Mixed Multi-Unit Combinatorial Auctions for Supply Chain - - PowerPoint PPT Presentation

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Mixed Multi-Unit Combinatorial Auctions for Supply Chain - - PowerPoint PPT Presentation

Aug 20, 2022 246 likes •819 views

Mixed Multi-Unit Combinatorial Auctions for Supply Chain Automation Andrea Giovannucci Meritxell Vinyals Jesus Cerquides Ulle Endriss Juan Antonio Rodriguez-Aguilar Pedro Meseguer Institut dInvestigaci en Intel.ligncia Artificial

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Andrea Giovannucci Meritxell Vinyals Jesus Cerquides Ulle Endriss Juan Antonio Rodriguez-Aguilar Pedro Meseguer

Mixed Multi-Unit Combinatorial Auctions for Supply Chain Automation

Institut d’Investigació en Intel.ligència Artificial (IIIA-CSIC)

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Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work

Outline

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The organisational structure of enterprises is changing Increment of outsourced activity From monolithic to collaborative structures that tend to reduce their size

Motivations

Motivations and Goals Motivations and Goals

3

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Chinese Motorbike Industry

Small firms meet in

  • nline places and

coffee shops Each one is assigned the task it is best at A self-organising system of design and production

Motivations and Goals Motivations and Goals

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Background

Business partners are moving from the roles of suppliers, manufacturers, and customers to the role of collaborators In this environment, the choice of the best business partners is critical

Motivations and Goals Motivations and Goals

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Goals

Design a selection and coordination process among multiple partners so that: it is easy to automate it meets particular production requirements it optimises production costs

Motivations and Goals Motivations and Goals

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SALE FORECAST 200 APPLE PIES

Example

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Motivations and Goals Motivations and Goals

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Procurement Stage

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Motivations and Goals Motivations and Goals

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Make-or-Buy

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Motivations and Goals Motivations and Goals

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Procurement Stage

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Motivations and Goals Motivations and Goals

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Make-or-Buy-or-Collaborate

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Motivations and Goals Motivations and Goals

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Make-or-Buy-or-Collaborate

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Motivations and Goals Motivations and Goals

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Make-or-Buy-or-Collaborate

Mixed Multiunit Combinatorial Auctions (MMUCA) Automatically selects the best Make-or-Buy-

  • r-Collaborate decisions

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Motivations and Goals Motivations and Goals

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MMUCA

Overview

Bidding Language (IJCAI 07) Winner Determination Problem (1) Definition (IJCAI 07) (2) Solvers

  • Empirical Evaluation (IJA 08)

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  • Petri-Nets based (AAMAS 07)
  • Direct Integer Programming (IJCAI 07)
  • Connected Component Integer

Program (AAMAS 08)

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Motivation Background (MMUCA) Limitations of WDP solvers for MMUCA The Improved Solver Empirical evaluation Future work

Outline

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Mixed Multi-unit Combinatorial Auctions

An extension of Combinatorial Auctions that provides: A formal language to express preferences over

  • perations across the supply chain

A formalisation of the optimisation problem that selects:

  • (1) The best business partners
  • (2)A feasible sequence of operations

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Automatically selects the best Make-or-Buy-or-Collaborate decisions

BACKGROUND BACKGROUND

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Mixed Multi-unit Combinatorial Auctions

€-10 €-11 €-8 €23 €25 €-9

H2O H2 O2

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FEASIBILITY OPTIMALITY

BACKGROUND BACKGROUND

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Atomic Bid and Supply Chain Operation

SCO4 = (2’H2O , 1’O2 + 2’H2) SCO5= (1’O2+2’H2, nothing)

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BID1=(1’SCO1+2’SCO2, - €2)

BID1 XOR BID2 XOR BID3 XOR BID4 BID1 OR BID2 OR BID3 OR BID4

Bidding Language Bidding Language BACKGROUND BACKGROUND

SCO=(Inputs, Outputs)

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Bidding Language

A bidder can express preferences over bundles of SCOs (Atomic Bid) A bidder can submit combinations of Atomic Bids (e.g. XOR, OR) Theorem: XOR is expressive enough to represent any valuation

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Bidding Language Bidding Language BACKGROUND BACKGROUND

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= +7

MMUCA WDP

Solution: <SCO1> Solution: <SCO1,SCO3> Solution: <SCO1,SCO3,SCO6>

€-10 €-11 €-8

€23 €25

€-9

Revenue:

