A strong formulation for Multiple Allocation Hub Location based on supermodular inequalities

TL;DR

This paper presents a novel formulation for the multiple allocation hub location problem that leverages supermodular inequalities and reduces variable complexity, achieving optimal solutions efficiently for large instances.

Contribution

It introduces a new supermodular-based formulation using fewer variables, matching the LP bounds of more complex models, and demonstrates computational efficiency on large instances.

Findings

Same LP bounds as the tightest formulations

Outperforms existing supermodular formulations

Solves instances of up to 200 nodes within two hours

Abstract

We introduce a new formulation for the multiple allocation hub location problem that exploits supermodular properties and uses 1- and 2-index variables only. We show that the new formulation produces the same Linear Programming bound as the tightest existing formulations for the studied problem, which use 4-index variables, outperforming existing supermodular formulations adapted to the considered problem. Computational results are presented with instances of up to 200 nodes optimally solved within a time limit of two hours.