Multi-product Capacitated Single-Allocation Hub Location Problems: Formulations and Inequalities

In this paper we extend the classical capacitated single-allocation hub location problem by considering that multiple products are to be shipped through the network. We propose a unified modeling framework for the situation in which no more than one hub can be located in each node. In particular, we consider the case in which all hubs are dedicated to handling a single-product as well as the case in which all hubs can handle all products. The objective is to minimize the total cost, which includes setup costs for the hubs, setup costs for each product in each hub and flow routing costs. Hubs are assumed to be capacitated. For this problem several models are proposed which are based on existing formulations for the (single-product) capacitated single-allocation hub location problem. Additionally, several classes of inequalities are proposed in order to strengthen the models in terms of the lower bound provided by the linear relaxation. We report results of a set of computational experiments conducted to test the proposed models and their enhancements.