# The Commute Trip Sharing Problem

## TL;DR

This paper formalizes the Commute Trip Sharing Problem (CTSP) to optimize carpooling by matching riders and drivers, introducing exact algorithms, and demonstrating significant potential reductions in vehicle usage and miles traveled.

## Contribution

It introduces the CTSP, a comprehensive vehicle routing model for ride sharing, and develops two exact algorithms to solve it efficiently.

## Key findings

- Algorithms solve small and medium problems optimally.
- Carpooling can reduce vehicle usage by up to 57%.
- Vehicle miles traveled can decrease by up to 46%.

## Abstract

Parking pressure has been steadily increasing in cities as well as in university and corporate campuses. To relieve this pressure, this paper studies a car-pooling platform that would match riders and drivers, while guaranteeing a ride back and exploiting spatial and temporal locality. In particular, the paper formalizes the Commute Trip Sharing Problem (CTSP) to find a routing plan that maximizes ride sharing for a set of commute trips. The CTSP is a generalization of the vehicle routing problem with routes that satisfy time window, capacity, pairing, precedence, ride duration, and driver constraints. The paper introduces two exact algorithms for the CTPS: A route-enumeration algorithm and a branch-and-price algorithm. Experimental results show that, on a high-fidelity, real-world dataset of commute trips from a mid-size city, both algorithms optimally solve small and medium-sized problems and produce high-quality solutions for larger problem instances. The results show that car pooling, if widely adopted, has the potential to reduce vehicle usage by up to 57% and decrease vehicle miles traveled by up to 46% while only incurring a 22% increase in average ride time per commuter for the trips considered.