A Branch-and-Cut algorithm for an urban dial-a-ride problem

TL;DR

This paper presents a Branch-and-Cut algorithm for urban dial-a-ride problems, improving solution quality and bounds by leveraging fixed path information and valid inequalities, tested on instances with up to 120 customers.

Contribution

The paper introduces a novel Branch-and-Cut algorithm with a new infeasibility detection technique and valid inequalities for urban dial-a-ride problems, enhancing solution efficiency.

Findings

Achieves more optimal solutions than MIP formulations.

Provides tighter lower and upper bounds.

Effective on instances with up to 120 customers.

Abstract

The paper investigates a dial-a-ride problem focusing on the residents of large cities. These individuals have the opportunity to use a wide variety of transportation modes. Because of this, ridepooling providers have to solve the tradeoff between a high pooling rate and a small detour for customers to be competitive. We provide a Branch-and-Cut algorithm for this problem setting and introduce a new technique using information about already fixed paths to identify infeasible solutions ahead of time and to improve lower bounds on the arrival times at customer locations. By this, we are able to introduce additional valid inequalities to improve the search. We evaluate our procedure in an extensive computational study with up to 120 customers and ten vehicles. Our procedure finds significantly more optimal solutions and better lower and upper bounds in comparison with a mixed-integer programming formulation.