Meta Partial Benders Decomposition for the Logistics Service Network Design Problem

Abstract: Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service provider seeks to cost-effectively source and fulfill customer demands of products within a multi-echelon distribution network. However, many industrial settings yield instances of the LSNDP that are too large to be solved in reasonable run-times by off-the-shelf optimization solvers. We introduce an exact Benders decomposition algorithm based on partial decompositions that strengthen the master problem with information derived from aggregating subproblem data. More specifically, the proposed Meta Partial Benders Decomposition intelligently switches from one master problem to another by changing both the amount of subproblem information to include in the master as well as how it is aggregated. Through an extensive computational study, we show that the approach outperforms existing benchmark methods and we demonstrate the benefits of dynamically refining the master problem in the course of a partial Benders decomposition-based scheme.