I
A Peer-to-Peer Matching System for Grocery Home Delivery
Amin Sazavar
Department of
Civil Engineering and Applied Mechanics
McGill University, Montréal
April 2014
A thesis submitted to McGill University in partial fulfillment of the requirements
of the degree of Master of Engineering – Thesis
© Amin Sazavar, 2014
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TABLE OF CONTENTS
ABSTRACT………………………………………………………………………. I
RESUMÉ………………………………………………………………….…….… I
DEDICATION……………………………………………………………..…...… I
ACKNOWLEDGEMENTS…………………………………………………....… I
CHAPTER 1. INTRODUCTION …………………………………….……….....1
1.1) Introduction …………………………………………………………………………….....1
1.2) Review of e-grocery operations ………………………………………………………......2
1.3) Research objectives …………………………………………………………………….....3
1.4) Delivery concept ……………………………………………………………………….....4
1.4.1) Definitions ………………………………………………………………………………..…4
1.4.2) Delivery system environment ……………………………………………………………..5
1.5) Importance of the research …………………………………………………………….….8
1.6) Outline of the research ……………………………………………………………………9
CHAPTER 2. LITERATURE REVIEW ……………………………………....11
2.1) Logistics and supply chain management ………………………………………………..11
2.2) Traditional grocery supply chain ……………………………………………………..…11
2.3) E-Grocery supply chain ………………………………………………………………... 13
2.3.1) E-Grocery supply chain structure ……………………………………………………...13
2.3.2) E-grocery operations and motivations ………………………………………………...14
II
2.4) Background for modelling home delivery operations ………………………………..…16
2.4.1) General ………………………………………………………………………………….…16
2.4.2) Vehicle Routing Problem (VRP) …………………………………………………….…16
2.4.3) Solutions to the VRP ……………………………………………………………………..20
CHAPTER 3. METHODOLOGY …………………….…………………..……22
3.1) Introduction ……………………………………………………………………………...22
3.2) Delivery scenarios …………………………………………………………………….....22
3.3) Modelling of delivery methods ……………………………………………………….…25
3.3.1) Regular shopping ……………………………………..……………………………….....25
3.3.2) Matching system ……………………………………………...…………………………..27
3.3.3) Truck delivery System …………………………………………………….……….........32
CHAPTER 4. CASE STUDY AND SENSITIVITY ANALYSIS …………….36
4.1) Study network (Sioux Falls network) ………………………………………………...…36
4.2) Carrier’s location …………………………………………………………………..…....37
4.3) Client’s location ……………………………………………………………………...….37
4.4) Sensitivity analysis ………………………………………………………………………38
4.4.1) Number of stores in the network ……………………………………………………....38
4.4.2) Client/carrier ratio …………………………………………………………………...…38
4.4.3) Truck capacity constraints ………………………………………………………….….39
CHAPTER 5. RESULTS …………………………………………………...…. 40
III
5.1) Introduction ………………………………………………………………….……..……40
5.2) Sensitivity analysis: client/carrier ratio ……………………………………………….…40
5.2.1) Scenario 1: Regular shopping for all clients and carriers (R) ………………..……40
5.2.2) Scenario 2 : Truck delivery fleet, regular shopping for all carriers (TR) …..……42
5.2.3) Scenario 3: Matching system, regular shopping for un-matched (non-delivery)
carriers and clients (MR) …………………………………………………………………..……45
5.2.4) Scenario 4: Matching system, truck delivery, regular shopping for un-matched
carriers (MTR) ………………………………………………………………………..…48
5.3) Comparison of scenario performance ………………………………………………......50
5.4) Analysis of the impact of the changes in the number of stores ………………………...54
5.4.1) Scenario 1: Regular shopping for all clients and carriers (R) …………………......54
5.4.2) Scenario 2: Truck delivery fleet, regular shopping for all carriers (TR)……..…...56
5.4.3) Scenario 3: Matching system, regular shopping for un-matched (non-delivery)
carriers and clients (MR) ………………………………………………………..……...58
5.4.4) Scenario 4: Matching system, truck delivery, regular shopping for un-matched
carriers (MTR) ……………………………………………………………………………63
5.5) Analysis of the impact of the changes in trucks load capacity on scenarios with truck
delivery fleet …………………………………………………………………………….67
CHAPTER 6. CONCLUSION ……………………………………………..…...71
6.1) Introduction …………………………………………………………………...………....71
6.2) How the research objectives are satisfied ………………………………………..……...72
6.3) Research significance…………………………………………………………………….72
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6.4) Limitations and recommendations for future research .....................................................73
REFERENCES ……………………………………………………………….…75
APPENDICES …………………………...………………………………………82
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Abstract
This thesis introduces a new delivery method for electronic grocery shopping. This method
involves a peer-to-peer matching system in which customers (carriers) who shop at a grocery
store are assigned other customers (clients) who have ordered groceries to be delivered to their
home. Carriers deliver groceries to the clients’ homes, in return for an incentive. The matching
system matches carriers to clients to minimize the total travel time on the network.
In order to examine how this new method of delivery performs, we compare it with the current
methods of grocery delivery: regular grocery shopping, where every customer visits the grocery
store, and truck delivery service, where groceries are delivered to customers who have ordered
them. Four different scenarios are designed and simulated. A set of performance measures is then
developed in order to evaluate the different scenarios.
The matching system is simulated by employing a mixed-integer optimization method and
solved by the IBM-CPLEX add-on in Matlab. The truck delivery service is presumed to be a
multi-depot split-delivery truck delivery service and is simulated by using a partial inference of a
multi-depot split-delivery vehicle routing problem heuristic. The scenarios are simulated and
examined on a hypothetical network –The Sioux Falls traffic network.
The most important finding from the results is that the new delivery system – the matching
system – performs well in terms of total travel time in the network and has the potential to be
implemented alongside the two other current methods of grocery shopping. The matching system
reduces the travel time in the network compared to regular grocery shopping, but does not
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outperform truck home delivery service. The performance of the matching system is found to be
the greatest when the number of carriers is equal to the number of clients.
The matching system produced acceptable results in the study presented in this thesis; however,
the need for a more detailed investigation is obvious to be able to judge its privileges to the
regular truck delivery service.
VII
RESUMÉ
Cette thèse propose une nouvelle méthode de livraison pour l'épicerie en ligne. Cette méthode
implique un système d'appariement de pairs dans laquelle les consommateurs (livreurs) qui
achètent à l'épicerie sont liés à d'autres consommateurs (clients) qui ont commandé en ligne une
épicerie à être livrée à leur domicile. Les livreurs livrent l'épicerie au domicile des clients, en
échange d'une rétribution. Le système de recherche assigne les livreurs aux clients dans le but de
minimiser le temps total du voyage sur le réseau.
Afin d'évaluer comment cette nouvelle méthode de livraison performe, on le compare avec les
méthodes actuelles de livraison d'épicerie: achats réguliers en épicerie, où chaque client se rend à
l'épicerie et où la livraison est effectuée par camion et où l'épicerie est livrée à des clients qui les
ont commandé. Quatre scénarios différents sont conçus et simulés. Un ensemble de mesures de
la performance est ensuite développé afin d'évaluer les différents scénarios.
Le système d'appariement est simulé en utilisant un procédé d'optimisation en nombres entiers et
résolu par l' IBM - CPLEX module dans Matlab. Le service de livraison par camion est présumé
être une fraction de la prestation de services de livraison de camion multi - dépôt et est simulé en
utilisant une déduction partielle d'un multi- dépôt véhicule split- livraison problème de routage
heuristique. Les scénarios sont simulés et examinés sur un réseau hypothétique - Le réseau de
circulation Sioux Falls.
Le point le plus important dans l'ensemble de ces résultats est que le nouveau système de
livraison - le système de correspondance - se comporte bien en termes de temps total de voyage
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dans le réseau et a le potentiel pour être mis en œuvre aux côtés des deux autres méthodes
actuelles de l'épicerie. Le système d'appariement réduit le temps de voyage dans le réseau par
rapport à l'épicerie régulière, mais ne surpasse pas un service de livraison par camion. La
performance du système d'appariement se trouve être la plus efficace lorsque le nombre de
livreurs est égal au nombre de clients.
Le système d'appariement a produit des résultats acceptables dans l'étude présentée dans cette
thèse, mais la nécessité d'une enquête plus approfondie est évident pour être en mesure de juger
de ses privilèges pour le service régulier de livraison par camion.
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DEDICATION
To
Saba, Hamed, Maman and Baba
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ACKNOWLEDGEMENTS
I am deeply indebted to my supervisors Dr. Marianne Hatzopoulou from McGill University and
Dr. Matthew Roorda from University of Toronto for their advice, support, encouragement and
friendship during my graduate studies. I wish all the best to them and their families.
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CHAPTER 1
INTRODUCTION
1.1) Introduction
Groceries are the most universal commodity and there is intense competition between
supermarkets, driving them to seek new technologies and methods of streamlining both their
supply chains and their marketing strategies. The internet is the element that can help link
customers with grocery stores from their homes and integrate the logistics and supply chains
with sales (Boyer et al. 2005). The developments that are brought by the internet and information
technology have been helpful in the initiation of new businesses and service concepts. The
grocery business is an important sector with a considerable market penetration in today’s society.
One of the important aspects of the grocery business is the way consumers gain access to
groceries. Basically, there are two different methods for consumers to access groceries; regular
grocery shopping and truck delivery following online shopping (e-grocery). E-grocery and the
truck delivery system is the newer method and is making its way into the households shopping
market: however, it has some drawbacks. Selling groceries online means incurring additional
costs and fees which may be higher than what customers are willing to pay for the delivery
service (Galante et al. 2013), and also significant investments are needed for the distribution
infrastructure (Kempiak and Fox 2002). The retail food industry has been forced to adapt and to
use new technologies in order to increase its efficiency, thus it is developing new business
practices and relationships with suppliers and customers (Kinsey and Ashman 2000). It can be
concluded that innovation in this business, especially in delivery operations, is essential. As the
need is felt for new delivery systems, we witness a range of innovations. For example, some
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French retailers have launched a service where customers can order their groceries online and
pick them up at a store (Galante et al. 2013).
