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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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slide1

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

Motivations & Goals

Modeling Transformation Relationships

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work

motivation
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.
example parts purchasing

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

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

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
  • 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
  • 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
  • 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

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work

modeling the t relationships
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
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.
Example of TNS
modeling a transformation
Modeling a Transformation

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

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

M0 + T x

agenda3
Agenda

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work

empirical evaluation
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
experimental setting
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
hardware setting
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)
experimental results costs ratios
Experimental Results: Costs’ Ratios

Cost without Transformations

Cost without Transformations

agenda4
Agenda

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work

agenda5
Agenda

Motivation & Goals

Modeling Transformation

The Winner Determination Problem

Empirical Evaluation

Demo

Conclusions and Future Work

conclusions pros
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
conclusions cons
Conclusions: cons
  • Bidding is more difficult.
  • The auctioneer has to reveal private information about his internal production process.
conclusions
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.
future work
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.
slide34

Electronic Negotiation

Negotiation of bundles of items

conclusions on experiments
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.
experimental setting1
Experimental Setting
  • 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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