Decentralized supply chain formation using max-sum loopy belief propagation

Michael Winsper*, Maria Chli

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Supply chain formation is the process by which a set of producers within a network determine the subset of these producers able to form a chain to supply goods to one or more consumers at the lowest cost. This problem has been tackled in a number of ways, including auctions, negotiations, and argumentation-based approaches. In this paper we show how this problem can be cast as an optimization of a pairwise cost function. Optimizing this class of energy functions is NP-hard but efficient approximations to the global minimum can be obtained using loopy belief propagation (LBP). Here we detail a max-sum LBP-based approach to the supply chain formation problem, involving decentralized message-passing between supply chain participants. Our approach is evaluated against a well-known decentralized double-auction method and an optimal centralized technique, showing several improvements on the auction method: it obtains better solutions for most network instances which allow for competitive equilibrium (Competitive equilibrium in Walsh and Wellman is a set of producer costs which permits a Pareto optimal state in which agents in the allocation receive non-negative surplus and agents not in the allocation would acquire non-positive surplus by participating in the supply chain) while also optimally solving problems where no competitive equilibrium exists, for which the double-auction method frequently produces inefficient solutions. © 2012 Wiley Periodicals, Inc.

Original languageEnglish
Pages (from-to)281-309
Number of pages29
JournalComputational Intelligence
Issue number2
Early online date4 Jul 2012
Publication statusPublished - May 2013

Bibliographical note

Winsper, M. , & Chli, M. (2012). Decentralized supply chain formation using max-sum loopy belief propagation. Computational intelligence, 29(2), which has been published in final form at


  • loopy belief propagation
  • max-sum algorithm
  • supply chain formation


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