Solving the Line-Based Dial-a-Ride Problem by Generating Stopping Patterns

TL;DR

This paper introduces a new variant of the line-based dial-a-ride problem without time windows, proposing a MILP formulation and a branch-and-price algorithm that efficiently generates stopping patterns for practical large-scale transportation problems.

Contribution

It develops a novel MILP formulation and a branch-and-price algorithm for liDARP without time windows, improving solution scalability and speed for large instances.

Findings

The branch-and-price algorithm finds solutions with less than 5% gap in 60 minutes.

The root node heuristic scales to 100 requests and reaches near-optimal solutions within 15 minutes.

The method outperforms state-of-the-art approaches in computational experiments.

Abstract

In the line-based dial-a-ride problem (liDARP), vehicles operate along a predefined bus line, with the possibility of skipping stations and turning when empty. Motivated by the practical observation that tight passenger time windows often limit pooling in on-demand services, we introduce a new variant of this transportation system by removing all temporal constraints, which we call the liDARP without TWs. We introduce a new MILP formulation for the liDARP without TWs, which constructs feasible tours as sequences of stopping patterns; first, we consider a fundamental single-vehicle, single-pass special case. Based on our insights, we develop a branch-and-price algorithm where the pricing problem generates profitable stopping patterns. For practical applications, we additionally propose a root node heuristic, using the stopping patterns generated at the root node. Computational experiments show that our branch-and-price algorithm is competitive, finding solutions with a MIP gap of less than 5% for large instances in 60 minutes. Further, the root node heuristic scales to instances with up to 100 requests, outperforming the state-of-the-art and reaching optimality gaps of less than 5% within 15 minutes. This method is highly effective in generating solutions for practical applications, where solving large problems quickly is more valuable than reaching optimality.