Multi-unit Combinatorial Reverse Auctions with Transformability Relationships among Goods
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Multi-unit Combinatorial Reverse Auctions with Transformability Relationships among Goods Andrea Giovannucci Juan A. Rodríguez-Aguilar Jesús Cerquides. Institut d’Investigació en Intel.ligència Artificial Consejo Superior de Investigaciones Científcias. TFG-MARA. Budapest 16-11-2005. Agenda.

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Multi-unit Combinatorial Reverse Auctions with Transformability Relationships among Goods

Andrea Giovannucci

Juan A. Rodríguez-Aguilar

Jesús Cerquides

Institut d’Investigació en Intel.ligència Artificial

Consejo Superior de Investigaciones Científcias

TFG-MARA. Budapest 16-11-2005


Agenda
Agenda Transformability Relationships among Goods

Motivations & Goals

Modeling Transformation Relationships

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work


Motivation
Motivation Transformability Relationships among Goods

  • 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.


Example parts purchasing

PART NUMBER Transformability Relationships among Goods

DESCRIPTION

UNITS

1

FRONT HUB

2

7

LOWER CONTROL ARM BUSHINGS

3

8

STRUT

4

9

COIL SPRING

2

14

STABILIZER BAR

1

Example. Parts purchasing

FRONT SUSPENSION, FRONT WHEEL BEARING ACQUISITION

GOAL: BUY PARTS TO

PRODUCE 200 SUSPENSIONS

TRANSFORMATION COST: 90$/UNIT


Motivations wdp and transformability relationships
Motivations: WDP and Transformability Relationships Transformability Relationships among Goods

RFQ

200 Suspensions

2

3

OFFERS

Transformation

Cost

90 $

4

2

1

ALLOCATION

PROVIDER 2

PROVIDER 1

600 $

100

5000 $

100 * 90$ =

9000$

400

100


Motivations
Motivations Transformability Relationships among Goods

  • 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.


Goals
Goals Transformability Relationships among Goods

  • 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.


Mucratr
MUCRAtR Transformability Relationships among Goods

  • 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.


Agenda1
Agenda Transformability Relationships among Goods

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work


Modeling the t relationships
Modeling the t-relationships Transformability Relationships among Goods

  • 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


Example of tns

  • Transformability Network Structure (TNS) Transformability Relationships among Goods

    • 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.

Example of TNS


Modeling a transformation
Modeling a Transformation Transformability Relationships among Goods

400$+90$=490$

  • The activation of transformations is modeled as firing of transitions

Item 3

1

Item 1

Item 2

Item 3

-2

-1

1

2

1

0

0

0

1

90$

*1

=

+

2

1

400$

M0 + T x = M’

Item 1

Item 2

Sufficient Condition:

ACYCLIC PETRI NET


Agenda2
Agenda Transformability Relationships among Goods

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work


The multi dimensional knapsack problem
The Multi-Dimensional Knapsack Problem Transformability Relationships among Goods

  • 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:


Extending the multi dimensional knapsack problem
Extending the Multi-Dimensional Knapsack Problem Transformability Relationships among Goods

  • We extend this model considering that we can transform some of the items bought

M0 + T x


Acyclic petri nets
Acyclic Petri Nets Transformability Relationships among Goods

ACYCLIC


Agenda3
Agenda Transformability Relationships among Goods

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work


Empirical evaluation
Empirical Evaluation Transformability Relationships among Goods

  • 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


Experimental setting
Experimental Setting Transformability Relationships among Goods

  • 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


Hardware setting
Hardware Setting Transformability Relationships among Goods

  • 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)


Experimental results computational hardness
Experimental Results: Computational Hardness Transformability Relationships among Goods


Experimental results scalability
Experimental Results: Scalability Transformability Relationships among Goods


Experimental results auctioneer cost
Experimental Results: Auctioneer Cost Transformability Relationships among Goods


Experimental results costs ratios
Experimental Results: Costs’ Ratios Transformability Relationships among Goods

Cost without Transformations

Cost without Transformations


Agenda4
Agenda Transformability Relationships among Goods

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work


E cats demo
e-CATS Demo Transformability Relationships among Goods


Agenda5
Agenda Transformability Relationships among Goods

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work


Conclusions pros
Conclusions: pros Transformability Relationships among Goods

  • 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


Conclusions cons
Conclusions: cons Transformability Relationships among Goods

  • Bidding is more difficult.

  • The auctioneer has to reveal private information about his internal production process.


Conclusions
Conclusions Transformability Relationships among Goods

  • 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.


Future work
Future Work Transformability Relationships among Goods

  • 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.


Thank you ... Any question? Transformability Relationships among Goods


Backup/Extra Slides Transformability Relationships among Goods


Electronic Negotiation Transformability Relationships among Goods

Negotiation of bundles of items


Conclusions on experiments
Conclusions on Experiments Transformability Relationships among Goods

  • 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.


Experimental setting1
Experimental Setting Transformability Relationships among Goods

  • An important consideration is that when transformation relationships hold among goods, the price distribution must take them into account.

400$*2 + 300$ +90$ = 1190$

1

90$

2

1

400$/unit

300$/unit


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