Large-Scale Supply Chain Optimization via Nested Partitions

Large-scale supply chain design problems are generally intractable when input as single entities to general purpose branch-and-bound solvers such as CPLEX. In this research we demonstrate that the nested partition (NP) method is capable of efficiently producing very high quality solutions to large-scale supply chain problems by taking advantage of their structure to generate an appropriate set of restricted subproblems. The implementation of NP that we describe here first employs an optimization-based heuristic to generate an efficiency ranking of the available warehouses and then employs biased sampling (from the ranked warehouse set) guided by the NP global optimization framework. The overall process is implemented using the looping 2 constructs available in the AMPL modeling language and employs the CPLEX mixed-integer branch-and-cut code to solve the optimization subproblems that arise. This implementation represents a novel use of CPLEX as an evaluator of samples generated using a global view that takes advantage of the stucture of the original problem. Our computational results demonstrate that NP also outperforms specialized approaches such as the Lagrange relaxation methods that previously have been regarded as the most effective techniques for large-scale supply chain optimization.