between these two objectives (Nisan, 2006).

2.3.2. Types Bidding Languages

According to Nisan (2006) seven bidding languages exist. First, he introduces three basic bidding

languages. Secondly, three combinations of these basic languages and last but not least an OR

language with dummy items called OR*. The three basic types of bidding languages are:

Atomic Bids

Atomic bid are bids that only seek a single bundle of items and are the most common type of

bids. With these atomic or single-minded bids, a bidder can hand in a pair (𝑆, 𝑝) with 𝑆 a subset

of the items in the auction and 𝑝 the price he offers for this bundle. This is the most basic form

of bidding language, it is relatively simple but lacks expressiveness.

27

OR Bids

In OR (additive-or) bids, a bidder can hand in any amount of atomic bids which increases the

expressiveness of the bidding language. The size of a bid is the amount of atomic bids it

contains. An OR bid is a set of pairs (𝑆𝑖, 𝑝𝑖), where each 𝑆𝑖 is a subset of the total amount of

goods and 𝑝𝑖 is the price he offers for that subset. This set is equal to a set of independent

atomic bids from various bidders. In an OR bid, the bidder is prepared to receive any amount of

disjoint atomic bids for the sum of their corresponding prices.

XOR Bids

XOR (exclusive-or) bids have the same principle as OR bids where a set of pairs (𝑆𝑖, 𝑝𝑖) can be

handed in. The difference here is that the bidder only wants to win one of the bids. XOR bids can

represent all possible bids and are considered as fully-expressive. Although it is not an easy task

to submit complex bids with this language.

The power of the OR bids and XOR bids can be combined to improve the effectiveness and efficiency

of a bidding language. The four combined bidding languages are:

OR-of-XORs Bids

In this case, the participant in the auction can enter any amount of XOR bids. This implies that

the bidder is willing to receive any amount of his stated bids, each for their corresponding prices.

OR-of-XOR bids conclude both the regular XOR bids and regular OR bids.

XOR-of-ORs Bids

In this bidding language, the bidder hands in a chosen amount of OR bids. Implicit here is that he

only wants to receive one of these bids at most.

OR/XOR Formulae Bids

An OR/XOR formulae bid represents any combination of OR bids and XOR bids. The bidder may

hand in an OR/XOR formula to define his bid. All previously explained bidding languages are

specific forms of the OR/XOR formula, where they are just limited to a precise syntactic form.

OR Bids with Dummy Items (OR*)

This bidding language is a variation of the regular OR language and admits dummy items into its

bidding structure. These dummy items have no intrinsic value but participants can use them to

help express their bid and to express disjunction in particular. In this language, bidders can

28

submit multiple atomic bids together with constraints to indicate which bids are mutually

exclusive. To define these constraints, the bidder can add dummy items to specify which pairs of

bids are mutually exclusive. This language proves to be the most effective language so far and

can reproduce all previously discussed bidding languages.

Besides these basic constructs and OR and XOR combinations, many extensions and special cases

exist. In a supply chain environment, it is also possible to transform input goods into another set of

output goods. For example, an automobile manufacturer transforms acquired car parts into a

working car. For auctions to deal with these transformability relationships, we assume that it is also

possible for an agent to bid for these transformation services. A pair (𝐼, 𝑂) defines a transformation

and states that it can produce output 𝑂 after obtaining input 𝐼. A model that supports these

transformations in its bidding process is the mixed multi-unit combinatorial auction (MMUCA).

Because the transformation of goods is a process that (mostly) can’t be undone, the order in which

agents consume and produce goods is of great importance. This order therefore also affects the

winner determination problem (Cerquides et al., 2007). More about this model can be found in

section 3.2.3. For a more detailed description of bidding languages, the reader is referred to Nisan

(2000, 2006).

2.4. Winner Determination

After handing in all the bids, the auction finds an appropriate allocation of the goods over the

participating bidders. Assuming the auctioneer decides on the allocation of the items (determine the

winning and losing bids), he in general wants to maximize his revenues. This problem is the winner

determination problem (WDP) and gives all the submitted bids a winning or losing tag, subject to

maximizing the revenues generated by the winning bids. In regular price based auctions the

determination of the winner is rather easy; the one who offers the highest price wins the good.

However, the WDP in combinatorial auctions takes all the possible bundles and prices for the goods

into account to find an optimal allocation. Therefore the winner determination can be really

complex.

The winner determination problem in combinatorial auctions is a weighted set packing problem for

forward (allocation) auctions and a weighted set covering problem for reverse (procurement)

auctions (Schwind, 2005). The weighted set packing problem can be described as follows: “in this

problem we are given a collection of subsets of a set M, each with a weight, and the target is to find

a sub-collection of non-intersecting sets of maximal total weight” (Lehmann, Müller, & Sandholm,

29

2006, p.562-563). This type of problem is similar to the set partitioning problem meaning that an

algorithm for the set packing problem can be transformed into an algorithm for the set partitioning

problem (Van Hoesel & Müller, 2001).

The set packing problem can be modelled as an integer programming (IP) problem. Consider a set 𝑀

of goods 𝑖 and a collection 𝑉 of subsets 𝑗 with a weight 𝑐𝑗 for each subset. The decision variable 𝑥𝑗 is

equal to 1 if subset 𝑗 is chosen as a winner and equal to 0 otherwise. 𝑎𝑖𝑗 is equal to 1 if good 𝑖 is

included in subset 𝑗 and is equal to zero if not. The objective is to maximize the weights (or values of

the bids):

max ∑ 𝑐𝑗𝑥𝑗

𝑗∈𝑉

𝑠. 𝑡. ∑ 𝑎𝑖𝑗𝑥𝑗

𝑗∈𝑉

≤ 1, ∀𝑖 ∈ 𝑀

𝑥𝑗 ∈ {0, 1}

This constraint ensures that every good in 𝑀 is assigned to one bidder at most. The difference with

the other problems lies in the sign of the first constraint, which is equal to (=) for the set partitioning

problem and greater than or equal to (≥) for the set covering problem (de Vries & Vohra, 2003).

Auctions for truckload transportation (infra section 4.2) use this last type of problem.

Another option is using dynamic programming, which solves the problem in a small subset at first

and systematically enlarges the subset until the optimal solution of the complete problem is found.

More information about the notation and mathematics behind these techniques can be found in

Sandholm (2002).

In practice, tree search algorithms can be used to solve the WDP to optimality. The purpose of this

algorithm is to decide for each bid to accept or reject it. The algorithm computes all the available

alternatives to compose the decisions until an optimal solution is found, which is the best result of

all the different scenarios. Calculating every possible way can take a long time to compute the

solution so instead of searching the space exhaustively, selectivity search techniques are often used

to reduce the calculation time of the winner determination problem. For a more thorough

description of the search algorithm and its dimensions, the reader is advised to read the paper of

Sandholm (2006).

In this section we will first clarify the complexity of the winner determination problem and

afterwards some approximation methods are given to deal with this complexity.

30

2.4.1. NP-hardness

The winner determination in combinatorial goods can be really hard and complex. The reason is that

a single good can be part of numerous different bundles. The WDP needs to check the feasibility of

the allocation of each bid. This must make sure that winning bids don’t share items because every

item can only be sold once. The auctioneer also has to take the revenues accompanying these bids

into account. An optimal solution is a set of bids that is feasible and generates the highest revenue

for the auctioneer. Determining how to allocate each good while maximizing the revenues is a

difficult and time consuming process (Lehmann et al., 2006).

In general, the encoding length or the amount of binary symbols in a computer memory defines the

complexity of an optimization problem. “An algorithm solves a problem in polynomial time if there

exists a polynomial function 𝑔 such that for every possible instance of the problem, the number of

basic arithmetic operations needed by the algorithm is no more than 𝑔(𝑙), where 𝑙 is equal to the

number of binary symbols needed to represent the instance” (Lehmann, Müller, & Sandholm, 2006,

p.567). The collection of decision problems solvable with a polynomial time algorithm is called 𝑃 and

is enclosed in non-deterministic polynomial time (NP).

The set partitioning, set packing and set covering problems are what they call NP-hard, meaning that

calculations for determining a winner can be highly time consuming, and depend on the problem

size. Search algorithms exists to solve the WDP to optimality but the time is determined by the

problem size, which depends on the amount of items in the auction, the amount of received bids,

and the structure of the problem (type of bids and prices). Unfortunately, until this day no efficient

algorithm exists yet that guarantees to solve these problems to optimality in polynomial time

(Sandholm, 2002). This implies that the time needed to determine the solution is not known in

advance and increases exponentially if the problem size becomes larger (more bids handed in and

more goods in the auction). Hence approximation methods and heuristics can be used to find a

reasonably good solution in a shorter time frame. More information about the theory of NP-

hardness and the WDP can be found in Lehmann et al. (2006).

2.4.2. Approximation

Approximation algorithms are efficient algorithms that calculate an ‘almost’ optimal solution and are

solvable in polynomial time. The trade-off between the choice for optimal and approximation

methods depends on the time and cost savings using the approximation method on the one hand

and the distance between the optimal and approximated solution on the other hand. If the expected

31

improvement of the solution is small, one would benefit greatly using an approximation algorithm

because it saves a lot of time and the solution is not far from optimal. However, approximation

methods can deteriorate the economic value and fairness of the auction and therefore have to be

handled with caution. Several techniques and methods exist to reduce calculation times.

One method to reduce calculation time of the winner determination problem is to put restrictions

on the allowed bids, for example restrictions on the possible bundles of items or limits on the bid

prices. These restrictions reduce the complexity and enable a faster calculation of the problem.

However, putting restrictions on the bids disables the full expressiveness of the bidders and can

carry along the same inefficiencies as non-combinatorial auctions (economic inefficiency, exposure

problem) (Lehmann et al., 2006).

Another method for reducing the search time is the usage of upper or lower bounding techniques.

Upper bounds give an indication on how much the unallocated item can maximally contribute to the

revenues. An upper bound can be narrowed by adding cuts or extra constraints that don’t influence

the solution but further reduce the search process time. At a node in the search process, lower

bounds are calculated to find out how much revenue the remaining items can contribute. If these

lower bounds are higher than the incumbent value at that node, the incumbent is updated. This

eliminates paths with a lower bound than the incumbent from the tree search process (Sandholm,

2006).

Decomposition techniques divide the bids into sets whereby bids from one set don’t have common

items in it with bids from another set. This enables the calculation of the winner determination in

each set separately. For more information about these approximation techniques, the reader is

again referred to Sandholm (2006).

32

3. Auctions in the Supply Chain

As mentioned before, auctions are becoming more and more common use in the supply chain. This

chapter starts with a short explanation about the supply chain and its formation. Next, some

methods are explained how to model the supply chain formation using auctions. To conclude this

chapter, reverse or procurement auctions are discussed in detail with special attention to the

benefits and risks for the buyers and suppliers.

3.1. Supply Chain Formation

The supply chain of a certain industry or product ranges from the raw materials provider(s) to the

eventual end consumer(s). It includes all the parties involved, direct or indirect, to satisfy the

demand of a specific product. A supply chain therefore contains not only the producer and its

suppliers but also the distribution centres, logistic companies, points of sale and the customers. A

supply chain typically includes different stages: raw material suppliers, manufacturers, distributors,

retailers and customers. Not every supply chain has to include all these stages (Chopra & Meindl,

2013).

A few remarks have to be given about the supply chain. The term supply chain is often associated

with just the transfer of goods between the different stages. Besides this product flow from supplier

to customer three other flows are also present. The four different flows in a supply chain are

(Chopra & Meindl, 2013):

A product flow of the materials from the supplier to the end consumer.

A reverse flow with returning or recycled goods.

A demand flow for the required products from the customers to suppliers, combined with the

funds paid for the products.

An information flow between the different stages in the supply chain in two directions.

A supply chain is therefore a dynamic process that exchanges constant flows of goods, funds and

information. Every stage in a supply chain doesn’t necessarily contain only one player. It is perfectly

possible to have multiple manufacturers, suppliers, and (hopefully) customers, as can be seen in

figure 4. A supply chain therefore is a network that connects all the involved parties. Ultimately, the

33

goal of every supply chain is to maximize the supply chain surplus or the total value generated by the

different firms in the chain. The supply chain surplus equals the value of the product for the buyer

minus the supply chain costs belonging to the execution of the customer’s order (Chopra & Meindl,

2013).

Figure 4: Supply chain stages and flows (Chopra & Meindl, 2013)

As mentioned before in the introduction chapter, the different stages in the supply chain are

interrelated. A company in the supply chain receives inputs and transforms them into outputs, which

are inputs for the next company in the chain. The output of a company is linked with the input of a

company further downstream the supply chain. The supply chain formation has to take these

complementarities into account, otherwise several issues can occur. For example, a producer can

remain with unsold goods if no purchaser is found. Another issue occurs if a producer already sold

his goods in advance but isn’t able to acquire the needed inputs. These issues can damage his

credibility on the market. A two way dependency of acquiring inputs and generating outputs is in

34

place and therefore exchange relationships exist between these companies. A supply chain can be

seen as an interactive system of consumers (buying products from companies upstream) and

producers (converting inputs into valuable outputs). This interactive system includes the

relationships between goods and also the transformation relationships in the different stages of the

supply chain. Supply chain formation deals with assembling these complex production and

transformation relationships. This can bring along coordination issues because these relationships

must be arranged at various levels, taking into account the interdependencies between inputs and

outputs at every level (Giovannucci, Rodriguez-Aguilar, Vinyals, et al., 2007).

