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

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.