A sequential insertion heuristic for the initial solution to a constrained vehicle routing problem

Jw Joubert,Sj Claasen

doi:10.5784/22-1-36

Abstract

The Vehicle Routing Problem (VRP) is a well-researched problem in the Operations Research literature. It is the view of the authors of this paper that the various VRP variants have been researched in isolation. This paper embodies an attempt to integrate three specific variants of the VRP, namely the VRP with multiple time windows, the VRP with a heterogeneous fleet, and the VRP with double scheduling, into an initial solution algorithm. The proposed initial solution algorithm proves feasible for the integration, while the newly introduced concept of time window compatibility decreases the computational burden when using benchmark data sets from literature as a basis for efficiency testing. The algorithm also improves the quality of the initial solution for a number of problem classes.

Highlights

The Vehicle Routing Problem (VRP) is a well-researched problem in the Operations Research literature
The authors investigate the feasibility of integrating multiple soft time windows, a heterogeneous fleet and double scheduling constraints into a single problem instance, referred to in this paper as the Vehicle Routing Problem with Multiple Constraints (VRPMC)
The results of the initial solution algorithm proposed in this paper demonstrate that multiple variants of the vehicle routing problem, i.e. multiple soft time windows, a heterogeneous fleet and double scheduling, may be integrated into a single initial solution algorithm

Summary

Introduction

The Vehicle Routing Problem (VRP) is a well-researched problem in the Operations Research literature. The basic VRP is based on a number of assumptions, such as utilizing a homogeneous fleet, a single depot, and allocating one route per vehicle These assumptions may be eliminated or relaxed by introducing additional constraints to the problem. The authors investigate the feasibility of integrating multiple soft time windows, a heterogeneous fleet and double scheduling constraints into a single problem instance, referred to in this paper as the Vehicle Routing Problem with Multiple Constraints (VRPMC). Gendreau et al [3] propose a solution methodology for cases where the fleet is heterogeneous, that is, where the fleet is composed of vehicles with different capacities and costs Their objective is to determine what the optimal fleet composition should be, and is referred to as either the Heterogeneous Fleet Vehicle Routing Problem (HVRP), or the Fleet Size and Mix Vehicle Routing Problem (FSMVRP).

An initial solution approach

Results

Conclusions