An Approximation Algorithm for Multi Allocation Hub Location Problems

TL;DR

This paper introduces an improved approximation algorithm for multi allocation hub location problems, significantly enhancing solution bounds and enabling the handling of larger instances than previous methods.

Contribution

It develops a new approximation algorithm with better bounds for MApHM, MAuHLP, and MApHLP, and creates new benchmark instances for large-scale testing.

Findings

Algorithm outperforms previous methods on most instances.

Enables solving larger problem instances than existing algorithms.

Provides new benchmark datasets for future research.

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.