Formulations and algorithms for the multiple depot, fuel-constrained, multiple vehicle routing problem

TL;DR

This paper introduces the FCMVRP, a complex routing problem involving multiple depots and fuel constraints, and proposes four MILP formulations to find optimal solutions, supported by extensive computational testing.

Contribution

It presents four new mixed integer linear programming formulations for solving the FCMVRP, a novel and complex vehicle routing problem with fuel constraints and multiple depots.

Findings

Four MILP formulations effectively solve the FCMVRP.

Computational results demonstrate the formulations' efficiency on large instances.

The approaches outperform existing methods in solution quality and computational time.

Abstract

We consider a multiple depot, multiple vehicle routing problem with fuel constraints. We are given a set of targets, a set of depots and a set of homogeneous vehicles, one for each depot. The depots are also allowed to act as refueling stations. The vehicles are allowed to refuel at any depot, and our objective is to determine a route for each vehicle with a minimum total cost such that each target is visited at least once by some vehicle, and the vehicles never run out fuel as it traverses its route. We refer this problem as Multiple Depot, Fuel-Constrained, Multiple Vehicle Routing Problem (FCMVRP). This paper presents four new mixed integer linear programming formulations to compute an optimal solution for the problem. Extensive computational results for a large set of instances are also presented.