In this thesis, a new method of delivery for e-grocery is proposed and simulated. The
performance of the new delivery method is compared against the regular shopping and the truck
delivery system. These three methods of delivery are simulated and run on a hypothetical traffic
network and their performances are judged according to their travel times. This new service
offers progress and greater capacity in the grocery delivery and grocery business in general.
Currently e-grocery is an important part of the grocery business and it seems that the next
developments in the grocery business will be in this field (e-grocery).
1.2) Review of e-grocery operations
With the emergence of e-commerce and the expansion of access to the internet, many consumers
are attracted to the practicality of e-grocery, to the extent that it could erode the traditional
methods of shopping for groceries (Hean Tat Keh and Shieh 2001).The growth in electronic
retailing business is fast. Annual growth rates in consumer electronic retailing businesses were
over 100% from 1995 to 2006 (Cullinane et al. 2008). E-grocery includes the ordering of
commodities via the internet and the delivery of the ordered commodities to the customer.
According to Statistics Canada, in 2010, 8 out of 10 Canadian households (79%) had access to
the Internet. Grocery shopping is one of the largest categories of electronic retailing business.
Implementation of the new services requires a desire to change the current scenarios and models
among various stakeholders; namely the customers, retailers, wholesalers, manufacturers and the
supply chain service providers.
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In the regular grocery supply chain, goods are delivered to the store by the supply chain service
providers and customers do the shopping and delivery on their own. Hence, there are no costs for
the store associated with the delivery operations. In the e-grocery service, however, significant
costs are incurred in picking and packing the goods ordered, and transportation for home
delivery (@Your Home 2001).
Picking and packing operations are done in two ways. The first method is called a channel
model, in which these operations take place in a dedicated distribution centre. The second
method is the intermediary method, in which these operations take place using the current store
facilities and equipment (Bartolotta, 1998; Dagher et al., 1998; Heikkilä et al., 1998; Holmström
et al., 1999; Kämäräinen et al., 2001).
The other major cost is the home delivery transportation, which is the Achilles heel of the e-
grocery business. Improving the logistical efficiency is one of the most important steps toward
profitability. Grocery products, in particular, need to be handled under appropriate conditions to
preserve their quality; hence vehicles with temperature controlled storage are needed and this
imposes high costs on the business.
1.3) Research objectives
As just stated, home delivery is a major problem in the e-grocery business and this problem is
not going to diminish as this business is expected to expand in future. Studies show that there is
latent demand for e-grocery shopping. In France, 33% of consumers who have never used e-
grocery services would begin to do so within the next six months if the service was available in
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their area. That is why the need for a new delivery concept which does not impose extra delivery
fees on consumers, requires little infrastructure, and has the potential to expand quickly, is
needed (Galante et al. 2013).
Therefore the first objective of this thesis is to introduce a new method of delivery which has the
potential to improve the delivery system in this business. The second objective is to analyze and
compare the efficiency of different e-grocery delivery methods in terms of travel time. This
thesis seeks to answer the following major questions:
What are the levels of different e-grocery delivery methods in terms of travel time?
In which conditions is each of the e-grocery methods more feasible?
1.4) Delivery concept
As discussed in section 1.2, home delivery operations play a crucial role in an e-grocery business
and the need for proper delivery systems is acute.
1.4.1) Definitions
The delivery concept rests on a number of definitions presented herein: Client: The customer
who places an order for groceries via the internet and expects to receive the ordered groceries,
delivered to his or her specified address.
Carrier: The customer who does his or her shopping, on his/her own effort, by visiting the
grocery store and is willing to also deliver groceries to other clients.
Customers: The group of all of the clients and carriers in a network.
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Shopping tour: A series of sequential trips that lead to shopping and/or delivery of groceries for a
customer in the network.
Best store for Customer/Carrier/Client: The store that provides the shortest overall distance for a
customer while traveling on a shopping tour.
Initial location: Every shopping tour starts from an initial location.
Final location: Every shopping tour ends at a final location.
Client/Carrier Ratio:
in a network is called the client/carrier ratio.
1.4.2) Delivery system environment
The new delivery system that we propose here operates in a network composed of numerous
zones (nodes). Customers are scattered in the network and are able to travel from one zone to any
other zone. There are several stores of a particular grocery business company stationed in the
zones; however there is not necessarily a store in every single zone of the network. The customer
who is willing to enroll in the delivery system creates an account on the grocery company’s
website which includes the customer’s address. The grocery company takes online orders
through its website. All of the stores in the network are connected and synchronized with each
other through a central communication unit which includes all of the current pending online
orders. Once an order is received by the website, it conveys the information to the central
communication unit. All of the stores in the network can see the current pending orders.
At the same time, there are “carriers”, customers who visit their preferred store to do their daily
grocery shopping. As mentioned before, all of the customers (clients and carriers) are registered
on the website with their addresses. There are mechanisms installed in all of the stores which can
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detect that a specific carrier is present in the store, e.g. the customer would scan or tap their
membership card when entering the store. Once the carrier has done his/her own shopping, the
cashier at the store would inform the carrier that the central communication unit has matched
them with a client. Upon the carrier’s willingness, he/she is expected to carry the client’s sealed
package containing their orders in it and deliver it to the client in a timely manner.
There are criteria for matching carriers and clients in a network which are applied by the central
communication unit. These match a carrier with a client in a way that imposes a reasonable extra
distance/travel time to the carrier’s routine shopping tour, so that the carrier would be willing to
take the opportunity. If the carrier picks up the client’s package from the store, he or she is
expected to deliver it within a specified time window. Once the sealed package is delivered to
the client, the client would pass a confirmation code to the carrier. This code is generated when
the client makes the online order. The carrier has to send this confirmation code to the central
communication unit in order to inform it of the successful delivery of the package. The carrier
would receive bonus points in his/her account on the store website that can be used when doing
grocery shopping later. The procedure for assignment of points is organized in such a way that
the new delivery system appeals to potential carriers. Besides the attractions of the matching
system for the carriers, this system could also have some benefits to the clients who are the
instigators of the whole process. For example, they would be charged less for the delivery than
for the regular truck delivery system, or they could be granted some points, or even the delivery
fee could be waived and they would be charged only for packing of their orders.
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It has to be taken into consideration that every matched carrier is only matched with one client
and also every matched client is only serviced once with a single carrier. The central
communication unit does not match carriers and clients who have exactly the same address in
their profile, in order to prevent any system abuse. It is noteworthy that once the carrier indicates
his or her willingness, the store’s staff is responsible for gathering all of the ordered groceries
and packing them in a sealed package. This delivery system is named the “carrier/client
matching system.” Figure 1 illustrates how the system works.
1. Client places order via grocery store website and receives a confirmation code
2. Order is transferred from the website to the central communication unit
3. Carrier leaves the initial location to visit the grocery store
4. Grocery store informs the central communication unit that the carrier has entered the store
5. Central communication unit matches the carrier with an appropriate client and informs the
grocery store
6. Grocery store staff pass the packaged order to the carrier and the carrier leaves the grocery store
for the client’s location
7. Order is delivered to the client by the carrier, and client provides the carrier with the confirmation
code to be sent by the carrier to the central communication unit
8. The carrier leaves the client’s location for his/her final location.
Figure1. Flowchart of matching system environment
Grocery
store
Client
location
Carrier final
location
Carrier initial
location
Central
communication
unit
Grocery store
website 1 2
5
3
6
8
4
7
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1.5) Importance of the research
In order to answer the two major questions, four different scenarios are defined, simulated and
compared with each other. These four scenarios are feasible shopping methods which are
different mixes of all available shopping modes, namely: regular shopping, truck delivery and
the matching system.
The reason that the main focus of this dissertation is the grocery business is that groceries have
greater demand than other products, e.g. clothing. Groceries are bought regularly and frequently
and they are the greatest portion of the shopping basket of a household at any time of the year.
The food and agricultural industry in US make up 9% of the gross domestic product; 60% of it in
sales activities. Retail food stores and restaurants sell over $890 billion of food and drink each
year, half of this amount is spent in grocery stores, which is why there is fierce competition
between companies in this business (Kinsey and Ashman 2000). In addition, groceries are a
commodity which is not always necessary to test or see before purchasing.
Another reason that this research focuses on e-grocery delivery is that the market growth is
expected to be high. E-grocery business has moved from the infancy stage to the growth stage
and its sales are expected to rise dramatically in coming years. E-grocery businesses forecast a
growth in their business. Although the profits are currently low, more profit is expected if the
business keeps growing at the expected rates. More frequent access to the internet by consumers
and less expensive computer prices are the major elements that would help this business to
further develop (Hean Tat Keh and Shieh 2001).
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In general we can classify shopping tours into two types: home-based shopping and non-home-
based shopping. Home-based shopping tours are generated from home and are terminated at
home as well. Non-home-based shopping tours are done by individuals who are on their way
home from some other location, e.g. their workplace. The proposed matching system offers an
alternative to home-based shopping and decreases some of its consequences, e.g. emissions,
traffic load. The reason for this claim is the fact that the carrier travels almost the same route
after purchasing his or her groceries as would the customer who would engage in home-based
shopping and lives close to that carrier. Now, according to the matching concept, the carrier has
done his/her own shopping and is heading home, it would be a productive endeavor to organize a
system in which the client’s order is carried in the carrier’s vehicle.
The agents in this system include clients, carriers and the grocery company. All of the agents
seek their benefit in any system and this system should be economically beneficial to all of them.
Clients would receive their groceries for a lower charge than if they were delivered by the store’s
delivery trucks. Carriers are attracted by rewards for travelling a reasonable extra distance and
taking a small detour. The grocery company is also a beneficiary, because the truck fleet imposes
a large initial cost (purchase of trucks) and continuing high maintenance costs. When the
matching system starts working well and becomes the first choice of the clients, the store can
eliminate the fleet of delivery trucks and the costs associated with it.
