Fleet Size and Mix Split-Delivery Vehicle Routing

TL;DR

This paper investigates a complex vehicle routing problem with split deliveries, heterogeneous fleets, and compatibility constraints, proposing multiple MIP models and a hybrid approach with Constraint Programming to optimize routing and fleet design.

Contribution

It introduces four MIP models for a rich VRP variant, compares their performance, and integrates CP for improved solution efficiency.

Findings

Four MIP models compared with extensive experiments

Hybrid CP-MIP approach provides good solutions and warm-starts models

Insights into strengths and weaknesses of different formulations

Abstract

In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to visit a set of customers while minimising the operations' costs. We study a rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and vehicle-commodity incompatibility constraints. Our goal is twofold: define the cheapest routing and the most adequate fleet. To do so, we split the problem into two interdependent components: a fleet design component and a routing component. First, we define two Mixed Integer Programming (MIP) formulations for each component. Then we discuss several improvements in the form of valid cuts and symmetry breaking constraints. The main contribution of this paper is a comparison of the four resulting models for this Rich VRP. We highlight their strengths and weaknesses with extensive experiments. Finally, we explore a lightweight integration with Constraint Programming (CP). We use a fast CP model which gives good solutions and use the solution to warm-start our models.