2VRP: a benchmark problem for small but rich VRPs

TL;DR

This paper introduces 2VRP, a versatile benchmark problem for small yet complex vehicle routing problems, along with a polynomial solution for a related simplified case and a dynamic programming framework for the general problem.

Contribution

The paper presents a new benchmark problem 2VRP, a polynomial solution for a simplified 2TSP, and a dynamic programming framework for solving general 2VRP efficiently.

Findings

Algorithms perform exceptionally well on published test data.

Framework easily extends to various constraints in VRP.

Use of easy solvable cases for generating test instances enhances evaluation.

Abstract

We consider a 2-vehicle routing problem (2VRP) which can be viewed as a building block for the variety of vehicle routing problems (VRP). As a simplified version of the 2VRP, we consider a 2-period balanced travelling salesman problem (2TSP) and describe a polynomially solvable case of this NP-hard problem. For the 2VRP with general settings, we suggest a framework based on the Held and Karp dynamic programming algorithm. Our algorithms based on this framework show an exceptionally good performance on the published test data. Our approach can be easily extended to a variety of constraints/attributes in the VRP, hence the wording "small but rich" in the title of our paper. We also introduce a new methodological approach: we use easy solvable special cases for generating test instances and then use these instances in computational experiments.