1.6) Outline of the research
This thesis is presented in six chapters as follows. Chapter 1 defines the problem and the new
delivery concept. It also presents the objectives of the research and the structure of the thesis.
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Chapter 2 contains a review of literature on electronic grocery retailing business with emphasis
on vehicle routing problems. Chapter 3 presents the different grocery shopping-delivery
scenarios and the methodology that is employed in modelling them. Chapter 4 introduces the
study network and the set-up of the sensitivity analysis. In Chapter 5 the results for four
scenarios are presented. In this chapter results are discussed based on the different set ups that
are produced in chapter 4. Chapter 6 presents the conclusions and limitations of the thesis and
makes recommendations for future research.
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CHAPTER 2
LITERATURE REVIEW
2.1) Logistics and supply chain management
Companies started to explore the management of logistics during the 1950s (Ballou 1999;
Bowersox et al. 1999). Logistics is that part of the supply chain process that plans, implements,
and controls the efficient, effective flow and storage of goods, services, and related information
from the point of origin to the point of consumption in order to meet costumer’s requirements
(Bowersox et al. 1999).Generally, a company is not able to control its entire supply chain
because a typical supply chain consists of several elements such as raw material suppliers,
production facilities, warehouses, distribution centers, transportation services, retailers and
customers. Thus, companies normally take a narrower view and control the immediate supplies
and distributions (Ballou 1999). Nowadays, the development of an economically efficient
operation is the main goal of both logistics and supply chain management. In these operations
several other goals are also taken into consideration such as flexibility and customer satisfaction.
It is expected that by developing new logistical models and by designing logistic networks with
new structures, companies may be able to offer more efficient and cost-effective services.
2.2) Traditional grocery supply chain
The elements of a supply chain include functions such as warehousing, transportation, customer
service and transportation. The consumers are the final part of the grocery supply chain, being
responsible for the picking and transporting of the goods. Figure 2 illustrates a simplified
structure of the traditional grocery supply chain.
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Figure 2. Simplified structure of supply chain for traditional grocery retail business (Yrjölä 2001)
Retail businesses may make their purchases from a wide range of suppliers, ranging from
farmers to wholesalers. The finished goods are transported from the suppliers’ plants to the
warehouse. Warehouses supply the retail stores and in the case of grocery products the
transportation from warehouse to retail store is performed by trucks. In traditional grocery
business the final transaction happens in the grocery store where the customer picks and buys the
groceries. After picking and buying, customers carry the groceries away on their own.
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2.3) E-Grocery supply chain
2.3.1) E-Grocery supply chain structure
In e-grocery business, the supply chain structure is similar to the traditional grocery supply chain
structure (Figure 2), except that the direction of the last arrow is downward, showing the
operation of delivery of goods to customers. In order to be practical and attractive to customers,
the e-grocery supply chain structure has to be more efficient than the traditional grocery supply
chain. In addition to this, customers can calculate the cost of doing their traditional grocery
shopping. Generally, customers consider the cost of the grocery shopping trip as the cost of gas
and parking, however they should note that the maintenance cost of the car and the opportunity
cost of their time play crucial roles in their choice of shopping mode.
Figure 3. Simplified structure of the e-grocery supply chain (Yrjölä 2001)
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The goal for e-grocery business is to provide cost-efficient picking, packing and delivery
services with no inconvenience for the customers. The picking operation is generally done in one
of three ways. The first strategy is when the operation is done in a retail store. The second option
is the use of a separate dedicated distribution centre: this is most popular with new companies. A
third strategy is that a traditional grocery store could be partly converted to a distribution centre
and all the picking operations could be managed there.
2.3.2) E-grocery operations and motivations
The first online grocer in the USA was Grocery Express which was founded in San Francisco in
1981. It offered home delivery of groceries with a simple user interface via phone and fax.
Grocery Express had 5,000 customers at its peak, but logistical challenges and the inability to
build to scale eventually doomed it to failure (Mendelson 2001). The US e-grocery market
experienced rapid market growth from the mid-1990s to the end of that decade and new
companies such as Webvan, Streamline, Homegrocer, Peapod, and Groceryworks were
established. Most of these companies have either gone out of business or converted to traditional
grocery retailing. However, successful businesses such as Tesco started their e-grocery
operations later and have evolved to the point where today Tesco.com is the leading e-grocery
business in the UK.
In the late 1990s e-grocery businesses in particular invested in dedicated distribution centers to
make the picking and packing process more efficient, however, because of high investments and
low customer demand, these businesses did not prosper financially. Currently, e-grocery
businesses are generally based on the traditional in-store picking and packing process; for
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example, Tesco.com uses 250 out of its 690 stores for e-grocery picking operations, covering
91% of the population in the UK (Jones 2001; Knichel 2001; Reinhardt 2001). It provides e-
grocery services through one third of its 690 stores which means that it is within a half-hour
reaching time to 91% of the British population (Kempiak and Fox 2002).
E-grocery shopping is attractive to people who lack the time or willingness to shop themselves.
These customer characteristics were also detected in earlier research on the typical e-grocery
customer (Lardner 1998; Ingram 1999). The customers’ main motivations for using e-grocery
services are, namely, the greater convenience and savings in time from not visiting the store, and
avoiding the picking operation while shopping in the store (Raijas 2000). Retailers believe that e-
grocery business will improve their market penetration and will play a crucial role in households’
grocery shopping preferences. Generally, the customers who are using e-grocery shopping
services are willing to pay more than the cost they would have to pay when shopping for
groceries traditionally, or alternatively the regular delivery fees for truck delivery service, in
order to enjoy the convenience they desire.
E-grocery business is also attractive to the grocery retailer by expanding the geographic area
covered by offering e-grocery services (Anckar et al. 2002). Considering the fact that the grocery
business is highly local because of transportation costs, e-grocery operations is a reasonable step
forward for grocery businesses to invest in. From society’s point of view also e-grocery business
is acceptable since it supports better services to elderly and disabled people.
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2.4) Background for modelling home delivery operations
2.4.1) General
Home delivery is the provision of groceries by a retailer to a customer who has placed an order.
Typically home delivery operations are done by the truck fleet of the retailer. The specified
trucks are dispatched and scheduled using the vehicle routing problem. The following section
presents the vehicle routing problem (VRP).
2.4.2) Vehicle Routing Problem (VRP)
The basic VRP is composed of one depot, vehicles of the same type and numerous customers
(demands) in a network. Generally the objective is to minimize the total cost in the network.
VRP is an extension of the Travelling Salesman Problem (TSP) and is an NP-hard problem. As a
more general definition VRP is defined as selecting the best possible sequence of routes in the
network while minimizing a cost function and satisfying any existing constraints like fleet
capacity, delivery time windows, etc. There is not a single universally accepted definition for
VRP (Laporte 2007). There are different types of VRP, and numerous assumptions and
constraint combinations can be applied to them. The major types of VRP are as follows:
Stochastic vs. deterministic
When one or more variables of the problem, e.g. travel time, are not fixed (deterministic) they
would be treated as a random (stochastic) variable, hence the stochastic VRP. This was first
introduced in 1982 by Stewart and Golden. The computational difficulty of solving the problem
increases enormously, no matter what is considered random in the network (Larson and Odoni
2007).
17
Dynamic vs. static
When a company has certain known demands (demand that is known before the service day),
plus some online demands that are unknown before the service day, the case is a dynamic VRP,
whereas in the static VRP, all of the demands are known in advance and no demands are made
during the trucks’ service. In dynamic VRP, the decision in each stage is dependent on the
decision made in previous stages. A stage is defined as the point when the decision is made.
(Figliozzi 2010; Powell et al. 2000).
VRP with time window
In this type of VRP there is a timeline and the vehicles have to set their arrival time at the
customer’s address at a certain time in order to deliver orders in a timely manner and also reduce
the vehicle waiting time. It means that the vehicle has to wait if it arrives sooner than the
specified time (Repoussis and Tarantilis 2009).
Open VRP
Generally in truck services, trucks are scheduled to return to their initial location, from where
they have been dispatched, after completing the deliveries. In open VRP, trucks do not
necessarily return to their initial location and their final location is not the same as their initial
location (Laporte 2009).
Time dependent VRP
In this type, the travel times in the network vary during the day, which happens mostly in urban
networks (Figliozzi 2009). This kind of VRP is introduced by Malandraki and Daskin in 1992. A
18
common way to solve this type of VRP is to divide the time into N time steps and solve the VRP
for each time step (Malandraki and Daskin, 1992, Figliozzi 2009).
There are some extensions to the VRP problem that could fit most of the different types of the
VRP that were presented above. These extensions are as follows:
Single depot vs. multi depot
Trucks are dispatched from a single depot in the basic form of the truck delivery services. In
some cases the company may have multiple depots in the network and trucks are dispatched
from these scattered depots. This extension to the VRP is called multi depot VRP (Laporte
2009).
Split delivery vs. single source
In some delivery services a single customer may receive orders from more than one vehicle and
his/her orders may be distributed among vehicles; these cases are split delivery VRP. In the basic
case all of the orders of a customer are delivered by a single vehicle and is called single source
VRP. The reason this extension is specifically mentioned is the fact that the VRP that is used in
this thesis is a single source VRP, which is actually a simplified derivation of a multi depot VRP
(Laporte 2009).
Homogeneous vs. heterogeneous fleet
In some cases the delivery fleet is composed of more than one vehicle type and forms a VRP
with heterogeneous fleet. In these cases a notation of vehicle type is used when formulating the
19
VRP for vehicle type used. Each type can have different capacity or other characteristics. In
simple cases the fleet is uniformly made up of the same type of vehicles and the fleet is
homogeneous (Laporte 2009).