The concept of supply chain is increasing in popularity in recent years. One of the reasons is the

increased globalization. Suppliers can be found all over the world and companies must therefore find

more effective ways to coordinate their in- and outbound material flows. Another reason is that

competition nowadays is more and more based on time and quality. These reasons, together with a

fast improving technology, increase the uncertainty in the marketplace. It is therefore necessary for

both the individual companies and the supply chain as a whole to create enough flexibility to deal

with this uncertainty (Mentzer et al., 2001).

This need for increased flexibility results in a change of the organizational structure of the firms.

Specialized and more focused companies replace the traditional vertical companies that control

large part of the production processes in a supply chain. Strategic outsourcing and designing

collaborative supply chain networks are gaining importance nowadays for successfully managing a

supply chain (Giovannucci et al., 2010). Today, market conditions are changing fast so companies are

in need of more automated supply chains. They must become more flexible and dynamic in their

partner selection and formation of their supply chain interactions. For this reason, automated

support in the form of combinatorial auctions can help in the formation of the supply chain and

speed up communications (Walsh et al., 2000).

A good formation of the supply chain gives the possibility to share and exchange information with

the entire chain. This can increase the accuracy of the production schedule of upstream producers

and reduce the harmful consequences of the bullwhip effect, which is the phenomenon of increased

unpredictability of demand and production decisions when going further up the stream (Leong,

2008).

35

3.2. Modelling Supply Chain Formation

Combinatorial auctions can be used in the supply chain to raise the automation and information

exchange, which is of increased importance these days. A few methods to increase the automation

in the formation of a supply chain are discussed next.

3.2.1. Double Auctions

In a supply chain, the different markets or stages are related to each other. It is important that a

company exchanges information with its suppliers, partners and customers. Auctions can be

integrated in the supply chain to ensure the coordination between these markets. This method of

double auctions enables every market in the chain to operate individually but assures efficiency over

the whole supply chain by exchanging information. “Each market that forms a link in the supply

chain operates as a double auction, where the bids on one side of the double auction come from

bidders in the corresponding segment of the industry, and the bids on the other side are generated

by the protocol to express the combined information from all other links in the chain“ (Babaioff &

Nisan, 2004, p.595). The double auctions dynamically adjust the trade amounts and corresponding

prices. Hence, it makes sure that changes in market conditions such as supply and demand are not

left unanswered. This section about double auctions is based on the paper of Babaioff & Nisan

(2004).

The next simple example explains how these related markets are modelled and share information.

Consider a market for computer chips for laptops and the related metal market (for the computer

chips) and the laptop market. This supply chain consists of three markets and involves 4 different

parties:

a) Metal prospectors put sell orders on the metal market and start the supply chain.

b) Computer chips manufacturers are responsible for both the buying bids on the metal market

and also the sell orders on the computer chips market.

c) Laptop producers are the buying side on the computer chips market and selling side on the

laptop market.

d) End consumers buy the laptops from the corresponding producers to conclude the chain.

These markets are related and if demand for laptops increases, its price also increases. This causes

the production of laptops to increase and therefore demand for computer chips also rises. This

results in an increased price of computer chips and so on. This chain reaction of information

36

exchange already occurs in real life but takes a rather long time to establish. Using double auctions

to model these markets, automates the information exchange (doesn’t need human interaction or

control) and occurs extremely fast. This can achieve the same or even more efficient outcomes

compared to human interaction outcomes.

However, a problem in designing occurs when bidders are simultaneously active in multiple markets.

In our example, computer chips manufacturers are active as a buyer in the metal market and as a

seller in the computer chips market. Evidently, the amount of metal bought for manufacturing the

computer chips is related to the amount that can be sold to the laptop producers. This means that

the prices are linked to each other and increasing one will also increase the other. A bid for a good in

one market can therefore not be constructed without a bid in the other market. Otherwise the

markets are not related anymore and the computer chips manufacturers cannot reasonably partake

in the other markets. Operating in a sequential way (buy metal first and sell computer chips

afterwards) is also not an option because this causes an exposure problem for the computer chips

manufacturer; they must be cautious in their metal buying policy because they don’t know the

selling price of computer chips in advance.

One way to deal with this interdependence between markets is to model the whole supply chain as

one single compound market. This centralized approach brings along a complex optimization

problem because all the markets are integrated into one central marketplace. Although this

approach holds the advantage of having an optimal solution for the complete chain, it also has some

disadvantages. All the information and communication has to be centrally collected which is not an

easy task. It is also difficult to make decisions at a single point.

Another method is to arrange the supply chain as a series of individual markets. In this decentralized

approach, the markets do not behave strategically but communicate with each other. This

communication is done by a defined protocol to create a distributed mechanism. A protocol relevant

in this case is that intermediate markets (e.g. computer chips market) transform products of one

market into products for the other (related) market further down the supply chain. In our example,

computer chips manufacturers place bids in the auction for transforming metal into computer chips.

This method holds several advantages:

The protocol ensures that the distinct markets make suitable decisions about the production

amounts. The total amount of metal transformed into computer chips matches with both the

amount of metal prospected and the amount of computer chips needed. The same holds true

for the transformation of computer chips into laptops.

37

The amounts realize economic efficiency over the whole supply chain.

The companies in the supply chain only need to know their own cost structure and can behave in

a self-interested and rational way. The end result therefore doesn’t require that companies have

global knowledge or know about the behaviour of the other companies.

The communication between the different markets happens in two phases. In the first phase, the

metal market aggregates the supply and communicates this amount to the computer chips market

further down the supply chain. This market also aggregates its supply and sends the sum of both

markets to the laptop market. This amount is the total supply for laptops, aggregated over the whole

supply chain. In the second phase, the laptop market sends the demand for laptops to the computer

chips market. This market subtracts its aggregated supply from the received demand and

communicates this difference with the metal market. This amount represents the total demand for

metal, aggregated over the whole supply chain. The demand on the computer chips market is then

calculated as the difference between the demand of the laptop market and the supply of the metal

market. Afterwards, each market can hold a double auction because all markets have a supply and

demand curve. An allocation in the double auction determines for every agent in the auction how

much of each good he will buy or sell. A more detailed example of how double auctions clear is

described in Babaioff & Nisan (2004).

3.2.2. Task Dependency Networks

Task Dependency Networks (TDN) is another method to automate the supply chain formation and

deal with the complementarities between markets. TDNs are introduced in the paper of Walsh et al.

(2000), on which this section is based. A task dependency network characterizes the

interdependencies between the markets and products and consists of several elements:

Goods (𝐺) which can represent products, resources or tasks.

Consumers (𝐶) who want to buy one or more goods and acquire a value 𝑣𝑐 for doing so.

Producers (𝑃) who create outputs for the consumers. A requirement for producing the goods is

that the producer obtains the right amount of inputs. This incurs a cost 𝑘𝑝 for buying the inputs

from suppliers.

A task dependency network can be represented as a directed and acyclic graph (𝑉, 𝐸), whereby

𝑉 = 𝐺 ∪ A. 𝐺 represents the collection of goods and 𝐴 is the collection of agents consisting of

producers and consumers (𝐴 = 𝐶 ∪ P). 𝐸 stands for the set of arcs and acts as connector between

38

the agents and the goods they consume or deliver. For example an arc (𝑎, 𝑔) states that agent 𝑎

delivers good 𝑔 and (𝑔, 𝑎) states that the agent obtains the good. A TDN is restricted to be acyclic,

which indicates that output goods cannot be used as inputs earlier in the supply chain. Hence they

are only usable as inputs further down the stream. An example of a TDN for an automotive supply

chain is visualized in figure 5. Rectangles and octagons represent agents, circles represent goods and

arrows dictate the usage or delivery of goods. The dollar amounts below the rectangles and

octagons specify values for the consumer or costs for the producers (Walsh & Wellman, 2003).

Figure 5: A TDN of an automotive supply chain (Walsh & Wellman, 2003)

A producer can be active or inactive and is assumed active if he produces an output. The inputs for a

producer are complementary, meaning that a producer cannot do anything with a partial set and

therefore needs all the inputs to deliver the outputs. Consumers are always feasible but producers

are only feasible if they obtain all the needed inputs or are inactive. An allocation is a subgraph of

the whole TDN and includes the agents that deliver or obtain a good and the traded goods. An

allocation is feasible if it satisfies two conditions: all the included consumers and producers are

feasible and the traded goods are in material balance. This last condition occurs if the amount of

arcs into a good is equal to the amount of arcs out of that good. The value of an allocation is

measured as the summation of all the values for the consumers (𝑣𝑐) minus the summation of the

incurred costs of the producers (𝑘𝑝) included in the allocation. The collection of efficient allocations

includes all the feasible allocation whereby their value is maximized. An allocation is seen as a

solution if one or more of the consumers obtain a requested good.

39

These networks can be used in a combinatorial auction setting. This contains an auction mechanism

and its inherent bidding procedures where agents can hand in bids for bundles of goods. The auction

mechanism makes sure that the bids are received correctly, bidding and auction rules are applied

properly, status reports are communicated to the participating agents and efficient allocations are

calculated. The bidding procedures or policies define how the agents have to hand in the bids. The

combinatorial setting coordinates all auction activities in a market and directly connects the

negotiations for all goods. This eliminates some coordination problems incurred with separate

negotiations. Combinatorial settings also remove the risk that bidders obtain undesirable bundles of

goods.

The combinatorial auction studied by Walsh et al. (2000) is a non-iterative auction meaning that it

consists of only one round. First, the agents hand in bids stating their costs and values. Afterwards

the auction closes and calculates feasible allocations that maximize the value over all the agents.

Finally, the auction notifies the winning bids to the agents. These agents then pay the stated amount

for its received allocations.

An agent 𝑎 can submit a bid 𝑏𝑎: [𝑟𝑎 , (𝑔1, 𝑞𝑎1), … , (𝑔𝑛, 𝑞𝑎

𝑛)] whereby 𝑟𝑎 is the stated value of agent 𝑎

for the requested bundle of goods and 𝑞𝑎𝑖 is the integer amount that agent 𝑎 requires of good 𝑔𝑖.

These requested amounts are positive for inputs (consuming) and negative for outputs (producing).

In case of production the stated value represents the amount the agent wants to receive for the

produced bundle of goods. For example, the bid of a producer who needs three units of good 𝑔1 and

two units of good 𝑔3 as input for producing one unit of good 𝑔2 as output and wants to be paid 10

for doing so is: [−10, (𝑔1, 3), (𝑔2, −1), (𝑔3, 2)]. The winning allocation of the goods is calculated

from the collection of bids B that maximizes the summation of the stated values (𝑟𝑎) of the agents

subject to the constraint that enough inputs are at hand to produce the outputs. With 𝑥𝑎 equal to

one if agent a wins its bid and equal to zero otherwise, the winner determination problem can be

formulated as:

max𝑥

∑ 𝑟𝑎𝑥𝑎

𝑏𝑎∈𝐵

𝑠. 𝑡. ∑ 𝑞𝑎𝑖 𝑥𝑎

𝑏𝑎∈𝐵

= 1, 𝑖 = 1 … 𝑛

A simple example to illustrate how these auctions can clear and determine the winning bids. Agent 1

wants to sell two units of good 2 for €7 [−7, (𝑔1, −2)]; agent 2 offers one unit of good 2 for €4

[−4, (𝑔2, −1)]. Agent 3 places a package bid of two units of good 1 and one unit of good 2 for €10

[−10, (𝑔1, −2), (𝑔2, −1)]. Agent 4 offers one unit of good 3 if he receives 2 units of good 1 and one

unit of good 2 and requires €5 for this transformation [−5, (𝑔1, 2), (𝑔2, 1), (𝑔3, −1)]. The last bid is

from agent 5 who want to pay €20 for one unit of good 3 [20, (𝑔3, 1)]. The solution in this case is

40

quite straightforward; the auction accepts the package bid of agent 3, the transformation bid of

agent 4 and the buy bid of agent 5. This generates a value of €5 (= 20 - 10 - 5) for the supply chain.

Of course these types of auctions become much more complex if more goods and bidders are

involved in the process.

More information about TDNs and the study about their efficiency can be found in Walsh et al.,

(2000) and Walsh & Wellman (2003).

As stated before in the introduction chapter, according to Giovannucci et al. (2007) task dependency

networks are valuable for dealing with the complementarities between the markets and automating

the supply chain formation but are limited to transformation relationships with a single output. It is

not possible with TDNs to express problems in which goods are divided in smaller parts (e.g. the

decision to sell a pig as a whole or in different parts) and therefore need further requirements. For a

more increased automation of the supply chain formation, three additional requirements are

needed:

Expressiveness Requirements: Fully expressive bidding languages are needed to deal with

complementarities between production processes and to characterize production connections

with numerous output goods.

