Supply Chain Optimization by Benders Decomposition

This paper introduces a formulation and a solution methodology for the problem of optimizing the supply chain (or logistics network) of a manufacturing firm. The problem is modeled as a linear mixed-integer program with binary variables associated with design decisions such as location, product range assignment and transportation mode selection, and continuous variables representing the flows of raw materials and finished products through the network. This natural separation of variables leads to a very efficient solution approach based on Benders decomposition. While being comparable to a simplex-based branch-and-bound approach when solving a single instance of the problem, the Benders decomposition approach offers outstanding reoptimization capabilities. Its performance can in addition be improved by the introduction of simple valid inequalities that strengthen the LP relaxation by exploiting the problem structure. The formulation and solution methodology can also be adapted to handle multiple planning periods with dynamic demand, multiple stages of production and distribution, and stochastic demand in the form of a finite set of scenarios.