MIP formulations and heuristics for two-level production-transportation problems

Authors:
Rafael A. Melo;Laurence A. Wolsey
Affiliations:
Center for Operations Research and Econometrics (CORE), Université catholique de Louvain. 34, Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium;Center for Operations Research and Econometrics (CORE), Université catholique de Louvain. 34, Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium
Venue:
Computers and Operations Research
Year:
2012

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Abstract

A two-level supply chain with multiple items, production sites and client areas and a discrete time horizon is considered. After introducing different mixed integer programming formulations, including an initial formulation that is small but provides weak bounds and a multi-commodity extended formulation that provides much improved bounds but is of large size, we develop a hybrid heuristic that uses the strong formulation to provide a good dual bound and suggest certain variable fixing, and the initial formulation restricted by the variable fixing to then provide the heuristic solution. For different classes of medium-sized instances, we show that the hybrid heuristic provides solutions of a guaranteed quality that are as good or better than those provided by the MIP optimizer with a considerably larger run time.