Computational Requirements: The supply chain formation must be computationally achievable

while maintaining optimality.

Formal Requirements: The structural and behavioural characteristics of a supply chain must be

supported.

These requirements are included in the method of Mixed Multi-unit Combinatorial Auctions

(MMUCA), which is described in the next section.

3.2.3. Mixed Multi-Unit Combinatorial Auctions

Another form of combinatorial auctions that has a good potential to increase the automation in

supply chain formation are mixed multi-unit combinatorial auctions, which are a generalisation of

the typical combinatorial auctions. Multi-unit implies that each good in the auction can have many

units. MMUCA integrates direct and reverse auctions. The bidder can both buy and sell goods in this

type of auction, hence the term mixed. Therefore MMUCAs are a generalisation of the typical

combinatorial auctions because it can include single- and multi-unit CAs, double CAs and supply

chain formation CAs (Giovannucci, Rodriguez-Aguilar, Cerquides, & Endriss, 2007).

41

The difference with a regular CA is that in a MMUCA the participants in the auction are also able to

bargain over transformations instead of just negotiating over regular goods. MMUCAs enable supply

chain formation auctions, which enables agents to bid for bundles of goods to buy and/or to sell and

also for transformations of goods. Transformations are represented by a collection of input and

output goods and can be of three different types (Vinyals & Cerquides, 2008):

Input transformations (I-transformations): These have no output goods and state a buyer’s

willingness to buy goods.

Output transformations (O-transformations): These have no input goods and state a producer’s

willingness to sell goods.

Input-Output transformations (IO-transformations): These have input and output goods and

state a bidder’s willingness to produce certain goods after buying certain input goods.

A bidder who offers a transformation (𝐼, 𝑂) wants to produce a defined collection of outputs (𝑂)

after obtaining the required collection of inputs (𝐼) and the payment enclosed with the

transformation. For example, a bid of [ ({ }, {𝑎}) , ({𝑏}, {𝑐}) ] means that the bidder can produce

good a (no input goods needed) and good c (after acquiring good b). It is possible for an agent to

offer multiple number of transformations and therefore bargain over bundles of transformations

(Giovannucci, Rodriguez-Aguilar, Cerquides, et al., 2007).

An atomic bid 𝑏 is in the form of [ ({𝐼1, 𝑂1 }, … , {𝐼𝑛1, 𝑂1𝑛 }), 𝑝, 𝑙 ] and defines a multiset of

transformations, a price 𝑝 and the identity 𝑙 of the bidder. An appropriate bidding language must be

able to fully express all the available bids for the bidder. As explained in the previous chapter, it is

possible to have an OR-combination of atomic bids meaning that the bidder accepts any amount of

sub-bids if he receives the sum of the combined prices. Another option is a XOR combination of bids

if the bidder only wants to accept one of the bids. In case of MMUCAs, the XOR language is fully

expressive to represent any combination of atomic bids. It is also possible for a bidder to express

that he accepts a given amount of duplicates of the same transformation by using quantity ranges.

The winner determination problem is the problem of deciding which bidders should receive which

goods so that the auctioneer maximizes his revenues. In production processes, the order of the

transformations in the supply chain is important. Hence, the order in which the auctioneer accepts

the transformations is of central importance in MMUCAs and has an impact on the WDP. The

auctioneer therefore has to make two decisions: which transformations to select and the sequence

of implementing the accepted transformations. MMUCAs are not the same as double auctions or

combinatorial exchanges because these auctions don’t have the notion of sequence of exchanges,

42

which is required in modelling a production process. A feasible solution for the WDP is a series of

transformations and has to satisfy two conditions:

a) Bidder Constraints: The transformation sequence must comply with the submitted bids. For

example, the auctioneer can only accept one bid if this bidder uses a XOR combination of bids.

b) Auctioneer Constraints: The transformation sequence must be implementable.

A feasible solution that maximizes the revenue (the summation of the prices of the selected bids) for

the auctioneer is an optimal solution. The WDP can be formulated as an integer programming

problem to identify a suitable solution in the form of a transformation sequence that converts the

initial goods into the final goods. This solution sequence must be conforming to several constraints:

If a transformation in an atomic bid is chosen to be in a solution, the rest of the transformations

in that bid also have to be included in the solution sequence.

A transformation can only be picked for one position in the solution sequence.

Every position in the solution sequence can only be filled by one transformation.

No gaps are allowed in the solution sequence.

All transformation must have sufficient input goods

As the amount of transformations in a bid increases, the amount of variables in the IP increases

quadratically. Unfortunately, the winner determination problem for normal combinatorial auctions

is NP-hard. Because MMUCAs are a generalisation of the standard CAs, the WDP stays NP-hard.

However, forming the supply chain is a process that often has to be able to quickly respond to

changing market conditions. In these cases, finding an optimal configuration of the supply chain is of

less importance than finding an acceptable one in a short time period because of the frequent

changes. The reader is referred to Cerquides et al. (2007) for more technical details and proof about

the bidding languages, the winner determination, and constraints in MMUCAs, on which this

explanation was based.

Consider this simple example of how such an auction can come to a solution. Bid 1 offers three kilo

of rough wood and wants a price a price of €9 for it. Bid 2 also offers three kilo of wood but for a

price of €7. Bid 3 offers to transform the rough woods into planks for a price of €5. Bid 4 offers to

buy the produced planks for €20. Bid 5 offers to buy the planks for €24. Because this is a simple

example with a small amount of bids, the optimal solution is clear: first buy the wood from bid 2,

next transform them into planks via bid 3 and afterwards sell the planks to bid 4. This results in a

gain of €8 (= 20 - (5 + 7)) for the supply chain (Giovannucci, Rodriguez-Aguilar, Cerquides, et al.,

2007). This example can become more complex if more bidders, products and transformations are

43

included in the auction and if bidders submit more than one bid. Other examples of the use of

MMUCAs in practice are described in section 4.4.2.

Petri Nets can be used to map the IP winner determination problem for a wide range of MMUCAs

and are especially useful for combinatorial auctions in supply chain formation. Petri Nets are a

mathematical and graphical tool for describing discrete distribution systems. In this case, Petri Nets

are introduced as Weighted Transition Petri Nets (WTPN) so that each transformation includes the

concept of transformation or production costs. This technique significantly reduces the amount of

needed decision variables from quadratic to linear, making the computations less complex. More

information about Petri Nets and their use for MMUCA can be found in Giovannucci, Rodriguez-

Aguilar, Cerquides, et al. (2007). Another option to reduce the calculation time is setting up

dependency relationships among transformations. These relationships aid the IP in designing the

sequence of transformations and when to implement them. This method constrains the position of

the transformation and hereby shrinks the search space, which reduces the solving time of the WDP

(Giovannucci, Vinyals, Rodriguez-Aguilar, & Cerquides, 2008).

An important extension of MMUCAs, especially in a supply chain setting, are the Multi-unit

Combinatorial Reverse Auctions with Transformability Relationships Among Goods (MUCRAtR)

introduced by Giovannucci et al. (2010). This type of auction aids in maximizing the auctioneers

revenues by selecting the right partners in his supply chain network design. MUCRAtR helps in

automating the partner selection by making make-or-buy decisions for the auctioneer, which means

deciding whether production of certain operations is performed in-house or outsourced. The WDP of

this auction implies finding a sequence of bids that produces the required goods at a minimum cost

for the auctioneer. This results in an optimal supply chain with decisions about what transformations

to perform in-house and what to outsource to a partner.

3.3. (Online) Reverse Auctions

Reverse auctions are the type of auctions most frequently used in the supply chain. In a reverse

auction, the roles of the buyers and sellers are reversed compared with regular forward or direct

auctions. In this type of auction, a single buyer wants to buy a good or offers a contract for the

delivery of a specific good or service. Afterwards, multiple sellers or suppliers compete in the auction

to win the contract. The buyer therefore controls the market because he offers something multiple

sellers want. Especially due to the emerging role of the internet, online reverse auctions (ORA)

became a popular means of conducting business and managing the supply chain. The process of

44

holding reverse auctions is often only achievable using electronic applications and is therefore

considered the same as online or electronic reverse auctions in this context. An ORA results in

dynamic pricing because the prices of the auctioned items change continuously on the electronic

platform. The suppliers in the auction can observe the price level of competitors and can easily see

when they are no longer competitive to participate in the sale (Smeltzer & Carr, 2003).

A reverse auction is a tool to enhance the strategic sourcing efficiency and can help in the

development of purchasing procedures (Smeltzer & Carr, 2003). Sourcing strategies are attempts to

redesign the supply chain, change the configuration of the supplier base, or aggregate volumes.

Buying firms can pursue a couple of these strategies by participating in auctions. Which strategy to

follow depends on the final objectives of the company and aims to reduce costs of the sourcing

process (Jap, 2002).

Most of the reverse auctions compete solely on price. If necessary, the buyer first screens the

suppliers on certain requirements (e.g. quality, ability to deliver, etc.) before they can participate in

the auction. However, it is also possible to hold multi-attribute reverse auctions. These types of

auctions, directly add other attributes than price (e.g. quality and delivery) to the winner

determination selection. Price is therefore not the only factor anymore in determining a winning bid.

This approach needs more preparation time for the suppliers because they have to state the value

for each attribute in the auction. Also, it is more difficult to determine a winner because the auction

has to take into account more than one attribute (Leong, 2008).

Online auctions in the business-to-business (B2B) environment became widespread in the 1990s by

companies as FreeMarkets Inc., CommerceOne, eBreviate and several others (Kros et al., 2011).

Auctions are common business nowadays and large multinationals such as Proctor & Gamble,

General Motors, PepsiCo and many others use them for the procurement of goods and services.

There are various reasons for the popularity and rapid growth of online reverse auctions in B2B (Jap,

2002):

Financial savings: ORAs can generate cost savings ranging from 5 up to 40 percent but the

savings are on average around 15 percent.

Process efficiencies: The process starting from the request for purchase until the winner

selection could take a few weeks in the traditional way and can be reduced to several hours by

using ORAs.

Enabling capabilities of emerging technologies: A lot of software (e.g. CommerceOne, Oracle,

and B2eMarkets) exists and enables firms to organize and host an online reverse auction.

45

The e-commerce presents many opportunities for growth in the B2B sector: rapid entry into

markets, transaction cost savings, extension of business models, and enhanced supply chain

management (Smart & Harrison, 2003). More about the benefits and risks of ORAs for buyers and

suppliers is discussed later in this section. First, the conditions of when and how to use reverse

auctions are explained.

3.3.1. How and When to Use Reverse Auctions

Reverse auctions can only take place if enough suppliers exist and their profit margin is able to

handle reduced prices. It is also important to look at the specifications of the service or good, the

industry type of the market, and the company’s infrastructure so that the potential of reverse

auctions can be maximized. For a successful usage of reverse auctions, Smeltzer & Carr (2003)

stipulate that these four conditions must be met:

a) Clear descriptions of the commodity specifications: Otherwise suppliers can be averse to

participate in the auction because they don’t know all the required conditions. Defining the

expectations and conditions for purchase must be done thoroughly. Some examples of

specifications are quality, location and transportation requirements, delivery time, order

amounts, etc.

b) Large enough purchase amounts: This encourages producers to bid on large volumes so they

can develop volume efficiencies and reducing transaction costs by achieving production

economies of scale. Several methods exist to increase the lot sizes: pool together a family of

goods in a single bid, standardize parts so that fewer custom parts are needed, or leverage the

buy over multiple departments in the firm.

c) Availability of appropriate supply market conditions: There must be enough competing

suppliers in the auction and the market prices are preferably elastic so an increase in demand

drives down the supply prices. Also, spare supply capacity or an economy of scale must exist for

suppliers to have an incentive to participate in the auction.

d) Presence of the right organizational infrastructure: For effectively organizing an electronic

reverse auction, a buying firm requires not only the appropriate software and technology but

also the availability of trained employees with the right skills and knowledge.

Online reverse auctions are often used for commodity goods (e.g. paper, agricultural products,

metals, etc.), original equipment manufacturing (OEM) materials, capital goods and services.

Products with only price as differentiator are ideal for reverse auctions. Products that are complex,

46

have many customizable options, need frequent adjustments in the design, are strategic and require

long-term contracts are all less appropriate for reverse auctions (Kumar, 2013). Some examples of

products often purchased through online reverse auctions are listed in figure 6. The total cost of

ownership includes the purchase price of the product, logistics, inventory and carrying costs,

services and all other costs related to the purchase and usage of the product.

Figure 6: Products purchased through ORAs (Jap, 2002)

3.3.2. Benefits of Reverse Auctions

In online reverse auctions, buyers control the auction. Therefore they have the biggest incentive to

start or participate in the auction. Some benefits or advantages of participating in reverse auctions

for buyers are (Smeltzer & Carr, 2003):

Cost savings: Buyers mainly use reverse auctions to push down the purchase prices. As already

mentioned above, the cost savings can be up to 40 percent but price reductions between 5 and

12 percent are more common.

