Lagrangian Relaxation for the Capacitated Single Allocation p-Hub Median Problem

Abstract

In this paper the authors consider a capacitated single allocation p-hub median problem (CSApHMP). The authors determine the location of p hubs, the allocation of non-hub nodes to hubs in the network. This problem is formulated as 0-1 integer programming model with the objective of the minimum total transportation cost and the fixed cost associated with the establishment of hubs. Optimal solutions are obtained using Gurobi optimizer for the small sized problems. Since the CSApHMP is NP-hard, it is difficult to obtain an optimal solution within a reasonable computational time. Therefore, a Lagrangian relaxation (LR) heuristic is developed to solve the problem. The LR performance is examined through a comparative study. The experimental results show that the proposed LR heuristic can be a viable solution method for the capacitated hub and spoke network design problem.