Recent Advances in Vehicle Routing with Stochastic Demands: Bayesian Learning for Correlated Demands and Elementary Branch-Price-and-Cut

TL;DR

This paper introduces a new branch-price-and-cut algorithm for the vehicle routing problem with stochastic demands, incorporating Bayesian learning for correlated demands, leading to significant cost savings and improved solution methods.

Contribution

The paper presents a novel BP&C algorithm for VRPSD with optimal restocking and a Bayesian demand model for correlated demands, advancing solution techniques and demand modeling.

Findings

The new BP&C algorithm solves several open benchmark instances.

Accounting for demand correlation reduces costs by over 10%.

Bayesian learning refines demand estimates as data is revealed.

Abstract

We consider the vehicle routing problem with stochastic demands (VRPSD), a stochastic variant of the well-known VRP in which demands are only revealed upon arrival of the vehicle at each customer. Motivated by the significant recent progress on VRPSD research, we begin this paper by summarizing the key new results and methods for solving the problem. In doing so, we discuss the main challenges associated with solving the VRPSD under the chance-constraint and the restocking-based perspectives. Once we cover the current state-of-the-art, we introduce two major methodological contributions. First, we present a branch-price-and-cut (BP&C) algorithm for the VRPSD under optimal restocking. The method, which is based on the pricing of elementary routes, compares favorably with previous algorithms and allows the solution of several open benchmark instances. Second, we develop a demand model for dealing with correlated customer demands. The central concept in this model is the "external factor", which represents unknown covariates that affect all demands. We present a Bayesian-based, iterated learning procedure to refine our knowledge about the external factor as customer demands are revealed. This updated knowledge is then used to prescribe optimal replenishment decisions under demand correlation. Computational results demonstrate the efficiency of the new BP&C method and show that cost savings above 10% may be achieved when restocking decisions take account of demand correlation. Lastly, we motivate a few research perspectives that, as we believe, should shape future research on the VRPSD.