DECENTRALIZED SUPPLY CHAIN FORMATION USING MAX‐SUM LOOPY BELIEF PROPAGATION

Abstract

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.