Contextual Stochastic Vehicle Routing with Time Windows

TL;DR

This paper introduces a new approach to vehicle routing with time windows that incorporates contextual features and stochastic travel times, using data-driven models and specialized algorithms to improve cost efficiency.

Contribution

It develops the first contextual stochastic VRPTW model with novel prescriptive methods and tailored algorithms, advancing the integration of feature variables into stochastic routing.

Findings

Feature-dependent sample average approximation outperforms other methods in most tests.

Specialized branch-price-and-cut algorithms effectively solve the proposed models.

Incorporating contextual features improves routing cost performance.

Abstract

We study the vehicle routing problem with time windows (VRPTW) and stochastic travel times, in which the decision-maker observes related contextual information, represented as feature variables, before making routing decisions. Despite the extensive literature on stochastic VRPs, the integration of feature variables has received limited attention in this context. We introduce the contextual stochastic VRPTW, which minimizes the total transportation cost and expected late arrival penalties conditioned on the observed features. Since the joint distribution of travel times and features is unknown, we present novel data-driven prescriptive models that use historical data to provide an approximate solution to the problem. We distinguish the prescriptive models between point-based approximation, sample average approximation, and penalty-based approximation, each taking a different perspective on dealing with stochastic travel times and features. We develop specialized branch-price-and-cut algorithms to solve these data-driven prescriptive models. In our computational experiments, we compare the out-of-sample cost performance of different methods on instances with up to one hundred customers. Our results show that, surprisingly, a feature-dependent sample average approximation outperforms existing and novel methods in most settings.