# Contextual Stochastic Vehicle Routing with Time Windows

arXiv: https://arxiv.org/abs/2402.06968 · HTML: https://mlsanity.com/paper/2402.06968/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 10 Feb 2024.

## Builds on (most cited first, 11 of 11)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems](https://mlsanity.com/paper/1911.10092/) (2019)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [PyEPO: A PyTorch-based End-to-End Predict-then-Optimize Library for Linear and Integer Programming](https://mlsanity.com/paper/2206.14234/) (2022)
- [Dynamic optimization with side information](https://mlsanity.com/paper/1907.07307/) (2019)
- [From Predictions to Prescriptions in Multistage Optimization Problems](https://mlsanity.com/paper/1904.11637/) (2019)
- [Optimization over Continuous and Multi-dimensional Decisions with Observational Data](https://mlsanity.com/paper/1807.04183/) (2018)
- [Bilevel Optimization for Feature Selection in the Data-Driven Newsvendor Problem](https://mlsanity.com/paper/2209.05093/) (2022)
- [Recent Advances in Vehicle Routing with Stochastic Demands: Bayesian Learning for Correlated Demands and Elementary Branch-Price-and-Cut](https://mlsanity.com/paper/2302.02538/) (2023)

## Built on by (most cited first, 1 of 1)

- [Data-Driven Stochastic VRP: Integration of Forecast Duration into Optimization for Utility Workforce Management](https://mlsanity.com/paper/2601.07514/) (2026)

## Abstract (arXiv)

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.