Reduced administration costs: The process of preparing the bid, participating in multiple rounds

and determining a winner is considerably faster because the process can be automated to a

great extent. This reduces the cycle time and can achieve time savings of 30 percent.

Reduced inventory level: It is possible to replenish inventories more rapidly and hereby maintain

the same service level with lower levels of buffer or safety stock. This benefit is especially

important for products with an unpredictable or irregular demand.

47

Increased supplier base: ORAs have the possibility to attract suppliers from all over the world

and therefore increase the supplier participation. This results in increased competition in the

auction which is a positive thing for buyers because fiercer competition increases the chance of

reducing the purchase prices (Kumar, 2013).

Many suppliers are averse to using reverse auctions because they believe it is only used to push

purchase prices down and lower their profit margins. However, participating in reverse auctions can

also yield some advantages for suppliers (Smeltzer & Carr, 2003):

New business: For suppliers, reverse auctions are a great way to expand their businesses. They

have the opportunity to generate more sales and increase their communications on the market.

Market penetration: Via reverse auctions, suppliers can create basic guidelines about the price

and competition in new market segments or geographies. This allows them to penetrate a new

market more easily. Suppliers can also approach new customers and markets because

geographic boundaries are somewhat dissolved.

Reduced administration costs: The process for bidding and awarding business is also accelerated

for suppliers. Auctioning via an electronic application reduces cycle time and brings along much

less paper work which results in lower transaction and administration costs.

Inventory management: It is easier for suppliers to plan their production schedules because less

time is wasted between bidding and selling. Suppliers can therefore better manage and reduce

their inventory levels.

Information: Reverse auctions give participating suppliers the opportunity to benchmark with

competitors. It is possible to acquire knowledge about competing bidders (e.g. pricing strategy

and production) and get an overview of the market activity. Furthermore, a reverse auction

provides learning opportunities for the sellers who can apply these in their own purchase

practices (Smart & Harrison, 2003).

A cautionary note has to be given about these benefits of ORAs. Most of the benefits, especially the

reduced purchase price, only occur when the reverse auction is introduced for the first time. The

benefits can be of a lesser extent when they are used for repeat purchases and not all benefits are

therefore sustainable over the long-term (Smart & Harrison, 2003). Of course organizing a reverse

auction doesn’t only generate advantages for the buyers and suppliers. Reverse auctions can also

bring along severe risks or disadvantages and are discussed next.

48

3.3.3. Risks of Reverse Auctions

The biggest disadvantage of using reverse auctions is that the buyer-supplier relationship can get

damaged. This obviously affects both parties. The reason for this is that buyers most often base their

purchase decision solely on the lowest price which makes it difficult for buyers to create loyalty and

a good relationship with their suppliers over the long-term. Every time the contract needs renewal,

the buyer chooses the supplier with the lowest price at that moment. The absence of a long-term

incentive for the suppliers results in the fact that they are not eager to invest in preparations,

training, and capital expenses needed for participating in the auction. Also, an online auction

requires less personal interaction between buyers and suppliers than traditional methods. It is

hereby even more difficult to build a trustworthy relationship. This relationship destroying character

is one of the main reasons why important strategic goods are not commonly traded via reverse

auctions (Smeltzer & Carr, 2003).

Besides the possibility of destroying the relationship with suppliers, a buyer can also risk not having

enough suppliers participating in the auction. This means that a competitive environment cannot

develop and therefore misses out several benefits of participating in a reverse auction. A successfully

organized auction needs a minimum of four or five suppliers (Smeltzer & Carr, 2003). Furthermore,

selecting a new and unknown supplier carries the risk that the supplier is not able to meet the

buyer’s requirements. This has the potential to result in delivery delays, contract default and

payment problems (Kros et al., 2011).

For suppliers, reverse auctions can bring along several other risks and disadvantages (Smeltzer &

Carr, 2003):

Lower profit margin: The auction often results in a lower purchase price and reduces the profit

margin of the suppliers. Therefore it is possible that some business may become unattractive

because they are not profitable anymore.

Race for the bottom: A supplier could get caught up in a race with competitors for the lowest

price. The emotion of the competition in the auction sometimes makes bidders offer

unprofitable low prices. This can result in sellers that bid below their cost structure or offer

undeliverable big quantities. This obviously isn’t a good reason for participating in an auction.

Negotiation trick: Some buyers only participate in an auction to get a grip of the current pricing

and activity on the market and have no intention of allocating business to the winner. The buyer

can use this knowledge as a comparison to negotiate a new contract with his current supplier.

49

This increases the bargaining power of the buyer but even only participating in an auction can

deplete trust with his current supplier.

Shorter contract periods: Buyers may shorten the contract periods because they want to be able

to change to another supplier quickly if they offer a lower price. This further reduces the trust

between buyers and suppliers (Smart & Harrison, 2003).

However, the alleged price savings for the buying firms need some additional remarks. The

generated savings have to be compensated with the costs of switching to a new supplier. Also, the

buyer must consider several hidden costs (e.g. return or warranty costs, process costs, intermediary

expenses such as software costs, registration and licensing fees, etc.). Another expense, which is

part of the total costs, is the service of the market maker for organizing the auction. This can be

commission based or a monthly fee. However, it is possible for buyers to set a reserve price in the

auction. Only bids lower than this price come into consideration for switching to a new supplier.

Hereby, the buyer can directly take the switching costs into account during the auction (Kumar,

2013). An example of how the gross savings (former historic price - lowest bid) can be misleading

compared to the actual net savings (gross savings - additional costs) is found in figure 7. Here, direct

and indirect costs of various causes erode the gross savings. This makes the end results much less

appealing for the buyers (Emiliani & Stec, 2002).

Figure 7: Gross versus net savings in an online reverse auction (Emiliani & Stec, 2002)

50

4. Practical Applications

Combinatorial auctions have many different application domains including industrial procurement,

truckload transportation procurement, allocating bus routes, airspace system resources (arrival and

departure slots), network routing, scheduling, allocation of radio frequency spectrums and many

others. This chapter discusses the application fields of combinatorial auctions that are useful in a

supply chain setting. We start with describing how combinatorial auctions can be used for industrial

procurement. Next, procurement in truckload transportation is discussed in detail. Afterwards,

possible applications for higher level supply chains are briefly handled. To conclude, this chapter

elaborates on some software packages and providers.

4.1. Industrial Procurement

As already mentioned in the previous chapter, reverse or procurement auctions are widely applied

in a supply chain setting. Therefore industrial procurement is an extensive domain for the

application of combinatorial auctions in the B2B environment. Most of the procurement auctions in

the private sector are single-unit English auctions but there are a lot of companies that use

combinatorial auctions for their procurement activities, mostly for the purchase of commodity goods

(e.g. basic resources, agricultural products, metals, energy resources, etc.) These auctions can

handle the complexities on the market and allow procurement managers to divide a contract into

smaller parts, something which is not possible in the regular price-only auctions. Unfortunately, not

much information and details about the design of these CAs are available because companies want

to protect their proprietary information and keep their competitive advantage versus their

competitors (Bichler et al., 2006). Only a few detailed case studies are available: application of

combinatorial auctions for distributing Chilean school meals and procurement of materials at

different locations for Mars Inc. These examples are detailed in section 4.1.3. First, current practices

of CAs in this application domain are described followed by the design of industrial procurement

auctions.

51

4.1.1. Current Practices

The current practices in industrial procurement described in this section are based on the paper of

Bichler et al. (2006). A procurement manager is responsible for the complete sourcing strategy of the

company. They have to decide on the many different available options regarding potential supplier

base, price conditions, and specifications. The sourcing cycle for procurement auctions, as depicted

in figure 8, starts with the procurement manager performing an analysis of their spending and

decides whether or not they want to renew a contract for a specific good or service. The buying firm

then specifies the requirements and evaluates the current market conditions. Afterwards,

procurement managers select the potential suppliers suitable for bidding in the auction. A difficult

task in designing the auction is defining the bidding rules and additional constraints because many

issues have to be compared. For example the importance of the needed good or service compared

with the overall business, cost and quality of the good or service, number of suppliers and their

bargaining power, cost of switching or managing extra suppliers, guarantee of long-term supply, etc.

Once the buyer has defined and stated these rules and constraints, the suppliers can analyse the

request and start bidding if they are interested. As a last step, the buyer evaluates all the bids and

determines a winner for the contract. The buyer then starts the negotiation process with this

supplier.

Figure 8: Sourcing cycle for procurement (Bichler et al., 2006)

Sometimes the winner determination is not fully automatic which gives the auctioneer the chance to

perform a scenario analysis after each round. This enables him to look for his most favourable

scenario if some of the conditions change. For this reason, the software packages for combinatorial

auctions must be very flexible. It needs to have a fully expressive bidding language and purchase

52

managers must be able to easily state diverse types of allocation constraints, because procurement

includes a broad variety of goods and services. This is because the requirements over the different

applications of the procurement auctions can change significantly. However, a good software

package can considerably lower the transaction costs of the negotiation process.

The amount of goods in a procurement auction can vary from 10 to almost 100.000. Because of the

automation via combinatorial auctions, the negotiations with every supplier need much less time so

buyers can selects bids from a broader supply pool to increase the competition in the auction. The

average is around 10 to 20 suppliers in an auction but this amount can also increase up to a few

hundred suppliers. These and some other numbers are summarized in figure 9, which is data

received from several software packages (Trade Extensions, CombineNet and Net Exchange) about

combinatorial auctions in industrial procurement.

Figure 9: Estimates and data about CAs in procurement (Bichler et al., 2006)

Combinatorial auctions are used in procurement for a couple of reasons:

Cost savings: Buying firms can use CAs to lower the purchase price and to reduce transaction

costs in the complex negotiations with suppliers.

Time efficiency: Combinatorial auctions allow processing more data with a greater efficiency.

Impact market structure: CAs grant auctioneers the possibility to divide the contract into smaller

pieces. The buying firm doesn’t need to allocate the contract to one big supplier and therefore a

lot of other (and often smaller) suppliers can compete in the auction.

Package bids: Allowing bids on bundles of goods eliminates the exposure problem for suppliers.

Furthermore, package bids give bidders the opportunity to bid on complementarities and

transformations, which is important in a production process. This enables the suppliers to freely

express their competitive strengths.

53

4.1.2. Design Combinatorial Procurement Auctions

The design of an auction is a set of rules for organizing the auction and consists of the different

decisions regarding the bidding languages, winner determination and payments. An objective of the

allocation can be to allocate efficiently, whereby the auction maximizes the total payoff for all the

participants. Another option is to maximize the revenues or minimize the costs for the auctioneer.

Procurement auctions in the private sector, use this last objective most. Besides this main goal,

other additional objectives are also important in procurement. For example, the fairness perceived

by suppliers is very valuable. The auction needs to be transparent so the bidders notice that the

auction considers all participants for the allocation and hereby have a fair chance of winning (part

of) the contract. Other important aspects are speed of the auction and the time bids arrive.

Procurement managers want to further increase the realized savings by making the process as

efficient as possible. Therefore when there is a tie to break, the auctioneer often gives preference to

early bids so that suppliers don’t delay their bids, this helps reduce the time of the auction. Most of

the procurement auctions are run in multiple rounds (iterative). This enables the auctioneer to give

feedback to the participants about the bids. In general, iterative auctions increase competition

among bidders because it gives them the possibility to look at competing bids and adjust their own.

Iterative CA also increase transparency in the market because it allows the bidders to receive more

knowledge about the competition on the market (Bichler et al., 2006).

Procurement auctions often use additional allocation constraints in determining the winners. These

are crucial for a procurement manager to attain implementable solutions and to deal with the

numerous strategic and operational problems. Auctioneers use these side constraints to improve

their supplier portfolio and to increase the fairness in the auction and in that way improve the

relationships with suppliers. Allocation constraints can have different forms (Bichler et al., 2006):

Winner constraints: This places an upper and lower limit on the number of allowed winning bids

in the auction. This is an important constraint because if only one or a few suppliers are

selected, the buying firm can become too reliant on these suppliers. On the other hand, picking

too many suppliers makes it more difficult to manage the large supplier portfolio and increases

overhead costs.

Market share constraints: These types of constraints give the auctioneer the possibility to

include minimum one minority supplier in the winning bids. This way, these suppliers can also

partake in the auction and are not scared away by the big suppliers. As a result, competition is

further increased in the auction.

54

Budget limits: Budget constraints can set a minimum and a maximum on the awarded business

to a single supplier so that the buying firm doesn’t get too dependent on a single supplier or

receives inefficient (too low volume) bids. Budget limits can be quantity based or calculated on

total spending.

Quality constraints: These constraints can put restrictions on the required quality of the goods.

Especially in multi-attribute auctions, quality constraints can impose that some attributes of the

winning bids must have the same value (e.g. packed in the same kind of box).

