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A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)
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A Scalable Message-Passing Algorithm for Supply Chain Formation (AAAI2012)

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  • 1. A Scalable Message-PassingAlgorithm for Supply Chain Formation by Toni Penya-Alba, Meritxell Vinyals, Jesus Cerquides, and Juan A. Rodriguez-Aguilar for the 26th AAAI Conference
  • 2. THE PROB LEMAlice Dave-$2 $7 Carol -$5Bob Eve-$3 $8
  • 3. THE PROB L EM Alice Dave -$2 $7 Carol -$5 Bob Eve -$3 $8The Supply Chain Formation problem is that of findingthe feasible configuration with maximum value.
  • 4. THE PROB L EMAlice-$2 Carol -$5 Eve $8 Supply Chain Value = $8 - $5 - $2 = $1
  • 5. THE GOALTo provide a scalable methodfor Supply Chain Formationin markets with highdegrees of competition.
  • 6. RI BUT IONCO NT Encoding in a novel graphical model. Optimized implementation of max-sum. BENEFReduced memory, communication and ITScomputation requirements.Higher quality solutions.
  • 7. factor graph is a graphical model torepresent functions. f g f(x,y) + g(y,z) x y zmax-sum is a message passing algorithm.max-sum can efficiently approximateoptimization problems.
  • 8. LoopyBeliefPropagation Michael Winsper Maria Chli
  • 9. LOOPY BELIEF PROPAGATIONmap the Supply Chain Formationproblem into a factor graph.apply max-sum over the factor graphto obtain a solution.
  • 10. MAPPING INTO A FACTOR GRAPH Alice Dave -$2 $7 Carol -$5 Bob Eve -$3 $8
  • 11. FACTOR GRAPH MAPPINGAlice Carol DaveBob Eve
  • 12. FACTOR GRAPH MAPPING Alice Carol Dave exchanges Bob Eve 0 do nothing 1 buy from Alice, sell to Dave 2 buy from Alice, sell to Eve 3 buy from Bob, sell to Dave 4 buy from Bob, sell to EveAgent variable encodes all of Carol’s possible exchanges.
  • 13. FACTOR GRAPH MAPPING Alice Carol Dave exchanges Bob Eve -5 inactive 0 otherwise -5Activation factor encodes Carol’s activation cost.
  • 14. FACTOR GRAPH MAPPING Alice Carol Dave-2 exchanges exchanges 7 exchanges Bob Eve-3 exchanges -5 exchanges 8
  • 15. FACTOR GRAPH MAPPING Alice Carol Dave -2 exchanges AC CD exchanges 7 exchanges Bob Eve -3 exchanges BC -5 CE exchanges 8Compatibility factors encode compatibility betweenCarol’s states and her neighbors’.
  • 16. LBP memory per O(G•A 2G+1) agentbandwidth per O(G•A G+1) agent computation O(G•A 2G+1)time per agent
  • 17. RB-LBPOur Approach
  • 18. RB-LBP OUR APPROACHmap problem into a binary factorgraph containing binary variablesand logical constraints.optimized max-sum implementation.apply max-sum over the factor graphto obtain a solution.
  • 19. MAPPING INTO A BINARY FACTOR GRAPH Alice Dave -$2 $7 Carol -$5 Bob Eve -$3 $8
  • 20. BINARY FACTOR GRAPH MAPPINGAlice Carol DaveBob Eve
  • 21. BINARY FACTOR GRAPH MAPPING Alice Carol Dave activate Bob EveActivation variable encodes Carol’s decision to be active.
  • 22. BINARY FACTOR GRAPH MAPPING Alice Carol Dave activate Bob Eve -5Activation factor encodes Carol’s activation cost.
  • 23. BINARY FACTOR GRAPH MAPPING Alice Carol Dave buy sell from A to D activate Bob Eve buy from B -5 sell to EOption variables encode Carol’s decision to trade each ofher goods with each of her potential partners.
  • 24. BINARY FACTOR GRAPH MAPPING Alice Carol Dave buy sell from A to D S activate S Bob Eve buy from B -5 sell to ESelection factors guarantee that only one of theproviders is selected for each good.
  • 25. BINARY FACTOR GRAPH MAPPING Alice Carol Dave-2 activate S sell to C buy from A sell to D buy from C S activate 7 S activate S Bob Eve-3 activate S sell to C buy from B -5 sell to E buy from C S activate 8
  • 26. BINARY FACTOR GRAPH MAPPING Alice Carol Dave -2 activate S sell to C = buy from A sell to D = buy from C S activate 7 S activate S Bob Eve -3 activate S sell to C = buy from B -5 sell to E = buy from C S activate 8Equality factors guarantee that Carol takes coherentdecisions with her neighbors’.
  • 27. }Factors as logical constraintsThere is no need to store factors inmemory. SimplifiedSingle-valued messages messageContain agents’ willingness to calculationcollaborate with each other.
  • 28. LBP RB-LBP memory per O(G•A 2G+1) O(G•A) agentbandwidth per O(G•A G+1) O(G•A) agent computation O(G•A 2G+1) O(G•A2)time per agent
  • 29. ExperimentalAnalysis
  • 30. EXPERIMENTAL SETUPSmall networks [Walsh2003].Large networks [Vinyals2008].Measure memory, communication,time, and quality.
  • 31. small networks <20 goods <40 agents
  • 32. SMALL NETWORKSup to 13 times less memory up to 5 times less bandwidth same solution quality negligible time differences
  • 33. large networks 50 goods40-500 agents
  • 34. LARGE NETWORKSup to 105 times less memoryup to 787 times less bandwidth up to 20 times faster up to twice bettersolutions
  • 35. LARGE NETWORKS up to 105 timesless memory
  • 36. FINAL RECA PEncoding in a novel graphical model.Optimized implementation of max-sum.Reduced memory, communication andcomputation requirements.Higher quality solutions.
  • 37. Coming soon ...
  • 38. Coming soon ... ... Better valued solutions
  • 39. ThankYou
  • 40. Questions?
  • 41. [Winsper2003] M. Winsper and M. Chli, Decentralised Supply Chain Formation:A Belief Propagation-based Approach, Agent-Mediated Electronic Commerce,2010.[Walsh2003] W. E. Walsh and M. P. Wellman, Decentralized Supply ChainFormation : A Market Protocol and Competitive Equilibrium Analysis, Journal ofArtificial intelligence Research (JAIR), vol. 19, pp. 513-567, 2003.[Vinyals2008] M. Vinyals, A. Giovannucci, J. Cerquides, P. Meseguer, and J. A.Rodriguez-Aguilar, A test suite for the evaluation of mixed multi-unitcombinatorial auctions, Journal of Algorithms, vol. 63, no. 1-3, pp. 130-150,2008.

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