General variable neighborhood search for the capacitated single allocation hub maximal covering problem

This paper introduces the capacitated single allocation hub maximal covering problem (CSAHMCP) which arises from optimizing delivery service networks. The goal of the problem is to determine locations for installing hubs and to allocate each non-hub node to one of the installed hubs with enough capacity, to minimize the sum of uncovered demand of all origin–destination pairs and the costs of hub installation. We propose four-index integer linear mathematical formulation of the CSAHMCP, and reformulations to a two-index and a three-index mixed integer linear programs. Having in mind NP-hardness of the novel CSAHMCP, we design and implement a General Variable Neighborhood Search (GVNS) heuristic as a solution method. Computational experiments are conducted on the standard Australian Post (AP) hub instances from the literature with up to 200 nodes. By analyzing the results of CPLEX solver with the three proposed CSAHMCP formulations on AP instances with up to 100 nodes, it can be concluded that the two-index formulation was generally the most efficient, followed by the three-index model, while the four-index one had the worst performance. The proposed GVNS metaheuristic reaches all known optimal solutions or improves upper bounds provided by CPLEX in short CPU times. In the case of the largest AP instances with 200 nodes, for which CPLEX provided no feasible solution, the proposed GVNS heuristic quickly returns solutions, showing its potential to solve problem instances of large dimensions in an efficient manner. In addition, sensitivity analysis regarding the value of coverage criterion parameter was preformed and the obtained results are discussed.