A comparative study of alternative formulations for the periodic vehicle routing problem

Abstract

This study investigates the periodic vehicle routing problem (PVRP) and its variant with time windows with a particular focus on alternative formulation approaches that can be solved by a state-of-the-art commercial solver. We propose a new vehicle flow formulation for the PVRP and strengthen it with valid inequalities. We also investigate two prominent formulations for the PVRP available in the literature: a commodity flow formulation, referred to as the load-based formulation, and a cut-based formulation which is adapted from a formulation originally developed for a variant of the PVRP. We also extend these formulations to model the PVRP with time windows (PVRPTW) and employ valid inequalities to tighten the resulting formulations. A comprehensive computational study is then carried out to compare the performances of alternative PVRP and PVRPTW formulations on various sets of benchmark instances with different characteristics. The results attest to the robustness and the consistency of the proposed formulation and its strengthened versions in producing good quality solutions, especially for large instances although the load-based formulations tend to perform well in small instances.