Mixed Multi-Unit Combinatorial Auctions for Supply Chain Automation Andrea Giovannucci Meritxell Vinyals Jesus Cerquides Ulle Endriss Juan Antonio Rodriguez-Aguilar Pedro Meseguer Institut d’Investigació en Intel.ligència Artificial (IIIA-CSIC)
Outline Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work 2
Motivations and Goals Motivations and Goals Motivations The organisational structure of enterprises is changing Increment of outsourced activity From monolithic to collaborative structures that tend to reduce their size 3
Motivations and Goals Motivations and Goals Chinese Motorbike Industry Small firms meet in online 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 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 5
Motivations and Goals Motivations and Goals 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 6
Motivations and Goals Motivations and Goals Example SALE FORECAST 200 APPLE PIES 7
Motivations and Goals Motivations and Goals Procurement Stage 8
Motivations and Goals Motivations and Goals Make-or-Buy 9
Motivations and Goals Motivations and Goals Procurement Stage 10
Motivations and Goals Motivations and Goals Make-or-Buy-or-Collaborate 11
Motivations and Goals Motivations and Goals Make-or-Buy-or-Collaborate 12
Motivations and Goals Motivations and Goals Make-or-Buy-or-Collaborate Mixed Multiunit Combinatorial Auctions (MMUCA) Automatically selects the best Make-or-Buy- or-Collaborate decisions 13
Overview Bidding Language (IJCAI 07) Winner Determination Problem (1) Definition (IJCAI 07) (2) Solvers MMUCA •Petri-Nets based (AAMAS 07) •Direct Integer Programming (IJCAI 07) •Connected Component Integer Program (AAMAS 08) o Empirical Evaluation (IJA 08) 14
Outline Motivation Background (MMUCA) Limitations of WDP solvers for MMUCA The Improved Solver Empirical evaluation Future work 15
BACKGROUND BACKGROUND Mixed Multi-unit Combinatorial Auctions An extension of Combinatorial Auctions that provides: A formal language to express preferences over operations across the supply chain A formalisation of the optimisation problem that selects: (1) The best business partners • (2)A feasible sequence of operations • Automatically selects the best Make-or-Buy-or-Collaborate decisions 16
BACKGROUND BACKGROUND Mixed Multi-unit Combinatorial Auctions H 2 O €-10 €-11 FEASIBILITY €-8 €-9 OPTIMALITY H 2 O 2 €23 €25 17
BACKGROUND Bidding Language BACKGROUND Bidding Language Atomic Bid and Supply Chain Operation SCO=(Inputs, Outputs) SCO 4 = (2’H 2 O , 1’O 2 + 2’H 2 ) SCO 5 = (1’O 2 +2’H 2 , nothing) BID 1 =(1’SCO 1 +2’SCO 2 , - €2) BID 1 XOR BID 2 XOR BID 3 XOR BID 4 BID 1 OR BID 2 OR BID 3 OR BID 4 18
BACKGROUND Bidding Language BACKGROUND Bidding Language 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 19
BACKGROUND BACKGROUND MMUCA WDP €-10 €-11 Solution: <SCO 1 > Solution: <SCO 1, SCO 3 > €-9 €-8 Solution: <SCO 1, SCO 3, SCO 6 > Revenue: -10 -8 +25 = +7 €23 €25
BACKGROUND Winner Determination Problem BACKGROUND Winner Determination Problem 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 21
Outline Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work 22
WDP SOLVERS LIMITATIONS WDP SOLVERS LIMITATIONS Comparing solvers for MMUCA #Decision SOLVER TOPOLOGY Variables Petri-Nets Based ACYCLIC O(N) Integer Program Direct Integer Program ANY O(N 2 ) Connected ANY O(N) ≤ ??<< O(N 2 ) Components IP N: overall number of Supply Chain Operations
Petri- -Nets Based Nets Based WDP SOLVERS LIMITATIONS Petri WDP SOLVERS LIMITATIONS Cyclic topologies 24
Petri- -Nets Based Nets Based WDP SOLVERS LIMITATIONS Petri WDP SOLVERS LIMITATIONS Cyclic topologies For instance ✓ Resource reuse ✓ Production Cycles 25
