Column Generation for Optimal Shipment Delivery in a Logistic Distribution Network

We consider a logistic distribution decision-making problem, in which a vehicle fleet must carry out a set of deliveries between pairs of nodes of the underlying transportation network. The goal is to maximize the number of deliveries that will be carried out, while also minimizing the number of vehicles utilized to this end. The optimization is lexicographic in the sense that the former objective exhibits higher priority than the latter one. For this problem, we develop an integer programming model formulation and an associated column generation-based solution methodology. The proposed methodology utilizes a master problem which tries to fulfill the maximum possible number of deliveries given a specific set of vehicle routes and a column generation subproblem which is used to generate cost-effective vehicle routes¹, for improving the master problem solution. We describe the steps of the proposed methodology, illustrating how it can be modified to accommodate interesting problem variations that often arise in practice. We also present extensive computational results demonstrating the computational performance of the proposed solution algorithm and illustrating how its behavior is influenced by key design parameters.