VRP with pickup and delivery
In some cases the vehicle is assigned with delivery duties in some parts of the route and pickup
duties and operations in other parts of the route. In these cases usually there are delivery time
windows and the problem is mostly solved by heuristic methods (Luo and Schonfeld 2007).
Consolidated delivery
In these cases different supplies have been sent to a warehouse and these supplies have been
bundled together. Vehicles visit these warehouses to pick up the bundles and deliver them to
customers. Such packaging and bundling operations can bring efficiency to the delivery services
in terms of time and cost (Laporte 2009).
2.4.3) Solutions to the VRP
VRP algorithms are divided into 3 major categories:
I. Exact algorithms
These algorithms are generally considered for classical VRP which has low complications, i.e. a
symmetric cost matrix, homogeneous fleet, limited number of depots. Dynamic Programming
(DP), branch-and-bound, and Integer Linear Programming are the three general formulation
techniques used when exact answers are being sought. Exact algorithms have poor success in
20
solving realistic problems. This algorithm may face difficulty in solving cases with more than
100 deliveries (Laporte 2009).
II. Classical heuristics
These solutions have more capacity for solving complicated VRP. Classical heuristics have two
parts; first part is the constructive heuristic and the second part is the improvement heuristic. The
first part proposes a fast, feasible solution to the problem and the second part tries to improve the
proposed solution (Laporte 2007). Some of the constructive heuristics are savings algorithms and
set partitioning heuristics. Clark-Wright is the best known savings algorithm which has been
used in this thesis as well. This algorithm is not the most accurate algorithm, but is the most
popular because it is fast and simple to implement (Cordeau et al. 2002).
III. Metaheuristic
These solutions are the most efficient way to solve large networks with noticeable complications,
which have been used in the past 15 years. Some of the best metaheuristic methods can solve
problems with more than 100 vertices and arrive to a solution much faster than any other
solution. The difference between these solutions and classical heuristics is the fact that the
objective function changes from one iteration to the next and that is why it is more efficient in
complicated VRP cases with numerous vertices (Laporte 2009).
21
CHAPTER 3
METHODOLOGY
3.1) Introduction
The new delivery concept proposed in this thesis – the matching system – is defined and
introduced in the previous section. In order to make this method of delivery more practical, it is
necessary to combine this new method with the other methods of delivery. In the next section,
four scenarios of delivery for grocery business are defined. All of these scenarios are practical
and are composed of the three different delivery methods.
3.2) Delivery scenarios
As briefly stated in the Introduction chapter, four different scenarios are considered for grocery
shopping and delivery. These four scenarios are intended to be feasible and practical mixes of the
three methods of shopping and delivery. The regular shopping method is the only method of
grocery shopping/delivery which does not essentially need to be combined with any other
methods to be deemed as a complete delivery system and a system can rely solely on it, however,
the two other methods of grocery delivery/shopping need to be combined with other methods to
form a complete and reliable delivery system for the network. That is why scenarios which are
mixtures of methods are defined and used in the network. The four proposed scenarios are as
follows:
Scenario 1: In this scenario all of the shopping and delivery operations are done by
customers on their own for their own use; thus this scenario is composed of one delivery
method which is the regular shopping mode.
22
Scenario 2: In this scenario all of the clients in the network are being serviced by the truck
delivery fleet of the store and the entire carriers do their own shopping and delivery
operations; thus this scenario is composed of two different delivery methods; the truck
delivery system and regular shopping.
Scenario 3: In this scenario initially carriers and clients are matched to the greatest extent
possible. Unmatched clients and carriers do their shopping and delivery operations on their
own; thus this scenario is composed of two different delivery methods which are the
matching system and regular shopping. Figure 4 illustrates how this scenario works in
detail.
Scenario 4: In this scenario initially carriers and clients are matched to the greatest extent
possible. Unmatched clients remain in the network and receive their orders by the truck
delivery fleet of the store and all unmatched carriers do their shopping and delivery
operations on their own; thus this scenario is composed of three different delivery modes;
the matching system, truck delivery system and regular shopping. Figure 5 illustrates how
this scenario works in detail.
23
Clients
(order)
Client & Carrier pool
(Matching system)
Carriers
Willingness to
do a delivery
Unmatched carriers
do their own
shopping (regular
shopping)
Clients and carriers are
matched
Unmatched clients do
their own shopping
(regular shopping)
SUCCESSFUL
MATCHING
UNSUCCESSFUL
MATCHING
YES
NO
Clients (order)
Client & Carrier pool
(Matching system)
Clients and carriers are matched
Carriers
Willingness to
do a delivery
Delivery by the truck delivery
fleet (truck delivery system)
SUCCESSFUL MATCHING
Unmatched carriers do
their own shopping
(regular shopping)
UNSUCCESSFUL MATCHING
NO
YES
Figure 5. Scenario 4
Figure 4. Scenario 3
24
3.3) Modelling of delivery methods
In order to model these four delivery scenarios, it is necessary to simulate the three delivery
methods respectively.
3.3.1) Regular shopping
As stated above, in this method of grocery shopping/delivery all customers (including both
clients and carriers) are assumed to visit their “best store” when shopping for groceries and
transport their groceries to their final destination themselves. In this mode, customers (either
client or carrier) leave their initial location and visit their “best store” and finally go to their final
destination. It is assumed that for clients the initial and final location of the shopping tour are the
same location (most likely home) and for carriers they are different locations (e.g. initial location
is the work office and final location is home). The total travel time for each customer is the sum
of the travel time of the stages of their shopping tours.
Total travel time for a carrier (regular shopping) =
(Equation 1)
i
K’’
i’
Figure 6. Carrier’s regular shopping tour
25
Total travel time for a client (regular shopping) =
(Equation 2)
Subscripts:
i = the carrier’s initial location zone in the shopping tour
i’= the carrier’s final location zone in the shopping tour
j= the client’s zone
k’’= the best store zone for the carrier
k’ = the best store zone for the client
Variables:
= travel time from carrier’s origin i to his best store k’’
= travel time from client’s zone j to his best store k’
= travel time from carrier’s origin i to his best store k’’ to carrier
destination i’
= travel time from client’s origin j to his best store k’ to client
destination j
j
K’
Figure 7. Client’s regular shopping tour
26
3.3.2) Matching system
In this method of grocery delivery each client is being matched with a carrier in the system as
long as there is an unmatched carrier to provide service such that the minimum possible travel
time is being spent by the matched carrier. Clients and customers are either matched or
unmatched in the network depending on the ratio. It is clear that in this method of grocery
delivery, matched clients do not travel in the network. Carriers (either matched or un-matched)
collectively comprise the total travel time spent in the network. The unmatched clients are
serviced by other methods of delivery, depending on the delivery scenario that is providing
delivery service in the system.
The shopping tour of a matched carrier starts from his initial location, from where he moves to
his best store, and then he travels from his best store to the location of the client who is matched
with him to deliver the groceries. Once the groceries are delivered to the client, the carrier travels
to his final location (Figure 8).
The shopping tour for an unmatched carrier starts from his initial location, followed by a visit to
his best store and ended by the movement from his best store to his final location.
The pattern of the movements of the carriers and clients in the network in this method of delivery
is as follows:
27
The total travel time for each customer is the sum of the travel time of the stages of their
shopping tours.
Total travel time by a matched carrier =
(Equation 3)
Subscripts:
i = the carrier’s initial location zone in the shopping tour
i’= the carrier’s final location zone in the shopping tour
j= the client’s zone
k’’= the best store zone for the carrier
Variables:
n = number of zones in the network
A = number of carriers in the network
B = number of clients
= number of clients in zone j
C= number of carriers’ shopping tours in the network
Number of carriers’ shopping tours in the network with initial location of and
final location of
i
K’’
j
i’
Figure 8. Matched carrier shopping tour (Matching system)
28
= number of carriers’ shopping tours in the network with initial location of .
= number of carriers’ shopping tours in the network with final location of .
= travel time from a carrier’s initial location i to his best store k’’
= travel time from client j to his matched carrier’s final location i’
= travel time from a carrier’s initial location i to his best store k’’ to
his matched client j
= travel time from a carrier’s initial location i, to his best store
k’’, to client j, to the carrier’s final location i’
= Total travel time by matched carriers in the network
A mixed integer optimization approach is employed to match the proper carrier and client in the
network. The optimization formulation is coded in Matlab and the optimization is solved using
CPLEX 12.5 on a dual core 2.20 GHZ laptop computer. The formulation and the optimization
details are presented in the following section.
Optimization objective
Objective is to minimize the total travel time by matched carriers in the network ( ) by
matching the carriers and clients as efficiently as possible.
Total travel time by matched carriers who are doing delivery to their matched clients is
calculated as follows:
∑
∑
(Equation 4)
29
Optimization method
In the first step, the best store matrix (BSM) for carriers is created. As defined above, the best
store for a carrier is the store which brings the carrier the shortest travel time possible, when he
does regular grocery shopping. BSM is a matrix that represents the store which provides
the shortest shopping tour for every possible pair of and . In this matrix the element (a,b) is
the store which provides the shortest regular shopping travel time for a carrier with the initial
location of a and final location of b.
The 3D matrix of T is created in the next step. This is a matrix which includes the
expected travel time for any possible combination of i,j and i’ in the network. For example, the
element in this matrix is the travel time of the shopping tour in which a carrier starts
from his initial location , proceeds to his/her best store , next to the matched client location
and at last to his/her final location .
(Equation 5)
Once the T matrix is formed, the X matrix is calculated. X is a 3D matrix with the same
dimensions as T in which cell (i,i’,j) shows the optimized number of delivery tours by matched
carriers which are started in initial location of i, and completed in final location of i’ while a
client located in j is serviced on the way after the best store is visited by the matched carrier.
The objective of this optimization is to find the optimum X. The optimum X matrix has to be
found considering these logical constraints:
1) Sum of all of the elements of X equals the smaller number between the number of
clients in the network (B) and number of carriers’ shopping tours in the network (C).
