Benders Decomposition Algorithms for Two Variants of the Single Allocation Hub Location Problem

Abstract

The hub location problem (HLP) is a special type of the facility location problem with numerous applications in the airline industry, postal services, and computer and telecommunications networks. This paper addresses two basic variants of the HLP, namely the uncapacitated single allocation hub location problem (USAHLP) and the uncapacitated single allocation p-hub median problem (USAp HMP). Exact solution procedures based on Benders decomposition algorithm are proposed to tackle large sized instances of these problems. The standard Benders decomposition algorithm is enhanced through implementation of several algorithmic refinements such as using a new cut disaggregation scheme, generating strong optimality cuts, and an efficient algorithm to solve the dual subproblems. Furthermore, a modern implementation of the algorithm is used where a single search tree is established for the problem and Benders cuts are successively added within a branch-and-cut framework. Extensive computational experiments are conducted to examine the efficiency of the proposed algorithms. We have been able to solve all the instances of the problems from all three main data sets of the HLP to optimality in reasonable computational times.