  • 10 -8 +25

BACKGROUND BACKGROUND

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Winner Determination Problem

Compute a sequence of SCOs selected among the ones submitted by bidders such that: it fulfils the constraints expressed by the bids it is feasible it maximises the auctioneer’s revenue

Winner Determination Problem Winner Determination Problem

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BACKGROUND BACKGROUND

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Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work

Outline

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Comparing solvers for MMUCA

SOLVER TOPOLOGY #Decision Variables

Petri-Nets Based Integer Program ACYCLIC O(N) Direct Integer Program ANY O(N2) Connected Components IP ANY

O(N) ≤ ??<< O(N2)

N: overall number of Supply Chain Operations

WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

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Cyclic topologies

Petri Petri-

  • Nets Based

Nets Based

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WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

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Cyclic topologies

For instance

✓Resource reuse ✓Production Cycles

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Petri Petri-

  • Nets Based

Nets Based

WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

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Direct Integer Program

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Positions Positions Solution Solution

1

SCO1

2

SCO1

3

SCO1

4

SCO1

5

SCO1

6

SCO1

Direct Integer Program Direct Integer Program

WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

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Positions Positions Solution Solution

1

SCO0

2

SCO0

3

SCO0

4

SCO0

5

SCO0

6

SCO0

Direct Integer Program Direct Integer Program

WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

Direct Integer Programming approach

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DIP explained

Positions Positions

1 2 3 4 5 6

SCOs SCOs

SCO1 SCO2 SCO3 SCO4 SCO5 SCO6 SCO1 SCO2 SCO3 SCO4 SCO5 SCO6 SCO1 SCO2 SCO3 SCO4 SCO5 SCO6 SCO1 SCO2 SCO3 SCO4 SCO5 SCO6 SCO1 SCO2 SCO3 SCO4 SCO5 SCO6 SCO1 SCO2 SCO3 SCO4 SCO5 SCO6

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Direct Integer Program Direct Integer Program

WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

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Problem

The search space associated to DIP is big This affects the computational performance of DIP Can we reduce the associated search space?

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Limitations Limitations

WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS

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Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work

Outline

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Solution sequence: SCO1

Equivalent Solutions

,SCO2 ,SCO2 ,SCO0

31 The improved Solver The improved Solver -

  • CCIP

CCIP

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Solution sequence: SCO1

Equivalent Solutions

,SCO2 ,SCO2 ,SCO0 ,SCO2 ,SCO0 ,SCO2 SCO1 ,SCO2 ,SCO1 ,SCO2 SCO0

32 The improved Solver The improved Solver -

  • CCIP

CCIP

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Reducing the search space

  • Can we avoid considering re-orderings
  • f the solution sequence?
  • Indeed: Assume that the auctioneer

doesn’t care about the ordering of a solution sequence as long as enough goods are available for every SCO in the sequence

The improved Solver The improved Solver -

  • CCIP

CCIP

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Solution sequence: SCO1

Equivalent Sequences

,SCO2 ,SCO2 ,SCO0 ,SCO2 ,SCO0 ,SCO2 SCO1 ,SCO2 ,SCO1 ,SCO2 SCO0

34 The improved Solver The improved Solver -

  • CCIP

CCIP

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How to remove some sequences

Each solution to the MMUCA WDP can be reordered into a solution that complies with a given TEMPLATE This template is built considering the dependency relationships among SCOs

35 The improved Solver The improved Solver -

  • CCIP

CCIP

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SCO Dependency Graph

SCO0 SCO1 SCO2 SCO4 SCO3

36 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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SCO Dependency Graph

SCO0 SCO1 SCO2 SCO4 SCO3 SCO2 depends on SCO0,SCO1

37 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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SCO Dependency Graph

SCO2 depends on SCO0,SCO1 SCO1 ,SCO2 ,SCO2 ,SCO0 ,SCO2 ,SCO1 ,SCO0 SCO2 ,SCO2 ,SCO1 ,SCO2 SCO0

38 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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SCO Dependency Graph

SCO0 SCO1 SCO2 SCO4 SCO3 SCO1 and SCO0 are independent

39 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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SCO Dependency Graph

SCO1 and SCO0 are independent

SCO1 ,SCO2 ,SCO2 ,SCO0 ,SCO2 ,SCO2 ,SCO1 SCO0

40 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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SCO Dependency Graph