30
∑∑∑
2) Number of delivery tours by matched carriers that provide service to any zone of the
clients (any j) is less than or equal to the number of orders in that specific zone.
∑∑
3) Number of delivery tours by matched carriers that are originated from each zone (any
i) is less than or equal to the number of carriers’ shopping tours with the initial
location in that specific zone ( ).
∑∑
4) Number of delivery tours by matched carriers that are completed in each zone is less
than or equal to the number of carriers’ shopping tours completed in that specific
zone ( .
∑∑
5) Number of delivery tours by matched carriers that are associated with any
combination of and is less than or equal to the number of carriers’ shopping tours
associated with and .
∑
31
By taking these constraints into consideration a mixed integer optimization is conducted to
calculate the optimized matrix.
Once the matrix is calculated, a third 3D matrix named is formed. is the 3D matrix with the
same dimensions as and . This matrix is the multiplication of the two corresponding elements
of and . (Element-by-element multiplication rather than regular matrix multiplication).
Thus:
(Equation 6)
Summation of the elements of is the minimum possible travel time of all delivery tours by
matched carriers in the network.
3.3.3) Truck delivery system
It is assumed in the present scenarios that the truck delivery fleet is delivering groceries based on
a specific type of vehicle routing problem (VRP). Our VRP is multi-depot split-delivery vehicle
routing problem (MDSDVRP) in which vehicles are dispatched from several depots scattered in
the network. In the proposed scenarios with truck delivery fleet, each zone in the network has
different number of clients. It is assumed that more than one delivery truck can visit each zone to
service the clients located in that specific zone.
32
The heuristic that is being used to solve the MDSDVRP is a derivation of the heuristic
introduced by Gulczynski, Golden and Wasil (2011) who were the first to solve a multi depot
split-delivery VRP.
Vehicle routing problem solution:
Step 1: Assigning nodes to depots
In this step each node in the network is assigned to a depot. For each node , is the travel cost
between node and the closest depot to in terms of travel time, and is the travel cost
between and the second closest depot to in terms of travel time. If
⁄ is less than a tolerance
then node is assigned to its closest depot in terms of travel time. If
⁄ , then is left
unassigned temporarily. Thus, a node that is much closer to one depot than other depots will be
immediately assigned to its closest depot. A node that is almost equidistant from multiple depots
will be assigned using the cheapest insertion. For each unassigned node and each depot , the
cost of inserting between each pair of nodes that is already assigned to is calculated. Node
is assigned to the same depot as nodes and where is the smallest number
among other possible pairs of nodes that are already assigned to the same depot.
Now, all nodes are assigned to a depot, however the sequentiality of nodes in tours is not
considered and is not yet optimized.
Step 2: Saving algorithm
The Clark-Wright algorithm is used to find out which nodes can be linked to each other and be
serviced with the same vehicle. Capacity constraints are taken into consideration as well. In this
33
saving algorithm, at first it is assumed that each truck is servicing only one zone; however it may
not be filled to capacity (Figure 9). Then the nodes are considered to be serviced by the same
truck when their pairing can save travel time for the truck and the truck’s capacity constraint is
not violated (Figure 10). However, it may be possible that a truck is able to service a portion of
the clients in a zone before reaching capacity. In such cases split delivery occurs and the truck
will service the zone to the greatest extent possible, and the zone is paired with its next best
possible saving pair and is serviced with another vehicle. The travel time saving after the
connection for the two nodes of and which are both assigned to the depot is calculated as
follows:
(Equation 7)
w
i j
i j
w
Figure 9. Truck delivery operation before two zones are connected
Figure 10. Truck delivery operation after two zones are connected
34
(Equation 8)
(Equation 9)
The savings for all possible pairs of nodes with the same depot are calculated and sorted from
largest to smallest and then nodes are paired considering the savings and the trucks’ capacity
constraints. At the end of this step, nodes are linked to each other to be serviced sequentially in a
tour with maximum savings in total cost (total travel time).
35
CHAPTER 4
STUDY NETWORK AND SENSITIVITY ANALYSIS
4.1) Study network (Sioux Falls network)
The study uses the Sioux Falls network which is composed of 24 nodes and 76 transportation
links. The properties of this hypothetical network are provided in two matrices; the Before-after
matrix which represents the frequency of tours (either shopping tour or otherwise) initiated in a
node and ending in another node. The Cost matrix is the other matrix which represents the travel
time between nodes in the network. Although the internal travel time for each node is zero in the
cost matrix, a constant travel time is considered for all of internal trips in order to simulate the
delivery trucks’ movements inside a node more precisely. These matrices are provided in the
appendix A.
Figure 11. Sioux Falls network
36
4.2) Carrier’s location
Locations of carriers in the network are randomized in order to reach a result independent of the
carrier’s location. As discussed above, the before-after matrix of carriers’ shopping tours is
derived from the before-after matrix of the Sioux Falls network. A probability can be calculated
for each cell in the Sioux Falls before-after matrix.
∑ ∑
(Equation 10)
With as the before-after matrix and its size is .
Considering that ∑ ∑
, a random number between 0 and 1 is generated by
Matlab. This random number defines the location of a carrier in the network. While doing this
randomization, it is noted that the number of carriers assigned to a zone in the Sioux Falls
network does not exceed its associated element in the Sioux Falls before-after matrix and the
total number of carriers in a carrier’s before-after matrix is confined to the total number of
carriers in that specific client/carrier ratio (Table 1).
4.3) Client’s location
Locations of clients are randomized in order to reach a result which is independent of the client’s
location. Considering that there are 24 nodes in the Sioux Falls network and also there are fixed
number of clients in the network for each client/carrier ratio (Table 1), a random integer
between 1 and 24 is generated which defines the node to which a client belongs. This generation
continues until the desired number of clients are randomly scattered.
37
4.4) Sensitivity analysis
In order to capture the differences between the four scenarios described in Chapter 3, it is
necessary to conduct a sensitivity analysis in order to gain a comprehensive insight into the
scenarios’ functions and behavior. Each scenario in every set-up has been run 30 times and its
results recorded. The average of the 30 runs is reported as the result for every scenario.
4.4.1) Number of stores in the network
Accessibility of the grocery stores plays an important role in the travel time of shopping tours. In
order to capture the effect of store availability in the network over different scenarios, the
modeling for scenarios is done for four different cases where there are 4, 8, 12 and 16 stores in
the network. Therefore, the performance of the four scenarios in these four different cases and
the effect of number of stores in the network are evaluated.
4.4.2) Client/carrier ratio
A constant number of 1500 customers are considered to be scattered in the network. These 1500
customers are either carriers or clients. In order to capture the effect of different client/carrier
ratios, the 1500 customers are divided into either clients or carriers in six different ratios. The
client/carrier ratios are set out in Table 1:
38
Client/Carrier
Ratio 0.25 0.5 1 1.5 2 4
No. of Clients 300 500 750 900 1000 1200
No. of Carriers 1200 1000 750 600 500 300
No. of customers 1500 1500 1500 1500 1500 1500
Table 1. Client/carrier ratios
4.4.3) Truck capacity constraints
The capacity constraint plays a crucial role in the number of truck delivery tours. The capacity
that is considered as the base case is 50 units of delivery per truck. In order to capture the effect
of this constraint and the way that the scenarios react to changes, three other cases with 10, 25
and 100 units of delivery are also examined.
39
CHAPTER 5
RESULTS
5.1) Introduction
The four shopping-delivery scenarios are simulated as presented in the methodology chapter.
Next the sensitivity analyses are taken into consideration and the performance of each scenario is
investigated and examined. This chapter reports the scenarios performance in two ways in
general; each scenario’s performance is investigated under different conditions, e.g. different
client/carrier ratio, or scenarios’ performances are compared to one another.
5.2) Sensitivity analysis: client/carrier ratio
In order to assess the impact of the changes of the client/carrier ratio in each scenario’s
performance, it is assumed that there are only four stores in the network. The performance of
each of the scenarios is investigated under this assumption.
5.2.1) Scenario 1: Regular shopping for all clients and carriers (R)
Figure 12 shows that carrier tours are longer than client tours, which explains why travel time
decreases with a greater proportion of clients. In addition, Figure 12 shows that for a
client/carrier ratio of 1.0 where there are equal numbers of clients and carriers in the network,
carriers’ regular shopping travel time is higher than the clients’ regular shopping travel time.
This happens because of the nature of home-based and non-home-based shopping trips. Carriers
are assumed to make non-home-based regular shopping trips and, on the other hand, clients are
assumed to make home-based shopping trips. Non-home-based shopping trips are generally
40
longer than home-based shopping trips, thus carriers’ regular shopping trips are longer than
clients’ regular shopping trips when client/carrier ratio is 1.0.
Figure 12. Travel times in scenario 1
Figure 13 demonstrates that, as expected, regular shopping travel time per carrier and regular
shopping travel time per client are almost constant and the changes in the client/carrier ratio do
not affect them. Regular shopping travel time per carrier is larger than the regular shopping
travel time per client because, as explained in Figure 12, carriers generally make non-home
based shopping trips as opposed to clients who make home-based shopping trips, and non-home-
41
based shopping trips are longer than home-based shopping trips. As the client/carrier ratio
increases, the network relies more on the clients’ regular shopping rather than the carriers’
regular shopping and this causes the decrease in the total travel time of the network.
Figure 13. Travel times per client/carrier/customer in scenario 1
5.2.2) Scenario 2 : Truck delivery fleet, regular shopping for all carriers (TR)
Figure 14 shows that, for scenario 2, delivery trucks’ travel time increases as the client/carrier
ratio increases because of the availability of more clients in the network and the greater demand
42
for the truck delivery service to serve the clients. The changes in delivery trucks’ travel time can
be seen with more precision in the next figure (Figure 15). Moreover, the carriers’ regular
shopping travel time decreases as the client/carrier ratio increases because of the decreasing
number of carriers in the network. The total travel time in the network decreases as the
client/carrier ratio increases. The reason is that carriers’ regular shopping decreases more
sharply than the increase in the trucks’ travel time, and also trucks’ travel times are considerably
lower than the carriers’ regular shopping travel times.
