A Set Cover Mapping Heuristic for Demand-Robust Fleet Size Vehicle Routing Problem with Time Windows and Compatibility Constraints
摘要
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.
引用
@article{arxiv.2406.07719,
title = {A Set Cover Mapping Heuristic for Demand-Robust Fleet Size Vehicle Routing Problem with Time Windows and Compatibility Constraints},
author = {Jordan Makansi},
journal= {arXiv preprint arXiv:2406.07719},
year = {2024}
}