Formulations for the Single Allocation Multimodal Uncapacitated $p$-Hub Coverage Problem

The multimodal uncapacitated $p$-Hub coverage problem with single allocation (MMSANCpHCP) is an optimization problem that aims to select nodes to be hubs, from a set of available nodes, and optimize the allocation of non-hubs to hubs. The goal is to minimize the cost of transport in the network, the fixed cost of installing the hubs and the operating cost of the transport links between hubs, considering multiple modes of transport. In this paper we propose two formulations for the MMSANCpHCP and evaluate the performance of both formulations using the Australian Post (AP) dataset using IBM CPLEX software. The results of computational experiments show the importance of analyzing and selecting the appropriate formulation, showing the impact on computational performance.