Direct Integer Program WDP SOLVERS LIMITATIONS Direct Integer Program WDP SOLVERS LIMITATIONS Direct Integer Program Positions Solution Positions Solution SCO 1 1 SCO 1 2 SCO 1 3 SCO 1 4 SCO 1 5 SCO 1 6 26
Direct Integer Program WDP SOLVERS LIMITATIONS Direct Integer Program WDP SOLVERS LIMITATIONS Direct Integer Programming approach Positions Solution Positions Solution SCO 0 1 SCO 0 2 SCO 0 3 SCO 0 4 SCO 0 5 SCO 0 6 27
Direct Integer Program WDP SOLVERS LIMITATIONS Direct Integer Program WDP SOLVERS LIMITATIONS DIP explained Positions Positions 1 2 3 4 5 6 SCO 1 SCO 1 SCO 1 SCO 1 SCO 1 SCO 1 SCO 2 SCO 2 SCO 2 SCO 2 SCO 2 SCO 2 SCO 3 SCO 3 SCO 3 SCO 3 SCO 3 SCO 3 SCOs SCOs SCO 4 SCO 4 SCO 4 SCO 4 SCO 4 SCO 4 SCO 5 SCO 5 SCO 5 SCO 5 SCO 5 SCO 5 SCO 6 SCO 6 SCO 6 SCO 6 SCO 6 SCO 6 28
Limitations WDP SOLVERS LIMITATIONS Limitations WDP SOLVERS LIMITATIONS Problem The search space associated to DIP is big This affects the computational performance of DIP Can we reduce the associated search space? 29
Outline Motivation Background (MMUCA) Limitations of WD solvers for MMUCA The Improved Solver Empirical evaluation Future work 30
The improved Solver The improved Solver - - CCIP CCIP Equivalent Solutions Solution sequence: ,SCO 2 ,SCO 0 ,SCO 2 SCO 1 31
The improved Solver The improved Solver - - CCIP CCIP Equivalent Solutions Solution sequence: ,SCO 2 ,SCO 0 ,SCO 2 SCO 1 SCO 1 ,SCO 0 ,SCO 2 ,SCO 2 ,SCO 2 SCO 0 ,SCO 1 ,SCO 2 32
The improved Solver - The improved Solver - CCIP CCIP Reducing the search space • Can we avoid considering re-orderings of 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 Equivalent Sequences Solution sequence: SCO 1 ,SCO 2 ,SCO 0 ,SCO 2 SCO 1 ,SCO 0 ,SCO 2 ,SCO 2 SCO 0 ,SCO 1 ,SCO 2 ,SCO 2 34
The improved Solver - The improved Solver - CCIP CCIP 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 dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph SCO Dependency Graph SCO 0 SCO 1 SCO 2 SCO 3 SCO 4 36
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph SCO Dependency Graph SCO 2 depends on SCO 0 ,SCO 1 SCO 0 SCO 1 SCO 2 SCO 3 SCO 4 37
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph SCO Dependency Graph SCO 2 depends on SCO 0 ,SCO 1 ,SCO 2 ,SCO 0 ,SCO 2 SCO 1 SCO 2 ,SCO 1 ,SCO 0 ,SCO 2 SCO 0 ,SCO 1 ,SCO 2 ,SCO 2 38
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph SCO Dependency Graph SCO 1 and SCO 0 are independent SCO 0 SCO 1 SCO 2 SCO 3 SCO 4 39
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph SCO Dependency Graph SCO 1 and SCO 0 are independent ,SCO 2 ,SCO 0 ,SCO 2 SCO 1 SCO 0 ,SCO 2 ,SCO 1 ,SCO 2 40
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph SCO Dependency Graph SCO 4 depends on SCO 2 SCO 0 SCO 1 SCO 2 depends on SCO 4 SCO 2 SCO 2 ,SCO 4 belong to a loop SCO 3 SCO 4 41
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph Strongly Connected Components SCO 2 ,SCO 3, SCO 4 cannot be ordered among them SCO 0 SCO 1 SCO 2 We group them: SCCs SCO 3 SCO 4 42
The dependency graph The improved Solver - The improved Solver - CCIP CCIP The dependency graph Strongly Connected Components Pos Solution Pos Solution SCO 1 1 SCO 0 SCO 1 SCO 0 2 SCO 2 ,SCO 3 ,SCO 4 3 SCO 2 SCO 2 ,SCO 3 ,SCO 4 4 SCO 2 ,SCO 3 ,SCO 4 5 SCO 3 SCO 4 SCO 2 ,SCO 3 ,SCO 4 6 43
The solution template The improved Solver - The improved Solver - CCIP CCIP The solution template Strongly Connected Components Pos Solution Pos Solution SCO 1 1 SCO 0 SCO 1 SCO 0 2 SCO 2 ,SCO 3 ,SCO 4 3 SCO 2 SCO 2 ,SCO 3 ,SCO 4 4 SCO 2 ,SCO 3 ,SCO 4 5 SCO 3 SCO 4 SCO 2 ,SCO 3 ,SCO 4 6 44
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