Obviously, imposing many allocation constraints can significantly impact the duration of the winner

determination and can make the WDP even more difficult. Therefore approximation methods can be

used to find a solution. However approximation is undesirable in procurement auctions with

commitments, which obligates the auctioneer to award the business to the winners determined in

the auction. This is because the amount and specific type of business awarded to a single supplier

can differ considerably with an approximate or an optimal solution. Obtaining business in an optimal

solution but nothing in an approximate one is unacceptable for a supplier and can have a negative

impact on the auction credibility. Luckily, procurement auctions in the private sector are often held

without commitment and approximation is therefore not such a big problem (Bichler et al., 2006).

4.1.3. Examples

Detailed case studies are available about how the implementation of combinatorial auctions in

procurement benefited Mars Inc. and the distribution of school meals in Chile. Combinatorial

auctions have a large potential value in the supply chain, something which is illustrated by the

introduction of CAs for the distribution of Chilean school meals. This enhanced the price-quality ratio

and generated savings of about $40 million per year for the Chilean state. An amount that equals the

cost of feeding 300.000 children per year (Epstein, Henríquez, Catalán, Weintraub, & Martínez,

2002). Both are examples of the client-supplier relationships so only the case of Mars Inc. is

discussed in more detail.

Mars Inc.

This case description about Mars Inc. is built on the paper of Hohner et al. (2003). The multinational

company Mars produces a lot of different products and therefore needs many different inputs from

all over the world. Their central focus of procurement consists of maintaining a reliable supplier base

55

while acquiring the best value for money for their procurement actions without damaging supplier

relationships. Because margins are low in the food industries, Mars decided to introduce

combinatorial auctions for their procurement operations and started a procurement auction

website4 which is active since 2001. Mars decided to use an iterative combinatorial auction because

this increased competition and enabled bidders to learn during the auction. Bidding in multiple

rounds also reflected the iterative character of the traditional negotiation process so suppliers were

kind of familiar with it and more willing to participate in the auctions. Suppliers were allowed to

place package bids, volume discount bids (stepwise lower prices for higher volumes) and multi-

attribute bids. Feedback was given after each round about the currently winning bids so that non-

winning suppliers were able to learn from competitors and adapt their bids.

Mars also imposed several allocation constraints such as a minimum and maximum number of

winning suppliers, lower and upper limits on the awarded business to a single supplier, and in case

of multiple winning bid sets, preference was given to early bids. The problem size had a maximum of

400 items and 30 participants per auction. Normally these problem sizes are solved to optimality

within seconds but these additional constraints can significantly increase the calculation time for the

winner and hereby lower the cost savings. Mars introduced these constraints to increase the

perceived fairness to the suppliers in the auction and to maintain long-term relationships. The WDP

was modelled as a set-covering problem with additional allocation constraints. It can effectively be

solved to optimality using IP to minimize the total cost of procurement for Mars while satisfying the

demand for each item. IP is effective for solving problems to optimality with 500 items and a

maximum of 5.000 bids so the winners in Mars auctions were determined within a few minutes.

Using combinatorial auctions for procurement generated significant cost savings for Mars. This result

was due to a better matching process between the company’s requirements and the capabilities of

the suppliers, and not because supplier margins were squeezed. Mars recovered the costs for this

investment in less than one year. The auctions normally ran for one hour so a lot of time was saved

compared to the traditional bilateral negotiations. However, it took a few days to construct the

auction in the software and teach the bidding process to the suppliers but this was still way faster

than the traditional method. Especially when organizing repeat auctions. Suppliers also perceived

the auctions as fair and transparent, so we can conclude Mars benefited greatly by introducing CAs

in their procurement operations (Bichler et al., 2006).

4 <www.number1traders.com>

56

4.2. Truckload Transportation

Another interesting domain for the usage of combinatorial auctions in the supply chain is the

application into the truckload transportation market. Auctions for the procurement of freight

transportation services consist of two actors: shippers and carriers. Shippers are the auctioneers in

the procurement process and are companies (manufacturers, retailers, distributors) that need to

transport cargo. Carriers are the bidders in the auction and offer transportation services to move the

freight of the shippers and hereby connects shippers with its customers. Carriers bid for winning a

specific lane (the items in the auction), which is a path where shipments have to be transported

from a starting point to a destination. The shippers offering the lanes often combine nearby

individual lanes into a single region, on which the carriers can bid in the auction. Aggregating the

lanes facilitates the analysis of the network but increases the chance of having empty cargo trucks

within a region. A typical procurement auction in truckload transportation consists of one shipper

and multiple carriers (Caplice & Sheffi, 2006).

In the 1980s, Reynolds Metals Company was the first to implement optimization for the WDP of a

transportation auction. The first usage of combinatorial auctions in the transportation market was in

1992 by Sears Logistics Services and generated savings between 6 and 20 percent. OptiBid was

launched in 1997 and was the first software available for CAs for truckload transportation (Caplice &

Sheffi, 2006). Afterwards, many other software packages followed. In this section the current

practices in the truckload transportation market are discussed first. Next, the design issues are

described and afterwards a few examples are detailed about the use of combinatorial auctions for

truckload transportation.

4.2.1. Current Practices

Contrary to normal allocation auctions, many procurement auctions do not swap goods immediately

but assign permission to the winner to sell its goods and services for an upcoming period.

Procurement auctions for truckload transportation grant the winning carrier the right to move

freight over a specific route, but the amount of freight to move depends on the situation of the

shipper and is not predefined. Furthermore, it is difficult for the shippers to forecast the needed lane

flows because these flows need to be determined on a more detailed level (e.g. cargos per lane per

week). These forecasts can be inaccurate and are highly variable but they are necessary for the

design of the auction. Another important concept in transportation is that economies of scope

influence the transportation costs more than economies of scale. Shippers and especially carriers

57

always prefer continuous moves when moving freight because this reduces transportation costs

significantly. Continuous moves are round trips and occur for example when an inbound carrier from

a certain location imports goods to a shipper’s facility and that same carrier can immediately export

the shipper’s goods to the same starting location. This reduces the carrier idle time and the distance

travelled with an empty truck. It is common practice that a shipper changes to another carrier for an

outbound lane on short notice if this results in a continuous move. Because of these characteristics,

the relationship between supplier and carrier is uncertain and therefore a carrier’s awarded amount

can differ significantly from the actual transported amount (Sheffi, 2004).

The awarded contract is a form of option that gives the shippers the right but not the necessity to

use the carriers as assigned in the auction. Commitments for exact shipping volumes with a carrier

are exceptional. However, shippers can’t change carriers on the last moment too often because this

gives them a bad reputation. Transportation contracts are often negotiated for a short term and a

shipper who doesn’t live up to its commitments is more likely to have a reduced participation rate of

the carriers in the auction. This non-commitment also occurs the other way around: a carrier can

reject a shipper’s tender to move freight. However, most contracts in transportation indicate a

minimum percentage on the carriers’ acceptance for shipping orders. Shippers often use this

acceptance rate to evaluate the performance of a carrier (Caplice & Sheffi, 2006).

It is not an easy task for the carriers to determine the cost structure for their bids on certain lanes in

the auction because the cost of moving freight over the different lanes is interdependent. This

interdependency comes from the fact that the cost for moving a cargo from one location to another

is affected by the rest of the carrier’s business network and the chance of finding follow-on

truckloads. A carrier is willing to bid a reduced price for transporting goods from A to B if he can also

transports goods from B to A. Another difficulty is that transportation flows between different

regions are mostly unbalanced because some regions produce more truckloads than it consumes.

Also, even if the production and consumption amounts in a region are the same, it often happens

that the shipments are not in time-balance meaning that some waiting time can occur until the

appropriate shipment is ready. These imbalances can affect the costs for transporting a shipment

through a specific lane. Controversially, it is possible that carriers increase their rates for additional

loads on a specific lane because these extra loads can unbalance a region and results in sending the

carriers’ trucks back empty. The other way around is also possible because carriers can decrease

their costs by choosing the right lanes and volumes to serve in their network. In transportation it is

therefore extremely beneficial for carriers to have a balanced network because in this way their

equipment is better utilized. Furthermore, having a balanced network enables the trucks to get back

58

at their starting position frequently. This allows the drivers to get home often and at predictable

times, which is an important aspect in driver satisfaction (Caplice & Sheffi, 2006).

Combinatorial auctions enable carriers to bid on packaged lanes and capture synergies between

certain lanes. This allows them to better balance their network and realize economies of scope in

truckload transportation. Hence, carriers can bid more aggressively because a good balanced

network reduces their transportation costs. More aggressive bids means more savings and an

increased profitability for the shipper so combinatorial auctions can be beneficial for both parties.

Typical savings in combinatorial transportation auctions vary between 3 and 15 percent (Sheffi,

2004).

4.2.2. Design Combinatorial Transportation Auctions

This description of the design of combinatorial transportation auctions is based on the work of

Caplice & Sheffi (2006). In general, the transportation procurement process consists of three

different stages:

a) Pre-Auction: Before the auction starts, the shipper estimates his upcoming transportation needs

and determines the desired carriers for participation in the auction. As a last step before moving

on to the actual auction stage, the shipper stipulates the requirements a carrier has to include in

his bid.

b) Auction: The shipper communicates his needed freight requirements. The carriers analyse the

shipper’s network needs and decide on their rates for the different transportation lanes.

Afterwards, they submit these rates as bids in the auction.

c) Post-Auction: After receiving all the bids, the shipper resolves the winner determination

problem. The shipper often applies many different business rules to the WDP so that he can

create multiple what-if scenarios. In this way, it is possible to capture some kind of sensitivity in

the calculations. The results are afterwards communicated to the carriers.

A procurement auction, in general, has one main objective, namely to minimize the total costs for

the auctioneer. This objective also stands in transportation but is often extended with several other

objectives valuable to the shipper. A distinction is made between lane-based objectives and system-

based objectives. Lane-based objectives are requirements that are evaluated for each lane

independently. For example, the service quality required on each lane. The auction grants penalties

or rewards to the bids depending on its performance on several service attributes (on-time

performance, percentage broken parts, availability of equipment, etc.). It adapts the bids before

59

entering the WDP so that they reflect the right service level. Another commonly used example of

these kinds of objectives is to favour the incumbent carriers slightly to reduce the churn rate (the

loss of customers or suppliers). The other types of objectives are system-based objectives. These are

more complex because they can cross different lanes, bids, or carriers and entails adapting the

model used for the WDP. Examples of system-based objectives are business guarantees for certain

carriers, size of the carrier base (lower and upper limit on amount of winning carriers), mix of the

carriers (different types of carriers), transit time (carriers need a minimum service level).

Besides these lane and system-based objectives, several other objectives such as speed, simplicity,

efficiency, and robustness can be added. Efficiency of the auction means that the business won by a

carrier depends on his other business and preferably fits in his current network or transportation

capabilities. Robustness of the auction is especially important in transportation auctions due to the

uncertainty of the business. The auction is robust if adjustments in the transportation network

(volume change, different carrier, customer going out of business, etc.) don’t result in big cost raises

for the shipper. Of course, adding all these additional constraints has a price. It is estimated that

these constraints cost the shippers about 7 percent of their yearly shipping costs and can lose

around 50 percent of their potential savings, all in exchange for a better constructed network.

Regarding the bidding language, it is common in a traditional transportation auction to hand in per-

load or per load-mile rates for moving freight on a lane. These are simple bids and are independent

on the possible volume of the shipments. However in combinatorial transportation auctions, the

bidders are able to express their price assumptions more extensively. These bids are conditional

because they depend on a set of actions to occur. Several different types of conditional bids exist.

The most popular bid type is the simple lane bid, which is the same as the simple bid explained

before but with several service attributes added. Other types are simple lane bids with volume

constraints, static and flexible package bids, and tier bids. Package bids can be of the AND type

(multiple sets can be awarded) or XOR type (only one set can be awarded) and are a bundle of lane

bids. Static means that the bundles are conditional on exactly assigning the carrier’s stated volume

levels for all the lanes in the bundle. Flexible package bids differ from static package bids in that the

volumes for each lane bid stated by the carrier can vary between specified ranges. If such a package

bid is awarded to a carrier, the shipper can freely choose the assigned volume to each lane, as long

as it is between the ranges. Tier bids go a bit further and allow the bidder to define a schedule of bid

rates for each lane in a bundle. The rate schedule is based on certain shipping volumes and the

actual transported volume in a certain time period determines the applied rate.

60

The WDP in a transportation auction is often called the carrier assignment problem. Two possibilities

exist to award business to the carriers. The first is by lane whereby this lane is assigned to one single

carrier. The second is by load whereby a specified amount of loads is awarded to a carrier to

transport on a lane. This last type of assigning is most frequently used by software packages. More

details about the bidding languages and winner determination in transportation auctions can be

found in Caplice & Sheffi (2006).

Combinatorial auctions offer several advantages over regular auctions in truckload transportation.

