Decomposition techniques for large-scale optimization in the supply chain

Abstract

Integrated supply chain models provide an opportunity to optimize costs and production times in the supply chain while taking into consideration the many steps in the production and delivery process and the many constraints on time, shared resources, and throughput capabilities. In this work, mixed integer linear programming (MILP) models are developed to describe the manufacturing plant, consolidation transport, and distribution center components of the supply chain. Initial optimization results are obtained for each of these models. Additionally, an integrated model including a single plant, multiple consolidation transport vehicles, and a single distribution center is formulated and initial results are obtained. All models are implemented and optimized for their given objectives using a standard MILP solver. Initial optimization results suggest that it is intractable to solve problems of relevant scale using standard MILP solvers. The natural hierarchical structure in the supply chain problem lends itself well to application of decomposition techniques intended to speed up solution time. Exact techniques, such as Benders decomposition, are explored as a baseline. Classical Benders decomposition is applied to the manufacturing plant model, and results indicate that Benders decomposition on its own will not improve solve times for the manufacturing plant problem and instead leads to longer solve times for the problems that are solved. This is likely due to the large number of discrete variables in manufacturing plant model. To improve upon solve times for the manufacturing plant model, an approximate decomposition technique is developed, applied to the plant model, and evaluated. The approximate algorithm developed in this work decomposes the problem into a three-level hierarchical structure and integrates a heuristic approach at two of the three levels in order to solve abstracted versions of the larger problem and guide towards high-quality solutions. Results indicate that the approximate technique solves problems faster than those solved by the standard MILP solver and all solutions are within approximately 20% of the true optimal solutions. Additionally, the approximate technique can solve problems twice the size of those solved by the standard MILP solver within a one hour timeframe.