Figure 14. Travel times in scenario 2
43
Figure 15. Delivery truck travel time in scenario 2
Figure 16 shows that as the client/carrier ratio increases and the number of clients in the
network grow, there would be a higher demand for the delivery truck service and consequently
the number of delivery trips would increase.
Figure 16. Number of delivery truck tours in scenario 2
44
5.2.3) Scenario 3: Matching system, regular shopping for un-matched (non-delivery)
carriers and clients (MR)
Figure 17 shows that un-matched carrier travel time decreases as the client/carrier ratio
increases and finally it becomes zero at a client/carrier ratio of 1.0 and higher. The reason for
this is that with a client/carrier ratio of 1.0 and higher, the number of clients exceeds the number
of carriers and all of the carriers are matched with a client. Unmatched clients’ travel times are
zero for client/carrier ratios of 0.25 to 1.0 because there is a matched carrier giving service to
them and clients do not have to shop for themselves. For client/carrier ratios greater than 1.0,
unmatched clients travel in the network and the sum of their travel time increases as the
client/carrier ratio increases because of the higher number of unmatched clients in the network.
Matched carriers’ travel time increases from the client/carrier ratio of 0.25 to 1.0, because as the
number of clients increases and there are enough carriers available, higher numbers of clients
and carriers are matched and there would be a higher number of matched carriers in the network.
The travel time for matched carriers reaches its maximum at a client/carrier ratio of 1.0 where
there are equal numbers of carriers and clients. Above a client/carrier ratio of 1.0, matched
carriers’ travel time decreases because the number of clients in the network dominates the
number of carriers and few are paired. In addition, the total travel time of all of the customers
(either clients or carriers) in the network decreases from the client/carrier ratio of 0.25 to 1.0.
This happens due to the fact that as the client/carrier ratio increases the network moves toward
equilibrium and consequently the matching system is utilized more and there are fewer regular
shopping tours. Beyond a client/carrier ratio of 1.0, total travel time in the network increases
due to the fact that the increase in the unmatched clients’ regular shopping travel time is sharper
than the decrease in matched carriers’ travel time. The total travel time for the client/carrier ratio
45
of 4.0 is higher than the total travel time for the client/carrier ratio of 1.0, however the number
of matched shopping (300) and the number of regular shopping (1200) is the same in both. This
could be explained by the fact that normally home-based shopping travel times (which clients are
more likely to do) are shorter than non-home based shopping travel times.
Figure 17. Travel times in scenario 3
Figure 18 shows that the travel time per carrier for the regular shopping trips of unmatched
carriers increases gradually for client/carrier ratios of 0.25 to 0.5 and then it drops to zero. In
46
addition, the travel time per client for regular shopping trip of unmatched clients experiences a
gradual decrease from the client/carrier ratio of 1.5 to 4.0. The travel time per carrier for
matched carriers increases from the client/carrier ratio of 0.25 to 1.0 because of fewer matches
and it stays even for the client/carrier ratio of 1.0 and greater. Moreover, total travel time per
customer in the network has its minimum and the most efficient condition occurs when clients
and carriers are balanced with the highest possible number of matches in the network.
Figure 18. Travel time per client/carrier/customer in scenario 3
47
5.2.4) Scenario 4: Matching system, truck delivery, regular shopping for un-matched
carriers (MTR)
According to Figure 19, the trend in the travel time for regular shopping of un-matched carriers
and the travel time of the matched carriers in scenario 4 are the same as in scenario 3. Figure 19
shows that as the client/carrier ratio increases and consequently more clients are distributed in
the network, trucks offer service to more clients. Figure 20 illustrates this with more precision.
Moreover, the total travel time in scenario 4 decreases as the client/carrier ratio increases from
1.5 to 4.0. This can be explained by the fact that as the client/carrier ratio increases, fewer
customers are matched and delivery trucks are relied upon. The travel time of the trucks is
considerably lower than the matched carriers’ travel times.
Figure 19. Travel times in scenario 4
48
Figure 20. Delivery truck travel times in scenario 4
Figure 21, illustrates that as the client/carrier ratio increases from 1.5 to 4.0 and more clients
place orders, delivery trucks get involved more frequently in the network and considering their
limited capacity, more trucks (tours) are needed to serve clients. The changes in travel times per
carrier for the regular shopping of un-matched carriers and the travel time per carrier of matched
carriers in scenario 4 is the same as their changes in scenario 3.
Figure 21. Number of truck delivery tours in scenario 4
49
This section has shown the changes in travel times of the four scenarios with four stores in the
network. The trends in travel times and the justifications are similar for the networks with 8, 12
and 16 stores, however, the absolute numbers change as the number of stores changes. The
related figures for cases with 8, 12 and 16 stores are available in appendix B.
5.3) Comparison of scenario performance
In this section, the four scenarios are compared with each other in terms of travel time. In these
comparisons we assume that there are four stores in the network.
The performance of scenarios 3 and 4 are identical for a client/carrier ratio ranging from 0.25 to
1.0. For the client/carrier ratio above 1.0, clients start regular shopping in scenario 3 and trucks
start delivery service in scenario 4. For client/carrier ratios higher than 1.0, the total travel time
in scenario 3 increases because of the increasing number of unmatched clients. However, in
scenario 4 the total travel time keeps decreasing because of the sharp decrease in matched
carriers’ travel time. The performance of scenarios 3 and 2 are close for client/carrier ratios
ranging from 0.25 to 1.0. Scenario 2 has a better performance than scenario 3 for client/carrier
ratios higher than 1.0, because fewer regular shopping tours are made. Scenario 1 has the longest
travel time for all client/carrier ratios, because it relies completely on regular shopping which
tends to have larger travel time in comparison with either the matching system or the truck
delivery service. Scenarios 2 and 4 have almost the same total travel time in the network for all
client/carrier ratios (scenario 4 performs slightly better than scenario 2). This proves that the
matching system is economical because although it performs almost the same as the truck
delivery system, it is less reliant on the truck delivery system and the high costs of operating a
50
truck fleet can be avoided. Moreover, the figure shows that scenario 4, which is the mix of the
new matched system and the truck delivery system, has the potential to perform better than all
other scenarios and its minimum occurs at a client/carrier ratio of 4.
51
Figure 22. Travel times for all scenarios
52
In Figure 23 the changes in truck delivery fleet travel time for scenario 2 and scenario 4 are
compared. Scenario 2 relies more on the truck delivery system. In scenario 2 the truck delivery
system is engaged in all ratios, however in scenario 4 it is launched for client/carrier ratios of
greater than 1.0 where there are not enough carriers in the matching system. Also, the travel time
for a client/carrier ratio ranging from 1 to 4 is always higher in scenario 2, which seems logical
because in scenario 4 the delivery fleet is serving the unmatched clients, while in scenario 2
trucks serve all clients.
Figure 23. Delivery truck travel time in scenarios 2 and 4
53
Now that this study is performed for the case with four stores, the other cases with 8, 12 and 16
stores are also investigated and their figures show that the comparisons between different
scenarios described above are applicable for all cases. The figures related to these comparisons
are available in appendix C.
5.4) Analysis of the impact of changes in the number of stores
5.4.1) Scenario 1: Regular shopping for all clients and carriers (R)
Figure 24 shows that as the number of stores in the network increases, travel times for carriers
and clients decrease. This decrease is sharper for clients than it is for carriers. Clients’ regular
shopping tours have two legs, the first leg is towards the store and the second leg is the return to
the initial location (presumably their home). It can be interpreted that the clients’ regular
shopping travel times are dependent on these two distances and these two distances are
dependent on the nearest store location. However, within carriers’ regular shopping trips there
are two other legs that are not as heavily dependent on the store’s availability. The first leg is
store-bound and the second leg is their destination (presumably their home). What makes the
store’s accessibility less of an important element in carriers’ regular shopping travel times is the
fact that store’s accessibility is only a factor that defines how far the carrier has to deviate from
his/her ideal route when going from his/her initial location (presumably his/her work location) to
his/her final destination (presumably his/her home) in order to do shopping. This deviation can
be an important factor in carriers’ regular shopping travel times, however it is not the only factor
in play because carriers are obliged to travel the long distances from their initial location to their
final destination anyway and store accessibility is only a portion of this.
54
Figure 24. Travel times in scenario 1
Figure 25 shows that as the number of stores in the network increases, travel time per carrier,
travel time per client and total travel time per customer decreases. This is due to higher
accessibility to the store for clients and carriers.
55
Figure 25. Travel time per client/carrier/customer in scenario 2
5.4.2) Scenario 2: Truck delivery fleet, regular shopping for all carriers (TR)
Figure 26 shows that a higher number of stores in the network lead to less shopping travel time
for either of the shopping methods in scenario 2. Figure 27, brings the delivery trucks travel time
of scenario 2 into focus. We observe that as the number of stores in the network grows delivery
truck travel times decrease because of the greater accessibility in the network. Finally, Figure 28
illustrates that as the number of stores in the network increases, the number of delivery truck
tours in scenario 2 increases. This increase is more severe in lower client/carrier ratios and as the
ratio grows, this difference is more graded.
56
Figure26. Travel times in scenario 2
Figure 27. Delivery truck travel times in scenario 2
57
Figure 28, illustrates that as the number of stores in the network increases, number of delivery
truck tours in scenario 2 increases. This increase is more severe in lower client/carrier ratios and
as the ratio grows, this difference is more graded.