First of all, shippers can offer the carriers data of enhanced quantity and quality. Furthermore, in a

combinatorial auction shippers can take non-financial information into account. Modelling the

numerous additional business constraints in the WDP is one of the most valued aspects in

transportation procurement. Shippers are also able to calculate multiple what-if scenarios and

estimate the value of each scenario. In CAs, shippers have to be more aware of the interactions

between carriers’ locations and assigned lanes. This obligates shippers to better understand the

economics of their carriers. In general, implementing combinatorial auctions in the procurement

process of truckload transportation results in more precise and cooperative interactions between

the carriers and shippers.

4.2.3. Examples

These days, a lot of big companies use combinatorial auctions for their transportation needs.

Examples are Sears Logistics Company, The Home Depot, Ford Motor Company, Procter & Gamble,

Compaq, Colgate, Nestlé, and many others (Sheffi, 2004). This section describes the case of two

companies, namely Sears Logistics Services and The Home Depot.

Sears Logistics Company

As an example, the first use of combinatorial auctions in truckload transportation is detailed

following the description of Ledyard, Olson, Porter, Swanson, & Torma (2002). Sears Logistics

Services introduced CAs in 1992 in an attempt to reduce its procurement costs. The services of Sears

controls several aspect of the supply chain, from manufacturers to distributors, cross-dock facilities

and retailers. Its main operation consists of the procurement of transportation contracts. Sears

opted to use an iterative sealed-bid format for their auctions. Multiple rounds improved the

allocation of the contracts because bidders could update their bids after receiving feedback. After

61

each round, only the conditional winners were announced with commitment requirements. This

made sure that winning bidders had to live up to their obligations and hereby reduced the incentive

to bid randomly or only to hurt competitors.

The objective of the auction was to minimize the total procurement costs, holding several business

requirements (service performance, incumbency benefits) into account. The auction stopped if total

cost wasn’t reduced by a certain percentage from the previous round. Because Sears was the first to

implement combinatorial auctions for transportation procurement, it was difficult to attract enough

carriers to participate and to educate them in the bidding process. Several experiments were run in

advance to test the auction and carriers were given proper trainings for efficient bidding. The first

auction ran by SLS took five months with one round every month. The amount of bids and results of

this auction can be found in figure 10. It took less than half an hour to calculate the winning bids.

Figure 10: Results of the first CA of SLS (Ledyard et al., 2002)

SLS generated savings of around $84 million (around 13 percent over their pre-CA procurement

costs) by holding six combinatorial auctions for the selection of its carriers. With these auctions it

obtained truckload services for 1390 lanes. The carrier’s reactions were also favourable and

considered it as a fair and time-efficient process so we can say implementing CAs was a great

success for Sears Logistics Services.

The Home Depot

Another large company that uses combinatorial auctions for its truckload procurement is The Home

Depot (THD) and is described by Elmaghraby & Keskinocak (2004). THD is the largest retailer for

home improvement products in the world. It has more than 50.000 different products over 1.000

stores and 37 distribution centres. This width of its operations brings along a complex logistics

planning process because it needs to coordinate with over 7.000 suppliers and carriers. Before the

introduction of combinatorial auctions at THD, the bidding process was done manually. Carriers had

62

to submit bids for each lane separately and were not able to capture synergies between lanes. In

2000, a new electronic bidding process was introduced and allowed carriers to bid on individual

lanes and also lane packages. This was achieved thanks to the help and software of i2 Technologies.

The Home Depot first screened carriers on certain quality attributes and financial stability, before

they could receive an invitation to participate in one of their auctions. If carriers passed this

screening, they could bid on any possible lane package and without any restrictions on the amount

of different bids for a lane.

The software used by The Home Depot assisted their bidding process in three ways. The first part

was the shipper bid support, which helped THD in analysing their network and facilitated the

selection of the lanes for auctioning. A second aspect was the carrier bid response tool, which aided

the carriers in visualizing the shipper’s network. This tool together with the trainings offered by The

Home Depot (one week training program for all its carriers) made sure the carriers were properly

educated to submit efficient package bids.

The format used was a single-round sealed bid combinatorial auction. The Home Depot opted for

sealed bids because it hoped to avoid price wars between carriers. In this way, the carriers only

submitted profitable bids, something which was also important for THD in the long run to keep its

high quality service. If the results of the first round were not satisfactory for all the lanes, a second

round was held for the remaining lanes (around 20 percent of total lanes). Some statistics about the

carrier participation is found in figure 11.

Figure 11: Statistics of the first CA at The Home Depot (Elmaghraby & Keskinocak, 2004)

In selecting the winning bids, The Home Depot had to solve a set partitioning problem. This selection

process needed to incorporate several shipper and carrier constraints. It also had several non-price

dimensions (carrier reliability, incumbent preference, etc.) besides the cost objective. The winner

determination was solved to optimality using integer programming. The results of the new bidding

process were successful because it gave THD better rates and an increased satisfaction with its

carriers. However, these results could have been even better if more training was given to the

carriers. THD therefore extended its training program to further increase the efficiency of the

bidding process.

63

4.3. Higher Level Supply Chains

Most of the available case descriptions about the use of combinatorial auctions only describe a part

of the supply chain. For example Mars uses combinatorial auctions to buy input goods needed for its

production but this isn’t connected to the distributors, retailers and customers further down the

stream. It is only a connection between Mars as a customer and its suppliers. The Home Depot only

uses CAs for a part of their transportation requirements; connecting its transportation needs to their

customers with potential logistics companies.

Unfortunately, until this day I haven’t found a case where a complete or large part of a supply chain

is controlled or regulated by auctions. It would be really interesting to automate a large part of the

supply chain, for example the supplier - wholesaler - retailer - customer relationships, using

combinatorial auctions. This means using CAs to automate the supply chain formation for a large

part of a supply chain. For instance, such an auction can have multiple suppliers offering input

goods, manufacturers bidding on transformations of these inputs into outputs goods, logistics

companies offering for truckload transportations and retailers bidding to buy the produced goods

from the manufacturers for sale to the end consumers. These auctions generate a centralized

solution which regulates the product flow between the different stages in the supply chain and

directly links the corresponding prices. After considering all the received bids from the companies in

the different stages of the supply chain, the combinatorial auction forms a feasible solution for the

supply chain that maximizes the revenues generated by the involved parties in the chain. Such

auctions highly automate the supply chain formation of companies and in this way the individual

companies in every stage don’t need to find suppliers and buyers independently. This can

significantly reduce the transaction costs for the participating companies and shortens its search and

negotiation processes.

However, a problem with expanding the scope of a supply chain is that in general the problem size

also increases because more stages are incorporated in a single combinatorial auction. More items

and parties included in the auction means more potential bids from the participants. A broader

scope often means that more agents can or are willing to participate in the auction. The winner

determination problem is in general NP-hard for combinatorial auctions and the time needed to find

a feasible allocation is related to the problem size. These wide spanning auctions generally make it

more difficult to determine the winning bids because it becomes a highly complex problem if the

problem size increases. This can be one of the reasons why I haven’t found any combinatorial

auctions covering large parts of a supply chain.

64

Another problem is the organization difficulties of holding such an auction. It is not straightforward

to let all the companies of the different stages in a supply chain work together and organize this type

of auction. If you do find a company of every stage to cooperate in its organization, they probably

won’t be eager to invite their competitors for participation in the auction. This can result in few

competing bids and reduces the efficiency of the auction. Even if an independent auctioneer is found

to completely organize this auction, he still faces several organizational issues such as what parties

to invite to the auction, the minimum service requirements, the best auction format to use in the

specific supply chain, etc. These results in a lot of additional business constraints which makes the

problem even more complex and therefore more difficult to determine the winners.

4.4. Software

Many different software platforms and websites exist for holding combinatorial auctions. Many of

these focus on the industrial procurement of commodities and transportation services. Also, a lot of

combinatorial auction providers exist for auctioning spectrum rights. This section will give an

overview of the available software providers and discusses some of them in more detail.

As mentioned before in the history about auctions (supra section 1.1), the first commercially

available software for combinatorial transportations auctions was OptiBid in 1997. Afterwards many

other software companies followed this example and created their own software packages for

combinatorial auctions. Examples are Trade Extensions, Saitech Inc. (SBids), Schneider Logistics Inc.

(BidSmart), Manugistics Inc. (RFQ Optimizer), i2 Inc. (Transportation Bid Collaborator), Baan Inc.

(BidPro), CombineNet Inc., Freemarkets Inc., etc. (Caplice & Sheffi, 2006). In later years, other big

companies acquired many of these mentioned software packages to expand their business scope

and optimize their supply chain software. Examples are the acquisition of Manugistics Inc. and i2 Inc.

by JDA Software, Baan Inc. by Infor Global Solutions, CombineNet Inc. by SciQuest, Freemarkets Inc.

by Ariba Inc., etc.

First, some of the major software providers of combinatorial auctions are described. Secondly, a

Mixed Multi-unit Combinatorial Auction Test Suite (MMUCATS) is tested and explained.

65

4.4.1. Overview Software Providers

In this section, an overview is given of companies that offer combinatorial auction software. A lot of

different firms offer software (not necessarily auctions) for optimization of the supply chain. Only

the companies whose core business is optimizing the supply chain by offering combinatorial auction

formats for its customers are included in this overview. Unfortunately, this is a non-exhaustive

overview because describing all the companies in the world that offer combinatorial auction services

would take us too far.

Tradeslot

Tradeslot offers its customers the technology and services to run a successful auction. They provide

services as participant training, design, and analysis of the results. Tradeslot produces some kind of

private markets and pre-screens the potential participants, this way only qualified participants

partake in the auction. Their software supports a wide variety of auction formats, including simple

price-only auctions for various sectors and combinatorial auctions to find the best value (not just

lowest price). This last type of auction is often used for selling spectrum rights, timber logging rights

(create synergies by acquiring adjacent lots), and for trucking freight allocations (“Tradeslot”, 2014).

Tradeslot uses multi-round combinatorial auctions with real-time feedback to the bidders. The

participants immediately receive information about the position of their submitted bid in the

auction. This gives them the possibility to refine their bids and learn from the market. The main

objective in their transportation auctions is to minimize the total costs for the supplier while

covering the offered lanes as much as possible or to cover all the lanes offered at the lowest cost. It

is possible to incorporate attributes other than price into the auction (quality scores, service levels,

loyalty, etc.). These attributes are directly reflected into the bid price, meaning a lower price if the

bidder can show a superior level for a certain attribute and a higher price otherwise. Another

important aspect of the auctions at Tradeslot is that they run with commitment. Winning bids in the

auction therefore guarantee contract award. If communication is really important it should be

factored in how much that is worth in monetary terms and reflect it in the bidding prices. This is the

only way to avoid the procurement department coming up with a result that the business doesn’t

agree with, despite being the lowest cost solution (d’Alquen J., personal communication, 8 May

2015).

An example of a combinatorial freight capacity auction performed by Tradeslot is the case of

Nufarm, which is a large agricultural company in Australia. Their transportation needs were operated

by third party logistics providers over 10 defined routes with an annual stock transfer of 17.000.

66

Tradeslot designed an auction platform that matched the requirements of Nufarm, including the

ability to bid on package lanes and weighing in non-price factors (reliability, communication, quality,

lead times, etc.). This resulted in reduced costs of 32 percent and it strengthened the relationship

with its carriers because factoring attributes other than price in the winner determination gave them

the assurance that their investments in service and quality are recognized (“Nufarm - Tradeslot”,

2014).

Trade Extensions

Trade Extensions was founded in the year 2000 and was one of the pioneers of the application of

combinatorial auctions at that time. In 2001, it held the first online CA (a packaging auction for

Volvo) with direct feedback to its participants. This day, they have large companies such as Coca-

Cola, Kellogg’s, P&G, Unilever, etc. as a customer. Trade Extensions allocates services and goods

worth more than one billion dollar trough their auctions every week. However, they also run simple

auctions so this amount is not completely generated through combinatorial auctions.

Trade Extensions provides a trade negotiation platform offering e-procurement and optimization

that enables companies to make sourcing decisions. Their software has been used for many different

reasons, such as production planning and supply chain design. They make use of advanced

optimization algorithms to ensure the best outcome and acquire maximum value from the supply

chain. Their software is flexible because it can handle multiple types and amounts of data and allows

buyers to specify their required objectives and additional business constraints. Buyers can also hold

a sensitivity analysis and investigate multiple scenarios by answering numerous what if questions.

This allows them to create a dynamic supply chain model and determine the effect of changes

before awarding the business (“Trade Extensions”, 2015).

Trade Extensions uses combinatorial auctions for a wide variety of goods and services and is active in

the private and public sector. In the private sector, Trade Extensions did a case study for Mars, Ineos

and many others. For the public sector, case studies are available concerning combinatorial auctions

for cleaning services, road resurfacing, domestic flights, care for the elderly, and bus services in

Sweden. This last case showed that package bids won almost 80 percent of the bus routes and

lowered the procurement costs with 5 percent compared to auctions based only on single bids

(“Case Studies - Trade Extensions”, 2015).

