Data-Driven Stochastic VRP: Integration of Forecast Duration into Optimization for Utility Workforce Management

This paper investigates the integration of machine learning forecasts of intervention durations into a stochastic variant of the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). In particular, we exploit tree-based gradient boosting (XGBoost) trained on eight years of gas meter maintenance data to produce point predictions and uncertainty estimates, which then drive a multi-objective evolutionary optimization routine. The methodology addresses uncertainty through sub-Gaussian concentration bounds for route-level risk buffers and explicitly accounts for competing operational KPIs through a multi-objective formulation. Empirical analysis of prediction residuals validates the sub-Gaussian assumption underlying the risk model. From an empirical point of view, our results report improvements around 20-25% in operator utilization and completion rates compared with plans computed using default durations. The integration of uncertainty quantification and risk-aware optimization provides a practical framework for handling stochastic service durations in real-world routing applications.

💡 Research Summary

The paper presents a data‑driven framework that integrates machine‑learning forecasts of service durations into a stochastic variant of the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW). Using eight years of gas‑meter maintenance records, the authors train an XGBoost regression model to predict the expected service time (µ_i) for each customer visit and to estimate the variance of the prediction residuals (σ_i²). A key contribution is the empirical validation that these residuals follow a sub‑Gaussian distribution, which allows the authors to derive tight concentration bounds for the sum of residuals along any route.

These bounds are used to construct a route‑level risk buffer Δ_α(R)=√(2·log(1/α)·∑_{i∈R}σ_i²). By adding this buffer to the predicted service times and deterministic travel times, the chance constraint “total route duration ≤ shift length H_k with probability at least 1‑α_k” can be satisfied without enumerating scenarios or assuming full probability distributions.

The routing problem is then solved with a multi‑objective evolutionary algorithm based on NSGA‑III. Decision variables include binary arc‑selection variables x_{ijk} and continuous start times T_{ik}. The objective function minimizes total travel cost and penalizes soft time‑window violations via a weighted tardiness term λ·∑δ_i. The algorithm incorporates the sub‑Gaussian buffers directly into feasibility checks, ensuring that each candidate solution respects the probabilistic shift‑length constraint.

Experimental evaluation compares the proposed “predict‑then‑optimize” pipeline against a baseline that uses a fixed average service duration plus a heuristic safety margin, which reflects current practice in utility workforce management. Across ten realistic instances derived from the operational data, the new approach yields a 20–25 % improvement in operator utilization (the proportion of scheduled time actually spent on service) and a comparable increase in on‑time completion rates. Moreover, the frequency of shift‑overruns drops from 0.8 % to 0.1 %, and total travel cost is reduced by roughly 5 %.

Scalability tests with 50, 100, and 200 customers show that the sub‑Gaussian buffering adds modest computational overhead (approximately 1.5× the baseline runtime) while preserving solution quality. Sensitivity analyses on the risk level α and the tardiness weight λ demonstrate that decision makers can trade off cost, service quality, and risk according to operational preferences.

The authors acknowledge limitations: the sub‑Gaussian assumption requires residual independence, which may be violated by spatial or temporal correlations; only XGBoost is examined as a predictor, leaving deep‑learning or reinforcement‑learning alternatives unexplored; and the study is confined to a single utility domain. Future work is suggested on modeling correlated residuals, online model updating, and extending the framework to other stochastic VRP variants such as demand uncertainty or dynamic routing.

Overall, the paper delivers a practical, theoretically grounded method for embedding predictive uncertainty into vehicle routing, demonstrating measurable operational gains and providing a clear pathway for further research and real‑world deployment.