Minimizing Travel Time and Latency in Multi-Capacity Ride-Sharing Problems

Kelin Luo,Frits C R Spieksma

doi:10.3390/a15020030

Abstract

Motivated by applications in ride-sharing and truck-delivery, we study the problem of matching a number of requests and assigning them to cars. A number of cars are given, each of which consists of a location and a speed, and a number of requests are given, each of which consists of a pick-up location and a drop-off location. Serving a request means that a car must first visit the pick-up location of the request and then visit the drop-off location. Each car can only serve at most c requests. Each assignment can yield multiple different serving routes and corresponding serving times, and our goal was to serve the maximum number of requests with the minimum travel time (called CSsum) and to serve the maximum number of requests with the minimum total latency (called CSlat). In addition, we studied the special case where the pick-up and drop-off locations of a request coincide. Both problems CSsum and CSlat are APX-hard when c≥2. We propose an algorithm, called the transportation algorithm (TA), which is a (2c−1)-approximation (resp. c-approximation) algorithm for CSsum (resp. CSlat); these bounds are shown to be tight. We also considered the special case where each car serves exactly two requests, i.e., c=2. In addition to the TA, we investigated another algorithm, called the match-and-assign algorithm (MA). Moreover, we call the algorithm that outputs the best of the two solutions found by the TA and MA the CA. We show that the CA is a two-approximation (resp. 5/3) for CSsum (resp. CSlat), and these ratios are better than the ratios of the individual algorithms, the TA and MA.

Highlights

In the multi-capacity ride-sharing problem, we are given a set of cars D, each car k ∈ D located at location dk, and a set of requests R, each request r ∈ R consisting of a source sr and a destination tr
This paper is concerned with two objectives when assigning the maximum number of requests: one is to assign requests to the cars such that each car serves at most c requests while minimizing the total travel time, and the other problem is to assign requests to the cars such that each car serves at most c requests while minimizing the total waiting time incurred by customers that have submitted the requests
We call the ride-sharing problem with the objective of minimizing the total travel time CSsum and the special case of CSsum where the pick-up and drop-off locations are identical for each request CSsum,s=t ; Minimize total latency: In this problem, we considered assigning the maximum number of requests to cars, each with no more than c requests, to minimize the total waiting time, which is the sum of the travel times needed for each individual request to arrive at the destination

Summary

Introduction

In the multi-capacity ride-sharing problem, we are given a set of cars (or trucks) D, each car k ∈ D located at location dk , and a set of requests R, each request r ∈ R consisting of a source sr (pick-up location) and a destination tr (drop-off location). Serving a request means that a car first visits the pick-up location of the request (customer or parcel) and the drop-off location. Each car can serve multiple requests at the same time. This offers the opportunity to share rides, which may reduce the travel time or traffic congestion. This paper is concerned with two objectives when assigning the maximum number of requests (min{| R|, c · | D |} requests): one is to assign requests to the cars such that each car serves at most c requests while minimizing the total travel time, and the other problem is to assign requests to the cars such that each car serves at most c requests while minimizing the total waiting time (called total latency) incurred by customers that have submitted the requests

Objectives

Results

Discussion

Conclusion