Figure 28. Number of truck delivery tours in scenario 2
5.4.3) Scenario 3: Matching system, regular shopping for un-matched (non-delivery)
carriers and clients (MR)
The travel times of the different methods of shopping and delivery (either regular shopping or
matching system) for each client/carrier ratio decrease as the number of stores in the network
increases because there would be more stores available and the travel time from each point to its
best store would be smaller. It is noteworthy to mention that the rate of the change in travel time
savings is decreasing as the number of stores increases; this means that the difference between
58
the case with four stores and eight stores is higher than when comparing the cases with eight
stores and 12 stores and consequently the comparison between 12 stores and 16 stores. This
means that it becomes less economical to increase the number of stores to reduce travel times. As
the number of stores increases, from client/carrier ratio of 0.25 to 1.0, the total travel time in the
network decreases more gradually. In the case with 4 stores, we observe an increase in travel
times between client/carrier ratio of 1.5 and client/carrier ratio of 4; this increase gets less acute
as the number of stores increases until the case with 12 stores. For 12 stores, the total travel time
decreases for client/carrier ratios above 1. This decrease is even sharper in case with 16 stores.
59
Figure 29. Travel times in scenario 3
60
As illustrated in Figure 30 the trend of the travel time per client/carrier/customer for different
numbers of stores is similar to the changes in Figure 29, meaning that as the number of stores
increases, a shorter travel time per client/carrier/customer is needed to complete a delivery and
shopping tour. In addition, the results confirm in Figure 29, that it is not necessarily economical
to invest in a larger number of stores in order to increase accessibility. The differences between
the cases with 12 stores and 16 stores are small.
61
Figure 30. Scenario 3 travel times per client/carrier/customer
62
5.4.4) Scenario 4: Matching system, truck delivery, regular shopping for un-matched
carriers (MTR)
As shown in Figure 31, the travel time for each shopping method (truck delivery, regular or
matching) decreases as number of stores increases in the network. Also, it is clear that for
client/carrier ratios above 3 as the number of stores increases, the “total travel times” line is
getting closer to the “matched carriers travel time” line. The reason can be found by looking at
delivery trucks. As the number of stores grow, trucks travel for shorter travel times, thus they
play a smaller role in total travel time. Figure 32 shows the changes in trucks travel time on a
better scale.
63
Figure 31. Travel times in scenario 4
64
Figure 32. Delivery trucks travel time in scenario 4
As the number of stores grows, the range of the number of tours is shrinking. This can be
interpreted by considering two facts; the first is that in our solution for the vehicle routing
problem, the only thing that is optimized is the cumulative travel times of the trucks in the
network and the optimization is not related to any other kinds of savings (e.g. savings in number
of used trucks). The second fact is that in our vehicle routing problem optimization there are no
constraints limiting the number of trucks used. Thus, we are allowed to use as many trucks as
required to reach the lowest overall trucks’ travel times in the network. In Figure 33, the
65
maximum number of tours for any number of stores occurs for the client/carrier ratio of 4, and
this is almost the same for cases with different number of stores. However, the number of tours
for client/carrier ratio of 2.0 and client/carrier ratio of 1.5 are approaching the number of tours
for client/carrier ratio of 4.0 as the number of stores grows. This is because with a higher
number of available stores and considering the fact that there are no limits on the number of
trucks and also because in our cost matrix (travel times between zones) the cost of inter-zonal
trips is much higher than the cost of intra-zonal trips, more trucks are dispatched from stores to
reach the clients in surrounding zones so that the inter-zonal movements are avoided.
Figure 33. Number of delivery truck tours in scenario 4
66
5.5) Analysis of the impact of the changes in trucks load capacity on
scenarios with truck delivery fleet
Load capacity of the delivery trucks is one of the constraints of the VRP in scenario 2 and
scenario 4. It is important to note that all the results presented in previous sections are based on
the assumption of having 50 units of delivery capacity in the trucks. In order to capture the
effects of different load capacities, three other cases with 10, 25 and 100 units are tested in
addition to the base case with 50 units of load capacity.
Figures 34 and 35 prove that as the truck capacity increases, the trucks’ travel times decrease.
This is because as the trucks carry more orders they would return to the store (depot) to reload
less often especially that intra-zonal travel times are lower than inter-zonal travel times. That is
why as the truck enters a zone to deliver the orders to clients of that zone, it is traveling short
distances with low travel times and after delivering to all the clients it drives the relatively longer
distance to the store to be reloaded and dispatched again. In addition, it is important to note that
the slope of the line decreases as the capacity increases. This is because with high capacity in the
truck, it can reach more clients with fewer legs of empty backhauling to the store or dispatching
from the store, thus the travel times of different client/carrier ratios stay close to each other.
67
Figure 34. Delivery truck travel time in scenario 2
Figure 35. Delivery truck travel time in scenario 4
0
200
400
600
800
1000
1200
1400
1600
1800
trav
el t
ime
client/carrier ratio
capacity 10 capacity 25 capacity 50 capacity 100
0.25 0.5 1.0 1.5 2.0 4.0
68
Figures 36 and 37 show that the changes in the number of delivery tours behaves the same as the
trucks’ travel times change. The explanations that are provided for Figures 34 and 35 are valid
here as well. Furthermore, the comparison of the four capacities and the behavior of each of the
capacities across the six client/carrier ratios is similar to what was observed in figures 34 and
35.
In order to study the effect of stores’ locations on the results, we assume that there are only four
stores in the network and stores are distributed in three different patterns. The reason to select the
case with four stores is that in this case travel times are higher, thus greater differences in results
are expected. We observe that the location of the stores does not play an important role in the
overall performance of the scenarios and their results. This is due to the fact that carriers and
clients locations are already randomized. Thus, there is no need to implement a third
randomization for the stores locations in the network.
Figure 36. Number of delivery tours in scenario 2
69
Figure 37. Number of delivery tours in scenario 4
The figures and tables related to this part are available in appendix D.
70
CHAPTER 6.
CONCLUSION
6.1) Introduction
Grocery retail is the largest sector of retailing business. This has unique aspects and several
players are seeking their own benefit including, business owners, grocery customers and society
in general. Delivery operations are a major part of this business which has a great impact on the
quality of the services and the customers’ satisfaction. Internet and information technology has
brought novel ideas especially in streamlining delivery operations and setting up more efficient
commodity circulation between customers. This thesis focuses on the delivery operations of
grocery businesses. In this thesis, a new delivery concept for groceries developed and simulated
in order to evaluate its performance. This delivery concept has been analyzed through a number
of scenarios. These scenarios include combinations of the current shopping-delivery modes;
truck delivery and regular shopping. This concept seems to be a potential step forward for e-
grocery businesses, because it is economically beneficial to all of the agents involved with this
delivery method. Carriers are rewarded with points for making a delivery to a client who lives a
reasonable distance from the carrier’s final location. Clients benefit because they would have
their groceries delivered to their address with a lower or no delivery fee. The grocery business
would benefit as well. A delivery system requires large distribution facilities and infrastructure;
by employing this method of delivery for customers, the store would be able to reduce its costs
of delivery.
71
6.2) How the research objectives are satisfied
The thesis set out to answer the two major questions that are presented in the introduction
chapter. The results provide important insight into how the new delivery concept works and the
benefits that it brings when combined with other delivery modes.
In general, the results prove that the ideal conditions for the matching system happens when
there are equal numbers of carriers and customers in the network (balanced network). In the
balanced network, the matching system brings its largest benefit to the total travel time in the
network. Scenario 4, which employs both truck delivery and the matching system, performs
better than the other three scenarios in terms of total travel time. Thus it can be concluded that,
on the basis of travel time estimates, the matching system seems to be a promising method of
shopping-delivery which can be combined with other methods of delivery to produce efficient
shopping-delivery scenarios for grocery shopping.
The results also prove the fact that as the number of stores in the network increase, travel times
in the network would decrease, however this change would be less intensive as more stores are
introduced.
6.3) Research significance
This research introduces and evaluates a new method of grocery delivery. The new method (the
matching system) is simulated and combined with other methods of delivery to form four
scenarios of shopping-delivery. The developed models of the four scenarios are capable of
72
quantifying the travel time of the delivery methods. Sensitivity analysis is conducted in order to
be able to compare the scenarios in a broader extent.
6.4) Limitations and recommendations for future research
This research is based on the Sioux Falls network which is a hypothetical network. Although we
consider the results to be robust, it would be a reasonable next step to model the shopping
scenarios based on a real traffic network and shopping data.
The psychological aspect of the matching system is very important. It is necessary to have an
insight into how the players of the matching system – client, carrier and the grocery business –
would react to this concept. In addition, the role of the government and communities in the
development of this delivery-shopping concept remains to be addressed.
In this thesis the truck delivery system is assumed to obey the multi-depot split-delivery vehicle
routing problem where every traffic zone is serviced by a truck unless the truck exceeds its
capacity. Each traffic zone can be serviced by several trucks depending on the entire set of orders
and their quantity in other traffic zones. More complicated algorithms can be employed to
maximize the savings from splitting deliveries to certain zones by reallocating some (or all) of
their demands to new routes (Gulczynski 2011). Although it adds considerable complexity to the
planning for the truck delivery system, it makes truck delivery systems more efficient.
Delivery time-windows are a logical add-on to the matching system where clients could order
their groceries to be delivered within a desired time-window. This would add more complexity to
73
simulate the matching system; however it would make the matching system more realistic in
satisfying customer demands.
The cost matrix of the Sioux-Falls network is a symmetric matrix which only includes travel
time between zones. A detailed asymmetric cost matrix that considers other factors such as the
costs associated with fuel, parking fees and customers’ value of time is recommended for future
research.
