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.