A Set Cover Mapping Heuristic for Demand-Robust Fleet Size Vehicle Routing Problem with Time Windows and Compatibility Constraints

TL;DR

This paper introduces a set cover heuristic for large-scale demand-robust vehicle routing with time windows and compatibility constraints, demonstrating efficiency and effectiveness through empirical evaluation.

Contribution

It presents the first large-scale solution approach for demand-robust vehicle routing, combining MILP formulation with a polynomial-time heuristic based on set cover.

Findings

Heuristic maintains an approximation ratio below 2.0.

Time complexity of the heuristic scales exponentially with problem size.

Empirical results outperform Gurobi on large instances.

Abstract

We study the demand-robust fleet size vehicle routing problem with time windows and compatibility constraints. Unlike traditional robust optimization, which considers uncertainty in the data, demand-robust optimization considers uncertainty in which constraints must be satisfied. This paper is the first to solve a practical demand-robust optimization problem at large scale. We present an MILP formulation and also propose a heuristic that maps the problem to set cover in polynomial time. We show that under modest assumptions the relative difference in time complexity from a standard branch-and-bound algorithm to the proposed heuristic scales exponentially with the size of the problem. We evaluate our heuristic using a simulation case study on the Solomon benchmark instances for a variety of practical problem sizes, and compare with Gurobi. The empirical approximation ratio remains below 2.0.