An Approximation Algorithm for Multi Allocation Hub Location Problems

Abstract: The multi allocation p-hub median problem (MApHM), the multi allocation uncapacitated hub location problem (MAuHLP) and the multi allocation p-hub location problem (MApHLP) are common hub location problems with several practical applications. HLPs aim to construct a network for routing tasks between different locations. Specifically, a set of hubs must be chosen and each routing must be performed using one or two hubs as stopovers. The costs between two hubs are discounted. The objective is to minimize the total transportation cost in the MApHM and additionally to minimize the set-up costs for the hubs in the MAuHLP and MApHLP. In this paper, an approximation algorithm to solve these problems is developed, which improves the approximation bound for MApHM to 3.451, for MAuHLP to 2.173 and for MApHLP to 4.552 when combined with the algorithm of Benedito & Pedrosa. The proposed algorithm is capable of solving much bigger instances than any exact algorithm in the literature. New benchmark instances have been created and published for evaluation, such that HLP algorithms can be tested and compared on huge instances. The proposed algorithm performs on most instances better than the algorithm of Benedito & Pedrosa, which was the only known approximation algorithm for these problems by now.