74
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APPENDICES
Appendix A
TT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1 2.00 17.40 3.90 12.94 17.16 21.96 30.21 25.47 20.67 24.27 18.15 13.20 27.30 24.15 30.27 29.70 30.76 34.28 35.30 42.22 38.71 35.68 29.55 32.11
2 17.40 2.00 21.30 13.86 9.65 4.84 13.38 8.63 13.16 16.76 22.19 27.14 41.24 28.19 22.77 12.87 15.87 17.45 20.41 27.34 32.37 28.17 33.59 37.79
3 3.90 21.30 2.00 9.04 13.26 18.06 26.31 21.57 16.77 20.37 14.25 9.30 23.40 20.25 26.37 25.80 26.86 30.38 31.40 38.32 34.81 31.78 25.65 28.21
4 12.94 13.86 9.04 2.00 4.21 9.02 17.27 12.52 7.72 11.32 8.34 13.28 27.38 14.34 17.33 16.76 17.81 21.33 22.35 29.28 26.94 22.74 19.74 23.94
5 17.16 9.65 13.26 4.21 2.00 4.81 13.05 8.31 3.51 7.11 12.55 17.49 31.59 18.55 13.12 12.54 13.60 17.12 18.14 25.07 22.73 18.53 23.95 28.15
6 21.96 4.84 18.06 9.02 4.81 2.00 8.54 3.79 8.32 11.92 17.36 22.30 36.40 23.36 17.93 8.04 11.04 12.62 15.58 22.50 27.54 23.34 28.76 32.96
7 30.21 13.38 26.31 17.27 13.05 8.54 2.00 4.74 9.54 13.14 20.34 25.29 39.03 26.05 19.15 8.99 11.99 8.10 16.53 20.40 27.62 24.56 31.16 34.22
8 25.47 8.63 21.57 12.52 8.31 3.79 4.74 2.00 4.80 8.40 15.60 20.55 34.65 21.31 14.41 4.24 7.24 8.82 11.78 18.71 24.02 19.82 26.42 30.62
9 20.67 13.16 16.77 7.72 3.51 8.32 9.54 4.80 2.00 3.60 10.80 15.75 29.85 16.51 9.61 9.03 10.09 13.61 14.63 21.56 19.22 15.02 21.62 25.82
10 24.27 16.76 20.37 11.32 7.11 11.92 13.14 8.40 3.60 2.00 7.20 12.15 26.25 12.91 6.01 5.43 6.49 10.01 11.03 17.96 15.62 11.42 18.02 22.22
11 18.15 22.19 14.25 8.34 12.55 17.36 20.34 15.60 10.80 7.20 2.00 4.95 19.05 6.00 12.90 12.63 13.69 17.21 18.23 25.16 22.20 18.00 11.40 15.60
12 13.20 27.14 9.30 13.28 17.49 22.30 25.29 20.55 15.75 12.15 4.95 2.00 14.10 10.95 17.85 17.58 18.64 22.16 23.18 30.10 25.51 22.95 16.35 18.91
13 27.30 41.24 23.40 27.38 31.59 36.40 39.03 34.65 29.85 26.25 19.05 14.10 2.00 14.41 21.02 31.68 30.10 30.93 25.56 18.63 11.41 15.61 9.01 4.81
14 24.15 28.19 20.25 14.34 18.55 23.36 26.05 21.31 16.51 12.91 6.00 10.95 14.41 2.00 6.90 18.34 18.08 22.92 13.54 20.05 16.20 12.00 5.40 9.60
15 30.27 22.77 26.37 17.33 13.12 17.93 19.15 14.41 9.61 6.01 12.90 17.85 21.02 6.90 2.00 11.44 11.18 16.02 6.64 13.46 9.61 5.41 12.01 16.21
16 29.70 12.87 25.80 16.76 12.54 8.04 8.99 4.24 9.03 5.43 12.63 17.58 31.68 18.34 11.44 2.00 3.00 4.58 7.54 14.47 21.05 16.85 23.45 27.65
17 30.76 15.87 26.86 17.81 13.60 11.04 11.99 7.24 10.09 6.49 13.69 18.64 30.10 18.08 11.18 3.00 2.00 7.58 4.54 11.47 18.69 16.59 23.19 25.29
18 34.28 17.45 30.38 21.33 17.12 12.62 8.10 8.82 13.61 10.01 17.21 22.16 30.93 22.92 16.02 4.58 7.58 2.00 12.12 12.30 19.52 20.35 26.95 26.12
19 35.30 20.41 31.40 22.35 18.14 15.58 16.53 11.78 14.63 11.03 18.23 23.18 25.56 13.54 6.64 7.54 4.54 12.12 2.00 6.93 14.15 12.05 18.65 20.75
20 42.22 27.34 38.32 29.28 25.07 22.50 20.40 18.71 21.56 17.96 25.16 30.10 18.63 20.05 13.46 14.47 11.47 12.30 6.93 2.00 7.22 8.05 14.65 13.82
21 38.71 32.37 34.81 26.94 22.73 27.54 27.62 24.02 19.22 15.62 22.20 25.51 11.41 16.20 9.61 21.05 18.69 19.52 14.15 7.22 2.00 4.20 10.80 6.60
22 35.68 28.17 31.78 22.74 18.53 23.34 24.56 19.82 15.02 11.42 18.00 22.95 15.61 12.00 5.41 16.85 16.59 20.35 12.05 8.05 4.20 2.00 6.60 10.80
23 29.55 33.59 25.65 19.74 23.95 28.76 31.16 26.42 21.62 18.02 11.40 16.35 9.01 5.40 12.01 23.45 23.19 26.95 18.65 14.65 10.80 6.60 2.00 4.20
24 32.11 37.79 28.21 23.94 28.15 32.96 34.22 30.62 25.82 22.22 15.60 18.91 4.81 9.60 16.21 27.65 25.29 26.12 20.75 13.82 6.60 10.80 4.20 0.00
Sioux Falls network cost (travel time) matrix
81
Before - After 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
1 0 1 1 5 2 3 5 8 5 13 5 2 5 3 5 5 4 1 3 3 1 4 3 1
2 1 0 1 2 1 4 2 4 2 6 2 1 3 1 1 4 2 0 1 1 0 1 0 0
3 1 1 0 2 1 3 1 2 1 3 3 2 1 1 1 2 1 0 0 0 0 1 1 0
4 5 2 2 0 5 4 4 7 7 12 14 6 6 5 5 8 5 1 2 3 2 4 5 2
5 2 1 1 5 0 2 2 5 8 10 5 2 2 1 2 5 2 0 1 1 1 2 1 0
6 3 4 3 4 2 0 4 8 4 8 4 2 2 1 2 9 5 1 2 3 1 2 1 1
7 5 2 1 4 2 4 0 10 6 19 5 7 4 2 5 14 10 2 4 5 2 5 2 1
8 8 4 2 7 5 8 10 0 8 16 8 6 6 4 6 22 14 3 7 9 4 5 3 2
9 5 2 1 7 8 4 6 8 0 28 14 6 6 6 9 14 9 2 4 6 3 7 5 2
10 13 6 3 12 10 8 19 16 28 0 40 20 19 21 40 44 39 7 18 25 12 26 18 8
11 5 2 3 15 5 4 5 8 14 39 0 14 10 16 14 14 10 1 4 6 4 11 13 6
12 2 1 2 6 2 2 7 6 6 20 14 0 13 7 7 7 6 2 3 4 3 7 7 5
13 5 3 1 6 2 2 4 6 6 19 10 13 0 6 7 6 5 1 3 6 6 13 8 8
14 3 1 1 5 1 1 2 4 6 21 16 7 6 0 13 7 7 1 3 5 4 12 11 4
15 5 1 1 5 2 2 5 6 10 40 14 7 7 13 0 12 15 2 8 11 8 26 10 4
16 5 4 2 8 5 9 14 22 14 44 14 7 6 7 12 0 28 5 13 16 6 12 5 3
17 4 2 1 5 2 5 10 14 9 39 10 6 5 7 15 28 0 6 17 17 6 17 6 3
18 1 0 0 1 0 1 2 3 2 7 2 2 1 1 2 5 6 0 3 4 1 3 1 0
19 3 1 0 2 1 2 4 7 4 18 4 3 3 3 8 13 17 3 0 12 4 12 3 1
20 3 1 0 3 1 3 5 9 6 25 6 5 6 5 11 16 17 4 12 0 12 24 7 4
21 1 0 0 2 1 1 2 4 3 12 4 3 6 4 8 6 6 1 4 12 0 18 7 5
22 4 1 1 4 2 2 5 5 7 26 11 7 13 12 26 12 17 3 12 24 18 0 21 11
23 3 0 1 5 1 1 2 3 5 18 13 7 8 11 10 5 6 1 3 7 7 21 0 7
24 1 0 0 2 0 1 1 2 2 8 6 5 7 4 4 3 3 0 1 4 5 11 7 0
Sioux – Falls before after matrix
82
Appendix B
8 stores:
Travel times in scenario 1
Travel times per client/carrier/customer in scenario 1
83
Travel times in scenario 2
Delivery truck travel time in scenario 2
84
Number of VRP trips in scenario 2
Travel times in scenario 3
85
Travel time per client/carrier/customer in scenario 3
Travel times in scenario 4
86
Delivery truck travel times in scenario 4
Number of truck delivery tours in scenario 4
87
12 stores:
Travel times in scenario 1
Travel times per client/carrier/customer in scenario 1
88
Travel times in scenario 2
Delivery truck travel time in scenario 2
89
Number of VRP trips in scenario 2
Travel times in scenario 3
90
Travel time per client/carrier/customer in scenario 3
Travel times in scenario 4
91
Delivery truck travel times in scenario 4
Number of truck delivery tours in scenario 4
92
16 stores:
Travel times in scenario 1
Travel times per client/carrier/customer in scenario 1
93
Travel times in scenario 2
Delivery truck travel time in scenario 2
94
Number of VRP trips in scenario 2
Travel times in scenario 3
95
Travel time per client/carrier/customer in scenario 3
Travel times in scenario 4
96
Delivery truck travel times in scenario 4
Number of truck delivery tours in scenario 4
97
Appendix C
8 stores:
Travel times of all scenarios
98
Delivery truck travel time in scenarios 2 and 4
99
12 stores:
Travel times of all scenarios
100
Delivery truck travel time in scenarios 2 and 4
101
16 stores:
Travel times of all scenarios
102
Delivery truck travel time in scenarios 2 and 4
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