DECENTRALIZED SUPPLY CHAIN FORMATION USING MAX-SUM LOOPY BELIEF PROPAGATION
Article first published online: 4 JUL 2012
© 2012 Wiley Periodicals, Inc.
Volume 29, Issue 2, pages 281–309, May 2013
How to Cite
Winsper, M. and Chli, M. (2013), DECENTRALIZED SUPPLY CHAIN FORMATION USING MAX-SUM LOOPY BELIEF PROPAGATION. Computational Intelligence, 29: 281–309. doi: 10.1111/j.1467-8640.2012.00446.x
- Issue published online: 7 MAY 2013
- Article first published online: 4 JUL 2012
- Received 2 February 2011; Revised 10 February 2012; Accepted 12 February 2012
- loopy belief propagation;
- max-sum algorithm;
- supply chain formation
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.