A primal decomposition method for the integrated design of multi-period production–distribution systems

We study the integrated design of strategic supply chain networks and the determination of tactical production-distribution allocations in the case of customer demands with seasonal variations. Given a set of potential suppliers, potential manufacturing facilities and distribution centers with multiple possible configurations, and customers with seasonal demands, the goal is to determine the configuration of the production-distribution system with the lowest sum of supply, production, transportation, inventory, and facility costs such that seasonal customer demands are met. We develop a mixed integer programming formulation and an integrated design methodology based on primal (Benders) decomposition. For a case study in the packaging industry, specialized acceleration techniques reduced the running times by a factor of 480. The company projects savings of 2% or $8.3 million by using the integrated rather than the optimal hierarchical configuration.