SCO0 SCO1 SCO2 SCO4 SCO3 SCO4 depends on SCO2 SCO2 depends on SCO4 SCO2,SCO4 belong to a loop

41 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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Strongly Connected Components

SCO0 SCO1 SCO2 SCO4 SCO3 SCO2,SCO3,SCO4 cannot be ordered among them

We group them: SCCs

42 The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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Strongly Connected Components

SCO0 SCO1 SCO2 SCO4 SCO3

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Pos Pos Solution Solution 1

SCO1

2

SCO0

3

SCO2,SCO3,SCO4

4

SCO2,SCO3,SCO4

5

SCO2,SCO3,SCO4

6

SCO2,SCO3,SCO4

The improved Solver The improved Solver -

  • CCIP

CCIP

The dependency graph The dependency graph

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Strongly Connected Components

SCO0 SCO1 SCO2 SCO4 SCO3

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Pos Pos Solution Solution 1

SCO1

2

SCO0

3

SCO2,SCO3,SCO4

4

SCO2,SCO3,SCO4

5

SCO2,SCO3,SCO4

6

SCO2,SCO3,SCO4

The improved Solver The improved Solver -

  • CCIP

CCIP

The solution template The solution template

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The Solution Template

Positions

1 2 3 4 5 6

Template SCO0 SCO1

SCO2 SCO3 SCO4 SCO2 SCO3 SCO4 SCO2 SCO3 SCO4 SCO2 SCO3 SCO4

SEQ A SCO0 SCO1 SCO3 SCO2 SEQ B SCO2 SCO1 SCO3 SCO0

SCO0 SCO1 SCO2 SCO4 SCO3

45 The improved Solver The improved Solver -

  • CCIP

CCIP

The solution template The solution template

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Proof of correctness

THEOREM: “each solution to the

MMUCA WDP can be reordered into

an equivalent solution that fulfils the solution template” If we reduce the search space to the sequences fulfilling the solution template we do not to lose any solutions

46 The improved Solver The improved Solver -

  • CCIP

CCIP

The solution template The solution template

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Comparing DIP and CCIP

The hypothesis behind DIP is that a

SCO can hold any position within the

solution sequence

5 x 6 = 30

Positions

1 2 3 4 5 6

Template

SCO0 SCO1 SCO2 SCO3 SCO4 SCO0 SCO1 SCO2 SCO3 SCO4 SCO0 SCO1 SCO2 SCO3 SCO4 SCO0 SCO1 SCO2 SCO3 SCO4 SCO0 SCO1 SCO2 SCO3 SCO4 SCO0 SCO1 SCO2 SCO3 SCO4

47 The improved Solver The improved Solver -

  • CCIP

CCIP

The solution template The solution template

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Positions

1 2 3 4 5 6

Template SCO0 SCO1

SCO2 SCO3 SCO4 SCO2 SCO3 SCO4 SCO2 SCO3 SCO4 SCO2 SCO3 SCO4

Comparing DIP and CCIP

The hypothesis behind CCIP is that a

SCO can hold only the positions allowed

by the template

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48 The improved Solver The improved Solver -

  • CCIP

CCIP

The solution template The solution template

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Comparing solvers

SOLVER TOPOLOGY #Decision Variables

Petri-Nets Based

ACYCLIC O(N)

Direct Integer Program

ANY O(N2)

Connected Component Integer Program (CCIP)

ANY O(k2 SCC) N: overall number of Supply Chain Operations

Conlusions Conlusions

The improved Solver The improved Solver -

  • CCIP

CCIP

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Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work

Outline

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Empirical Evaluation

Empirical Evaluation Empirical Evaluation

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MMUCA WDP Generator

Empirical Evaluation Empirical Evaluation

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Empirical Evaluation Empirical Evaluation

The improved Solver The improved Solver -

  • CCIP

CCIP

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Conclusions

  • The scalability of an IP implementation of

MMUCA is affected by the size of the largest connected components

  • When there is a “natural” flow in the supply

chain, CCIP scales reasonably well wrt number

  • f transformations and goods

Empirical Evaluation Empirical Evaluation

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Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work

Outline

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Future Work

Incorporate time time to perform operations time to finish before a deadline Incorporate uncertainty bidders may fail maximise the expected value Study connections to Planning

Future Work Future Work

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