Post on 30-Dec-2015
description
Multi-unit Combinatorial Reverse Auctions with
Transformability Relationships among Goods
Andrea GiovannucciJuan A. Rodríguez-Aguilar
Jesús Cerquides
TFG-MARA. Budapest 16-11-2005
Institut d’Investigació en Intel.ligència Artificial
Consejo Superior de Investigaciones Científcias
2
Motivations & Goals
Modeling Transformation Relationships
The Winner Determination Problem
Empirical Evaluation
Demo
Conclusions and Future Work
Agenda
3
Motivation
Combinatorial Auctions have recently deserved much attention in the literature.
The literature has considered the possibility to express relationships among assets on the bidder side (as complementarity and substitutability).
The impact of eventual relationships among different assets on the bid-taker side has not been addressed so far: a bid-taker may desire to express transformability relationships among the goods at auction.
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Example. Parts purchasingFRONT SUSPENSION, FRONT WHEEL BEARING ACQUISITION
PART NUMBER
DESCRIPTION UNITS
1 FRONT HUB 2
7 LOWER CONTROL ARM BUSHINGS
3
8 STRUT 4
9 COIL SPRING 2
14 STABILIZER BAR 1
GOAL: BUY PARTS TO
PRODUCE 200 SUSPENSIONS
TRANSFORMATION COST: 90$/UNIT
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Motivations: WDP and Transformability Relationships
SUSPENSION
FRONT HUB
LOWER CONTROL ARM BUSHINGS
STRUT
COIL SPRING
STABILIZER BAR
Transformation
Cost
90 $
200 Suspensions
2
3
4
2
RFQ
OFFERS
ALLOCATION
1
100 5000 $
100
400
600 $
PROVIDER 1 PROVIDER 2
100 * 90$ =
9000$
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Motivations
Thus the buyer/auctioneer faces a decision problem:• Shall he buy the required components to assemble them in house
into suspensions?• Or buy already-assembled motherboards?• Or maybe opt for a mixed-purchase solution?
This concern is reasonable since the cost of components plus the assembly costs may be eventually higher than the cost of already assembled suspensions.
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Goals
The Buyer requires a combinatorial auction mechanism that provides:
• A language to express required goods along relationships that hold among them.
• A winner determination solver that not only assesses what goods to buy and to whom, but also the transformations to apply to such goods in order to obtain the initially required ones.
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MUCRAtR
We extend the notion of RFQ (Request-For-Quotation) to allow for the introduction of transformation relationships
(t-relationships) We extend the formalization of the well known Multi Unit
Combinatorial Reverse Auction Winner Determination Problem to introduce transformability.
We provide a mapping of our formal model to integer programming that assesses the winning set of bids along with the transformations to apply.
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Motivation & Goals
Modeling Transformation
The Winner Determination Problem
Empirical Evaluation
Demo
Conclusions and Future Work
Agenda
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Modeling the t-relationships
We need a model that expresses different configurations of goods, and the possibility of switching among them at a certain cost.
PETRI NETS is the model that best fits the requirements
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Example of TNS Transformability Network Structure
(TNS)• Places represent the goods at auction.• Transitions represent t-relationships.• Arcs indicate how goods are related
through transformations.• Arc weights stand for the number of
goods either produced or consumed by a transformation.
• Each t-relationship is labeled with a transformation cost.
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Modeling a Transformation
The activation of transformations is modeled as firing of transitions
2 1
1
90$
400$
400$+90$=490$
2
1
0
-2
-1
1
0
0
1
* 1+ =
M0 + T x = M’Sufficient Condition:
ACYCLIC PETRI NET
Item 1 Item 2
Item 3
Item 1
Item 2
Item 3
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Motivation & Goals
Modeling Transformation
The Winner Determination Problem
Empirical Evaluation
Demo
Conclusions and Future Work
Agenda
14
The Multi-Dimensional Knapsack Problem
It is a well known result in optimization theory that the winner determination problem in a multi-item multi unit combinatorial auction can be modeled as a MDKP:
BIDSjiijjITEMSi
BIDSjjj
uby
py
,
min
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Extending the Multi-Dimensional Knapsack Problem
We extend this model considering that we can transform some of the items bought
BIDSji
tionsTransformakkkiijjITEMSi
tionsTransformakkk
BIDSjjj
uqtby
cqpy
,,
min
M0 + T x
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Motivation & Goals
Modeling Transformation
The Winner Determination Problem
Empirical Evaluation
Demo
Conclusions and Future Work
Agenda
18
Empirical Evaluation
In our preliminary experiments we compared the impact of introducing transformation relationships analyzing two main aspects:
• The added computational complexity.• The potential variation in the auctioneer cost.
With this aim we compared the new mechanism to a state-of-the-art combinatorial auction winner determination solver in terms of:
• CPU time• Auctioneer cost
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Experimental Setting
We employed a modified version of a state-of-the-art multi-unit combinatorial bids generator (Leyton-Brown).
In these early experiments the only variable was the number of bids, whereas we fixed:
• Price distribution - Normal with variance 0.1• Number of items - 20• Number of t-relationships - 8• Maximum cardinality of an offer – 15
The number of bids ranged from 50 to 270000
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Hardware Setting
Pentium IV, 3.1 GhZ. 1 Gb RAM. OS Windows XP Professional. MATLAB release 14.1 (To create the test set). ILOG OPL Studio and CPLEX 9.0. (Commercial
Optimization Library, www.ilog.com)
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Motivation & Goals
Modeling Transformation
The Winner Determination Problem
Empirical Evaluation
Demo
Conclusions and Future Work
Agenda
27
Motivation & Goals
Modeling Transformation
The Winner Determination Problem
Empirical Evaluation
Demo
Conclusions and Future Work
Agenda
28
Conclusions: pros
No significant burden in the computational complexity is added introducing transformations.
We experimented revenue savings ranging from 3% to 30% (Although we have to further study the variables that affect the phenomenon).
Competence among bidders is increased Providers of components vs. Providers of suspensions.
Efficiency is increased
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Conclusions: cons
Bidding is more difficult.
The auctioneer has to reveal private information about his internal production process.
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Conclusions
We presented a new type of combinatorial auction in which it is possible to express transformability relationships on the auctioneer side.
To the best of our knowledge it is the first system that introduces this type of information into a combinatorial auction.
We studied the associated winner determination problem providing an integer programming solution to it.
We empirically evaluated it comparing with a state-of-the-art solver:
• The scalability.• The difference in the auctioneer revenue.
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Future Work
Design and analysis of the auction mechanism. Decision support to bidders to elaborate winning bids. Theoretical analysis of the auctioneer’s cost of our
mechanism with respect to multi-unit combinatorial auctions.
Extending the model in order to support combinatorial offers over range of units.
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Conclusions on Experiments
Auctioneer revenues increased by 10 % to 30 % in medium-small scenarios (< 200 bids).
Solving times of around 0.3 sec. in middle-large scenarios (2500 bids).
Largest instance solved: 270000 bids.