Commuting with Autonomous Vehicles: A Branch and Cut Algorithm with Redundant Modeling

TL;DR

This paper presents a novel branch and cut algorithm with redundant modeling for the CTSPAV, demonstrating significant reductions in vehicle counts, miles, and congestion in a case study, while analyzing associated tradeoffs.

Contribution

It introduces a combined MIP and DARP formulation approach for the CTSPAV, improving solution quality and computational efficiency over traditional methods.

Findings

Reduces vehicle counts by 92% in case study

Decreases vehicle miles by 30%

Cuts congestion by 60% during peak times

Abstract

This paper studies the benefits of autonomous vehicles in ride-sharing platforms dedicated to serving commuting needs. It considers the Commute Trip Sharing Problem with Autonomous Vehicles (CTSPAV), the optimization problem faced by a reservation-based platform that receives daily commute-trip requests and serves them with a fleet of autonomous vehicles. The CTSPAV can be viewed as a special case of the Dial- A-Ride Problem (DARP). However, this paper recognizes that commuting trips exhibit special spatial and temporal properties that can be exploited in a branch and cut algorithm that leverages a redundant modeling approach. In particular, the branch and cut algorithm relies on a MIP formulation that schedules mini routes representing inbound or outbound trips. This formulation is effective in finding high-quality solutions quickly but its relaxation is relatively weak. To remedy this limitation, the mini-route MIP is complemented by a DARP formulation which is not as effective in obtaining primal solutions but has a stronger relaxation. The benefits of the proposed approach are demonstrated by comparing it with another, more traditional, exact branch and cut procedure and a heuristic method based on mini routes. The methodological contribution is complemented by a comprehensive analysis of a CTSPAV platform for reducing vehicle counts, travel distances, and congestion. In particular, the case study for a medium-sized city reveals that a CTSPAV platform can reduce daily vehicle counts by a staggering 92% and decrease vehicles miles by 30%. The platform also significantly reduces congestion, measured as the number of vehicles on the road per unit time, by 60% during peak times. These benefits, however, come at the expense of introducing empty miles. Hence the paper also highlights the tradeoffs between future ride-sharing and car-pooling platforms.