Solving Large-Scale Dynamic Vehicle Routing Problems with Stochastic Requests

TL;DR

This paper introduces a novel approach for large-scale dynamic vehicle routing with stochastic requests, using knapsack-based models to optimize online scheduling and initial route planning, demonstrated on real street networks.

Contribution

It develops knapsack-based linear models for approximating expected rewards and integrates them into online scheduling policies for dynamic routing problems.

Findings

High-quality route plans and scheduling decisions achieved on large real-world instances.

Effective approximation of expected reward-to-go improves decision-making.

Proposed methods outperform existing approaches in large-scale scenarios.

Abstract

Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed dynamically with the goal of maximizing the number of served requests. We model the DVRPSR as a multi-stage optimization problem, where the first-stage decision defines route plans for serving scheduled requests. Our main contributions are knapsack-based linear models to approximate accurately the expected reward-to-go, measured as the number of accepted requests, at any state of the stochastic system. These approximations are based on representing each vehicle as a knapsack with a capacity given by the remaining service time available along the vehicle's route. We combine these approximations with optimal acceptance and assignment decision rules and derive efficient and high-performing online scheduling policies. We further leverage good predictions of the expected reward-to-go to design initial route plans that facilitate serving dynamic requests. Computational experiments on very large instances based on a real street network demonstrate the effectiveness of the proposed methods in prescribing high-quality offline route plans and online scheduling decisions.