Branch & Solve for Hub Location

TL;DR

This paper presents a novel formulation and a Branch & Solve framework for hub location problems, capable of efficiently solving large instances by exploiting problem structure and using aggregated flow variables.

Contribution

It introduces a new 2-index aggregated flow formulation with demand constraints and develops a Branch & Solve method that handles large instances effectively.

Findings

Successfully solves instances with up to 200 nodes

Demonstrates good computational performance on benchmark problems

Provides a flexible approach applicable to various hub location models

Abstract

This paper introduces a new formulation and solution framework for hub location problems. The formulation is based on 2-index aggregated flow variables and incorporates a set of aggregated demand constraints, which are novel in hub location. With minor adaptations, the approach applies to a large class of single- and multiple-allocation models, possibly incorporating flow bounds on activated arcs. General-purpose feasibility and optimality inequalities are also developed. Because of the small number of continuous variables, there is no need to project them out, differentiating the method from solution algorithms that rely heavily on feasibility and optimality cuts. The proposed Branch & Solve solution framework leverages the nested structure of the problems, by solving auxiliary subproblems at selected nodes of the enumeration tree. Extensive computational experiments on benchmark instances from the literature confirm the good performance of the proposal: the basic version of the algorithm is able to solve to proven optimality instances with up to 200 nodes for several hub location families.