The Line-Based Dial-a-Ride Problem

TL;DR

This paper introduces the line-based Dial-a-Ride problem (liDARP), a model combining fixed bus stop sequences with ridepooling flexibility, and presents efficient MILP formulations validated on real-world data.

Contribution

The paper proposes three MILP formulations for liDARP, demonstrating a fast, scalable approach that outperforms classical DARP in computational speed with minimal cost increases.

Findings

Event-Based graph formulation is the fastest MILP model.

liDARP is computationally faster than classical DARP.

Minimal increases in total distance and ride times compared to classical DARP.

Abstract

On-demand ridepooling systems offer flexible services pooling multiple passengers into one vehicle, complementing traditional bus services. We propose a transportation system combining the spatial aspects of a fixed sequence of bus stops with the temporal flexibility of ridepooling. In the line-based Dial-a-Ride problem (liDARP), vehicles adhere to a fixed, ordered sequence of stops in their routes, with the possibility of taking shortcuts and turning if they are empty. We propose three MILP formulations for the liDARP with a multi-objective function balancing environmental aspects with customer satisfaction, comparing them on a real-world bus line. Our experiments show that the formulation based on an Event-Based graph is the fastest, solving instances with up to 50 requests in under one second. Compared to the classical DARP, the liDARP is computationally faster, with minimal increases in total distance driven and average ride times.