Offline Vehicle Routing Problem with Online Bookings: A Novel Problem Formulation with Applications to Paratransit

TL;DR

This paper introduces a new vehicle routing problem formulation for paratransit services that combines offline trip planning with online booking constraints, and proposes a novel solution approach validated on real-world data.

Contribution

It formulates the offline vehicle routing problem with online bookings, addressing a gap in existing VRP models, and develops a combined anytime algorithm and learning-based policy for real-time decision making.

Findings

Significantly improved routing outcomes over existing algorithms

Effective handling of large request sets with strict time constraints

Validated approach on real-world paratransit data from Chattanooga, TN

Abstract

Vehicle routing problems (VRPs) can be divided into two major categories: offline VRPs, which consider a given set of trip requests to be served, and online VRPs, which consider requests as they arrive in real-time. Based on discussions with public transit agencies, we identify a real-world problem that is not addressed by existing formulations: booking trips with flexible pickup windows (e.g., 3 hours) in advance (e.g., the day before) and confirming tight pickup windows (e.g., 30 minutes) at the time of booking. Such a service model is often required in paratransit service settings, where passengers typically book trips for the next day over the phone. To address this gap between offline and online problems, we introduce a novel formulation, the offline vehicle routing problem with online bookings. This problem is very challenging computationally since it faces the complexity of considering large sets of requests -- similar to offline VRPs -- but must abide by strict constraints on running time -- similar to online VRPs. To solve this problem, we propose a novel computational approach, which combines an anytime algorithm with a learning-based policy for real-time decisions. Based on a paratransit dataset obtained from the public transit agency of Chattanooga, TN, we demonstrate that our novel formulation and computational approach lead to significantly better outcomes in this setting than existing algorithms.