67

DotEcon

DotEcon was founded in 1999 and provides strategy and consulting advice. They offer a platform for

holding procurement auctions to save money and streamline the supply chain of companies in the

private sector and government bodies in the public sector. For complex high-value auctions, they are

currently the primary worldwide supplier of design and build services. DotEcon uses an online

auction system called WebBidder. This platform runs high-value and complex online auctions, tests

auction formats and bid strategies, and trains auction bid teams. It is highly configurable and can be

quickly adapted to the different auction formats, strategies and rules. The platform also gives real-

time feedback to the bidders. Governments from all over the world mostly run combinatorial

auctions on this platform to allocate spectrum rights. For these types of auctions, DotEcon invented

a novel and improved version of a combinatorial clock auction format (supra section 2.2.2). They

also make use of BidTracker software which estimates the developments in multiple round auctions.

This software aids them in the implementation of the bidding strategies (“DotEcon”, 2013).

Optimal Auctions

Optimal Auctions was established in 1998 and provides complete end-to-end auction solutions for

their customers, meaning they aid them in every step including the auction design, set-up, bidding,

and winner determination. The software used by Optimal Auctions is highly flexible and supports

many different auction formats, such as Dutch auctions, single- and multiple round (sealed) auctions,

combinatorial clock auctions, etc. Every client can generate a personally customized auction design

within 24 hours. Recently, Optimal Auctions helped many companies in preparing and optimizing

their bidding strategies for wireless 4G auctions held by multiple governments. They determined

that one server supports up to 300 bidders and more servers can be added to support additional

bidders. This way Optimal Auctions can deal with large scale auctions (“Optimal Auctions”, 2015). An

example of a bidder entry screen of a fictive combinatorial clock auction ran with software from

Optimal Auctions is found in figure 12.

68

Figure 12: Bidder entry screen at Optimal Auctions (“Combinatorial Clock Auctions - Optimal

Auctions,” 2015)

Saitech Inc.

Saitech started in 1993 and is currently a marketer of decision support systems and optimization

tools. It solves complex decision problems and optimizes resource allocation to realize cost savings

for large corporations in manufacturing, distribution, supply chain logistics, transportation, etc. In

2000, they launched SBids, which is a software package for carrier selection and bid management

that can be used in combinatorial transportation auctions. SBids determines the optimal allocation

of carriers to lanes for a distribution company (supplier). It helps the suppliers in two different ways.

First, it can generate lanes (the items in the auction) with corresponding bid rates based on historical

records of traffic volumes. Secondly, after receiving the (package) bids of the carriers for the

available lanes, SBids optimizes the assignment of these lanes to the different carriers while

minimizing the costs for the supplier. It also carries out multiple what if analyses on the prices per

lane, amount of assigned carriers, level of commitment, etc. The supplier can also model additional

constraints into the assignment problem to improve the quality of the solution (“Saitech, Inc.”,

2015).

69

CombineNet

CombineNet started in 2000 and provided advanced sourcing, optimization and supply chain

software solutions. It offered an e-sourcing product called Advanced Sourcing Application Platform

(ASAP), which assisted customers in the creation, launch and management of their sourcing events

(e.g. auctions). It also offered support and training for their customers and it included the feature

Expressive Bidding. This improved the bid collection in the auction with greater flexibility, allowed

participants to submit package bids and also included the possibility to bid on extensive non-price

attributes. CombineNet offered services to companies in many different sectors, including

manufacturing, consumer packaged goods, food and beverage, transportation and logistics, etc.

(“CombineNet”, 2015). In 2013, CombineNet was acquired by SciQuest to enhance their advanced

sourcing optimizer, which is only a small part of their wide variety of supply chain services

(“SciQuest”, 2015).

Manhattan Associates

OptiBid, the first optimization-based software for transportation procurement was originally created

by the company PTCG. “It was the first commercially available software specifically designed for

combinatorial auctions for transportation services” (Caplice & Sheffi, 2006, p.1019). Afterwards it

was sold to Sabre Logistics and in 2000 to Logistics.com. In 2002, Logistics.com was acquired by

Manhattan Associates to enhance their offerings of logistics services. The OptiBid software has been

used in situations with up to 350 bidders and a maximum of 10.000 lanes. It is also possible to

include additional capacity and budget constraints for the different lanes with this software (de Vries

& Vohra, 2003).

Schneider

Schneider was founded in 1935 and is a premier provider of truckload, logistics and intermodal

services. Schneider has 80 years of expertise in transportation procurement and combines this with

their offered service BidSmart, which is an optimization technology that allows bidders to submit

customizable bid packages on shipping lanes. It also assists in the bid preparation, gives real-time

feedback on submitted bids and conducts scenario analysis. This helps companies in optimizing their

supply chain (“Schneider,” 2015).

70

Besides the two companies described above, many other logistics companies or software providers

exist that offer combinatorial auctions for transportations services. For example Oracle, TIContract,

Sears Logistics Services, etc.

4.4.2. Mixed Multi-unit Combinatorial Auction Test Suite

The mixed multi-unit combinatorial auction test suite is a program in which it is possible to test,

compare and optimize fictive auctions by using different kinds of basic (atomic) and complex

package bids (“The Mixed Multi-Unit Combinatorial Auctions Test Suite”, n.d.). The test suite follows

the formulation of the MMUCA model (supra section 3.2.3) introduced by Cerquides et al. (2007). It

allows loading or randomly creating artificial data about a supply chain with multiple stages and

incorporates transformations in the production process. The test suite can analyse the formed

auctions by looking at a bid graph structure with the relationships between the bids and goods. It

also visualizes a supply chain structure with the distribution of the different goods and

transformation between the stages of the supply chain. Finally, MMUCATS allows solving the auction

to optimality (maximize the revenues) by using a WDP algorithm and shows the optimal supply

chain, including the path of transformations and the consumed and produced goods (Giovannucci et

al., 2009). This test suite is incredibly useful for supply chain settings because it allows the

incorporation of transformations in the bidding process.

In this test suite, agents participating in the auction are represented by orange circles, goods by

yellow rectangles and bids by blue rectangles. A negative bid means the bidder offers something, a

good or a transformation of goods. A positive bid means the bidder wants to buy a good or

transformation. A simple example of a MMUCA extracted from this test suite is visualized in figure

13.

71

Figure 13: A simple auction example in MMUCATS

This is a three staged supply chain starting with suppliers that offer goods, a manufacturer that

offers a transformation and a customer that wants to buy the transformed goods. In the first stage,

agent 1 offers two lemons and wants to receive €3 for it; agent 2 submits a package bid of two

lemons and one gin for €7 and agent 3 offers one gin for €5. In the second stage agent 4 bids on a

transformation of two lemons and one gin into one gin-lemon and wants €5 for doing so, agent 5

offers the same transformation as agent 4 but wants €6 for it. Finally, agent 6 offers to buy one

transformed gin-lemon for €15. Using this test suite the auction can be optimized to maximize the

total value for the supply chain. The optimal supply chain, extracted from the test suite, is

highlighted in figure 14. The supply chain starts with accepting the bid of agent 2, followed by the

transformation proposed by agent 4 and concludes with the offer of agent 6 to buy the transformed

good. This results in a surplus value of +3 (= 15 - (7 + 5)) for the supply chain.

72

Figure 14: Optimal supply chain of the simple auction example in MMUCATS

Besides this simple example it is possible to visualize more complex networks in the test suite. The

user can choose the amount of agents, goods, bids, transformations, stages in the supply chain, etc.

The test suite allows to generate bids and to create a customizable supply chain using a random,

Matlab, or generic auction generator. The program can afterwards calculate the maximum revenues

for the formed supply chain. After the optimization, the user can easily examine the results because

the test suite highlights the winning bidders and transformations of the optimal supply chain.

In my opinion, MMUCATS is a good program to test and visualize large parts of a supply chain using

combinatorial auctions. However, it lacks the option of handing in the goods and bids of each agent

separately. This makes it more difficult to represent real life situations and supply chains.

73

5. Conclusions

Combinatorial auctions were introduced for the first time in 1982 by Rassenti et al. (1982) for the

allocation of airport landing slots. In the last two decades and especially with internet emerging,

they increased in popularity in the B2B environment. Nowadays, combinatorial auctions are

widespread and have many different application domains.

Combinatorial auctions bear many advantages over regular single-item auctions. They allow

participants in the auction to submit all-or-nothing bundles or packages of multiple products. This

option enables bidders to better declare their preferences and capture synergies between the

available products in the auction. Also, all-or-nothing packages make sure that a bidder doesn’t end

up with unwanted goods, a problem that is possible when a bidder needs multiple products but is

only allowed to hand in single-item bids.

However, combinatorial auctions also bring along some difficulties. In these types of auctions, price

is no longer the only factor to take into account. A bidder who offers the highest price for a certain

good is therefore not necessarily the winner of that good in the auction. An optimal allocation of the

products over the bidders is the collection of packages that achieves the highest revenues for the

auctioneer in total. This makes the winner determination problem quite complex and not

straightforward to find the winning bidders. The design or mechanism of an auction also consists of

many different rules. Changing such a rule can alter the auction type; so many different types exist.

It is not an easy task to find the auction mechanism that best fits the specific situation and

application.

Modern day organizations are in need of outsourcing strategies and collaborative supply chain

networks to effectively manage their supply chain. This calls for an increased automation and

flexibility in its partner selection. Combinatorial auctions are useful for modelling the supply chain

formation and to increase its automation (Giovannucci et al., 2010). An interesting theoretical

method to model the supply chain formation is the mixed multi-unit combinatorial auction,

introduced by Cerquides et al. (2007). This type of auction enables participants to place bids on

transformations in the production process (convert certain input goods into output goods). These

transformations can link the different stages in a supply chain to each other because bidders can

submit bids to buy, sell, or transform goods. The companies in the different stages of the supply

74

chain place their bids and the auction can calculate a solution for the production processes

afterwards while maximizing the generated value for the supply chain.

Combinatorial auctions are often used for the purchase of commodity goods (e.g. basic resources,

agricultural products, metals, energy resources, etc.) and are especially applicable in the supply

chain for industrial procurement and the allocation of truckload transportation. This is because the

various items in these applications (e.g. input products, transportation lanes) hold a high potential of

having synergies between the items (e.g. bundles of specific input products, well-balanced

transportation networks). Combinatorial auctions are able to capture these positive effects, which

makes them an attractive method for companies to improve their supply chain. This is illustrated by

the fact that there are many software providers of combinatorial auctions available for these types

of applications.

There are a few keys to success for organizing and holding an effective combinatorial auction in the

supply chain. Even before the start of the auction it is essential to offer enough training to the

participating bidders to educate and help them in the complex bidding process. Another important

aspect is screening the potential bidders before sending them an invite to the auction. This reduces

the chance of having complications with suppliers after the auction. In allocating the goods, it is

important not to focus solely on the lowest price because this can damage the buyer-supplier

relationship. It is better that companies search for the best value by incorporating non-price

attributes (e.g. quality standards, service levels, loyalty, etc.) in the determination of the winning

bidders. This creates open and fair auctions where both parties can benefit.

If these rules are applied properly, combinatorial auctions can have many benefits for companies in

a supply chain setting. It can achieve higher allocation efficiencies because bidders are better able to

declare their preferences due to the package bidding. A well-chosen auction format allows a much

faster transfer of information between the involved parties, increased transparency and fairness for

the bidders, and can generate significant cost savings (lower purchase price, transaction costs). This

makes combinatorial auctions a more time-saving and efficient negotiation process compared to

traditional negotiation methods (Schwind, 2005).

This literature review is subject to a few limitations. First, almost all of the available papers and

literature have a theoretical viewpoint on the subject and lack practical experience with real

software packages. Secondly, the available case studies about the use of combinatorial auctions all

indicate a positive effect on the company’s costs and procurement processes. In my opinion, it must

have happened in the past that combinatorial auctions weren’t able to create a significant positive

75

effect, or even had a negative effect. Unfortunately, these cases are not described or publicly

available yet. Thirdly, most case studies describe the introduction of combinatorial auctions at a

company, which generates the highest impact on the results because it is a new approach of doing

business. These positive cases could have influenced my mind-set and biased it in favour of a

positive attitude towards combinatorial auctions for supply chain applications.

Future research should find out if there are any other applications available for the use of

combinatorial auctions in the supply chain. For instance, it would be very interesting to investigate

the possibility of connecting a whole supply chain (from raw material providers to customers, and

the different stages in between) into one combinatorial auction. This would increase the automation

of the supply chain formation tremendously but brings along severe organizational issues. Another

interesting study would be to analyse the benefits and shortcomings of combinatorial auctions in its

different application domains with a summary for the different auction types.

VI

References

Abrache, J., Crainic, T. G., Gendreau, M., & Rekik, M. (2007). Combinatorial Auctions. Annals of

Operations Research, 15(3), 131–164.

Anderson, A., Birgean, I., & MacKie-Mason, J. K. (1999). Bilateral Negotiation With Fees. In First IAC

Workshop on Internet Based Negotiation Technologies. Hawthorne, NY.

