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

Matteo Garbelli

TL;DR

This work addresses stochastic vehicle routing under uncertain service durations by embedding ML-based duration forecasts into a SVRP framework. It combines XGBoost forecasts with calibrated sub-Gaussian risk buffers and a multi-objective NSGA-III evolutionary algorithm to balance travel cost, tardiness, overtime, and service coverage. The authors introduce dual, variance-aware forecast architectures to capture heterogeneity in intervention types (notably Type-Z meter replacements) and validate the approach on eight years of gas-meter data, reporting 20-25% improvements in operator utilization and task completion versus default durations. The framework demonstrates practical viability for utility workforce planning, offering risk-aware, forecast-informed routing with scalable training and fast online inference. The study also provides a structured integration of uncertainty quantification into optimization, enabling principled route-level buffers and robust decision-making in real-world settings.

Abstract

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.

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

TL;DR

This work addresses stochastic vehicle routing under uncertain service durations by embedding ML-based duration forecasts into a SVRP framework. It combines XGBoost forecasts with calibrated sub-Gaussian risk buffers and a multi-objective NSGA-III evolutionary algorithm to balance travel cost, tardiness, overtime, and service coverage. The authors introduce dual, variance-aware forecast architectures to capture heterogeneity in intervention types (notably Type-Z meter replacements) and validate the approach on eight years of gas-meter data, reporting 20-25% improvements in operator utilization and task completion versus default durations. The framework demonstrates practical viability for utility workforce planning, offering risk-aware, forecast-informed routing with scalable training and fast online inference. The study also provides a structured integration of uncertainty quantification into optimization, enabling principled route-level buffers and robust decision-making in real-world settings.

Abstract

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.
Paper Structure (33 sections, 1 theorem, 24 equations, 17 figures, 3 tables, 1 algorithm)

This paper contains 33 sections, 1 theorem, 24 equations, 17 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Organization of the paper
  3. Literature Review
  4. Solving the VRP via Evolutionary Algorithm
  5. The Capacitated VRP with uncertain activity durations
  6. The optimization algorithm
  7. Predictive algorithms for informed optimization methods
  8. Mathematical Framework and Architecture Overview
  9. Model Architectures
  10. 1) Standard Gradient Boosting Model
  11. 2) Frequency-Weighted Gradient Boosting Model
  12. Dual Models
  13. 3) Dual Models Architecture
  14. 4) Dual Models with Frequency Weighting
  15. Residual Analysis.
  16. ...and 18 more sections

Key Result

Proposition 3.1

Let $R_k$ be the sequence of customers on vehicle $k$'s route and suppose $S_i=\mu_i+\varepsilon_i$ with independent sub-Gaussian $\varepsilon_i$ having proxy variances $\sigma_i^2$. If then $\mathbb{P}\{T_{n+1,k}-T_{0k} \le H_k\}\ge 1-\alpha_k$.

Figures (17)

  • Figure 1: Training framework for duration prediction.
  • Figure 2: Inference framework for operational deployment.
  • Figure 3: Distribution of prediction residuals ($\hat{y} - y$) from the Dual Weighted forecast model. The symmetric, bell-shaped curve supports the sub-Gaussian assumption used for risk modeling.
  • Figure 4: Duration predictions with uncertainty estimates.
  • Figure 5: (a) Original and smoothed duration distributions. (b) Corresponding probability density functions showing the smoothing effect.
  • ...and 12 more figures

Theorems & Definitions (3)

  • Proposition 3.1: Route-level chance feasibility via sub-Gaussian buffer
  • proof
  • Remark 3.1