Ausubel, L. M., & Milgrom, P. (2006). The Lovely but Lonely Vickrey Auction. In P. Cramton, Y.

Shoham, & R. Steinberg (Eds.), Combinatorial Auctions (pp. 57–95). Boston: MIT Press.

Babaioff, M., & Nisan, N. (2004). Concurrent Auctions Across The Supply Chain. Journal of Artificial

Intelligence Research, 21, 595–629.

Babaioff, M., & Walsh, W. E. (2003). Incentive-Compatible, Budget-Balanced, yet Highly Efficient

Auctions for Supply Chain Formation. In 4th ACM Conference on Electronic commerce (pp. 64–

75). San Diego, USA.

Bichler, M., Davenport, A., Hohner, G., & Kalagnanam, J. (2006). Industrial Procurement Auctions. In

P. Cramton, Y. Shoham, & R. Steinberg (Eds.), Combinatorial Auctions (pp. 1116–1147). Boston:

MIT Press.

Caplice, C., & Sheffi, Y. (2006). Combinatorial Auctions for Truckload Transportation. In P. Cramton,

Y. Shoham, & R. Steinberg (Eds.), Combinatorial Auctions (pp. 1016–1075). Boston: MIT Press.

Case Studies - Trade Extensions. (2015). Retrieved May 6, 2015, from

http://www.tradeextensions.com/case-studies

Cerquides, J., Endriss, U., Giovannucci, A., & Rodriguez-Aguilar, J. (2007). Bidding Languages and

Winner Determination for Mixed Multi-unit Combinatorial Auctions. In 20th International Joint

Conference on Artificial Intelligence (pp. 1221–1226). Hyderabad, India.

Chopra, S., & Meindl, P. (2013). Supply Chain Management: Strategy, Planning, and Operation

(Global Edi.). Pearson.

VII

Combinatorial Clock Auctions - Optimal Auctions. (2015). Retrieved May 8, 2015, from

http://www.optimalauctions.com/combinatorial.jsp

CombineNet. (2015). Retrieved May 9, 2015, from

http://www.bloomberg.com/research/stocks/private/snapshot.asp?privcapId=1338499

Cramton, P., Shoham, Y., & Steinberg, R. (2007). An Overview of Combinatorial Auctions. ACM

SIGecom Exchanges, 7(1), 3–14.

De Vries, S., & Vohra, R. (2003). Combinatorial Auctions: A Survey. INFORMS Journal on Computing,

15(3), 284–309.

DeMartini, C., Kwasnica, A. M., Ledyard, J. O., & Porter, D. (2005). A New and Improved Design for

Multiobject Iterative Auctions. Management Science, 51(3), 419–434.

DotEcon. (2013). Retrieved May 8, 2015, from http://www.dotecon.com

Doyle, R. A., & Baska, S. (2002). History of Auctions: From Ancient Rome to Today’s High-Tech

Auctions. The Auctioneer. Retrieved December 20, 2014, from

http://web.archive.org/web/20080517071614/http://auctioneersfoundation.org/news_detail.

php?id=5094

Elmaghraby, W., & Keskinocak, P. (2004). Combinatorial Auctions in Procurement. In T. P. Harrison,

H. L. Lee, & J. J. Neale (Eds.), The Practice of Supply Chain Management: Where Theory and

Application Converge (Vol. 62, pp. 245–258). Springer US.

Emiliani, M. L., & Stec, D. J. (2002). Insight From Industry: Realizing Savings From Online Reverse

Auctions. Supply Chain Management: An International Journal, 7(1), 12–23.

Epstein, R., Henríquez, L., Catalán, J., Weintraub, G. Y., & Martínez, C. (2002). A Combinational

Auction Improves School Meals in Chile. Interfaces, 32(6), 1–14.

Giovannucci, A., Cerquides, J., Endriss, U., Vinyals, M., Rodriguez, J. A., & Rosell, B. (2009). A Mixed

Multi-unit Combinatorial Auctions Test Suite. In Decker, Sichman, Sierrra, & Castelfranchi

(Eds.), 8th International Conference on Autonomous Agents and Multiagent Systems (AAMAS

2009) (Vol. 2, pp. 1389–1390). Budapest, Hungary.

VIII

Giovannucci, A., Cerquides, J., & Rodríguez-Aguilar, J. A. (2010). Composing Supply Chains Through

Multiunit Combinatorial Reverse Auctions With Transformability Relationships Among Goods.

IEEE Transactions On Systems, Man, and Cybernetics - Part A: Systems and Humans, 40(4), 767–

778.

Giovannucci, A., Rodriguez-Aguilar, J. A., Cerquides, J., & Endriss, U. (2007). Winner Determination

for Mixed Multi-unit Combinatorial Auctions via Petri Nets. In 6th International Joint

Conference on Autonomous Agents and Multiagent Systems (pp. 710–717). Honolulu, Hawaii,

USA.

Giovannucci, A., Rodriguez-Aguilar, J., Vinyals, M., Cerquides, J., & Endriss, U. (2007). Mixed Multi-

unit Combinatorial Auctions for Supply Chain Management. ACM SIGecom Exchanges, 7(1), 58–

60.

Giovannucci, A., Vinyals, M., Rodriguez-Aguilar, J. A., & Cerquides, J. (2008). Computationally-

efficient Winner Determination for Mixed Multi-Unit Combinatorial Auctions. In Padgham,

Parkes, Müller, & Parsons (Eds.), 7th International Conference on Autonomous Agents and

Multiagent Systems (pp. 1071–1078). Estoril, Portugal.

Hohner, G., Rich, J., Ng, E., Reid, G., Davenport, A. J., Kalagnanam, J. R., … An, C. (2003).

Combinatorial and Quantity-Discount Procurement Auctions Benefit Mars, Incorporated and Its

Suppliers. Interfaces, 33(1), 23–35.

Jap, S. D. (2002). Online Reverse Auctions: Issues, Themes, and Prospects for the Future. Journal of

the Academy of Marketing Science, 30(4), 506–525.

Kalagnanam, J., & Parkes, D. C. (2004). Auctions, Bidding and Exchange Design. International Series in

Operations Research & Management Science, 74, 143–212.

Kros, J. F., Nadler, S., & Chen, H. (2011). The Adoption and Utilization of Online Auctions by Supply

Chain Managers. Transportation Research Part E: Logistics and Transportation Review, 47(2),

105–114.

Kumar, S. (2013). Is Your Supply Chain Business Operation a Good Fit for Online Reverse Auctions?

Transportation Journal, 52(1), 121–133.

IX

Ledyard, J. O., Olson, M., Porter, D., Swanson, J. a., & Torma, D. P. (2002). The First Use of a

Combined-Value Auction for Transportation Services. Interfaces, 32(5), 4–12.

Lehmann, D., Müller, R., & Sandholm, T. (2006). The Winner Determination Problem. In P. Cramton,

Y. Shoham, & R. Steinberg (Eds.), Combinatorial Auctions (pp. 555–596). Boston: MIT Press.

Leong, L. (2008). Value Chain Management in Online Reverse Auction: Towards Strategic and

Operational Excellence. Academy of Information and Management Sciences Journal, 11(1), 13–

29.

McAfee, P. R., & McMillan, J. (1987). Auctions and Bidding. Journal of Economic Literature, 25, 699–

738.

Mentzer, J. T., DeWitt, W., Keebler, J. S., Min, S., Nix, N. W., Smith, C. D., & Zacharia, Z. G. (2001).

Defining Supply Chain Management. Journal of Business Logistics, 22(2), 1–25.

Milgrom, P. R. (1981). Rational Expectations, Information Acquisition, and Competitive Bidding.

Econometrica, 49(4), 921–943.

Milgrom, P. R. (1985). Auction Theory. Cowless Foundation Discussion Paper, 779.

Milgrom, P., & Weber, R. (1982). A Theory of Auctions and Competitive Bidding. Econometrica:

Journal of the Econometric Society, 50(5), 1089–1122.

Myerson, R. B. (1981). Optimal Auction Design. Mathematics of Operations Research, 6(1), 58–73.

Nisan, N. (2000). Bidding and Allocation in Combinatorial Auctions. In 2nd ACM Conference on

Electronic Commerce (pp. 1–12). Minneapolis, Minnesota, USA.

Nisan, N. (2006). Bidding Languages. In P. Cramton, Y. Shoham, & R. Steinberg (Eds.), Combinatorial

Auctions (pp. 400–420). Boston: MIT Press.

Nufarm - Tradeslot. (2014). Retrieved May 8, 2015, from http://www.tradeslot.com/nufarm-freight-

capacity-auctions

Olivares, M., Weintraub, G. Y., Epstein, R., & Yung, D. (2012). Combinatorial Auctions for

Procurement: An Empirical Study of the Chilean School Meals Auction. Management Science,

58(8), 1458–1481.

X

Optimal Auctions. (2015). Retrieved May 8, 2015, from http://www.optimalauctions.com

Parkes, D. C. (2006). Iterative Combinatorial Auctions. In P. Cramton, Y. Shoham, & R. Steinberg

(Eds.), Combinatorial Auctions (pp. 96–149). Boston: MIT Press.

Porter, D., Rassenti, S., Roopnarine, A., & Smith, V. (2003). Combinatorial Auction Design.

Proceedings of the National Academy of Sciences of the United States of America, 100(19),

11153–11157.

Rassenti, S., Smith, V., & Bulfin, R. (1982). A Combinatorial Auction Mechanism for Airport Time Slot

Allocation. The Bell Journal of Economics, 13(2), 402–417.

Rothkopf, M., & Park, S. (2001). An Elementary Introduction to Auctions. Interfaces, 31(November -

December), 83–97.

Saitech, Inc. (2015). Retrieved May 9, 2015, from http://www.saitech-inc.com

Sandholm, T. (2002). Algorithm for Optimal Winner Determination in Combinatorial Auctions.

Artificial Intelligence, 135, 1–54.

Sandholm, T. (2006). Optimal Winner Determination Algorithms. In P. Cramton, Y. Shoham, & R.

Steinberg (Eds.), Combinatorial Auctions (pp. 633–700). Boston: MIT Press.

Schneider. (2015). Retrieved May 9, 2015, from http://www.schneider.com

Schwind, M. (2005). Design of Combinatorial auctions for Allocation and Procurement Processes. In

Seventh IEEE International Conference on E-Commerce Technology (pp. 391–395).

SciQuest. (2015). Retrieved May 9, 2015, from http://www.sciquest.com

Sheffi, Y. (2004). Combinatorial Auctions in the Procurement of Transportation Services. Interfaces,

34(4), 245–252.

Smart, A., & Harrison, A. (2003). Online Reverse Auctions and Their Role in Buyer-Supplier

Relationships. Journal of Purchasing and Supply Management, 9(5-6), 257–268.

Smeltzer, L. R., & Carr, A. S. (2003). Electronic Reverse Auctions: Promises, Risks and Conditions for

Succes. Industrial Marketing Management, 32(6), 481–488.

XI

Spieksma, F. (2003). Over Versnijden, Volgorde’s en Veilingen: Combinatorisch Optimaliseren in de

Praktijk. Tijdschrift Voor Economie En Management, 48(1), 97–118.

The Mixed Multi-Unit Combinatorial Auctions Test Suite. (n.d.). Retrieved May 10, 2015, from

http://www.iiia.csic.es/Projects/IEA/MMUCAP/

Thomas, D., & Griffin, P. (1996). Coordinated Supply Chain Management. European Journal of

Operational Research, 94, 1–15.

Trade Extensions. (2015). Retrieved May 6, 2015, from http://www.tradeextensions.com

Tradeslot. (2014). Retrieved May 8, 2015, from http://www.tradeslot.com

Van Hoesel, S., & Müller, R. (2001). Optimization in Electronic Markets: Examples in Combinatorial

Auctions. Netnomics, 3(1), 23–33.

Vickrey, W. (1961). Counterspeculation, Auctions, and Competitive Sealed Tenders. Journal of

Finance, 16(1), 8–37.

Vinyals, M., & Cerquides, J. (2008). On the Empirical Evaluation of Mixed Multi-Unit Combinatorial

Auctions. Agent-Mediated Electronic Commerce and Trading Agent Design and Analysis, 13,

135–150.

Walsh, W. E., & Wellman, M. P. (2003). Decentralized Supply Chain Formation: A Market Protocol

and Competitive Equilibrium Analysis. Journal of Artificial Intelligence Research, 19, 513–567.

Walsh, W. E., Wellman, M. P., & Ygge, F. (2000). Combinatorial Auctions for Supply Chain Formation.

In 2nd ACM Conference on Electronic Commerce (pp. 260–269). Minneapolis, Minnesota, USA.

Wilson, R. B. (1969). Competitive Bidding with Disparate Information. Management Science, 15(7),

446–452.

Wurman, P. R., Wellman, M. P., & Walsh, W. E. (2001). A Parametrization of the Auction Design

Space. Games and Economic Behavior, 35, 304–338.