Efficient algorithms for ridesharing of personal vehicles

Abstract

Given a set of trips in a road network, where each trip has an individual, a vehicle and some requirements, the ridesharing problem is to select a subset of vehicles to deliver the individuals of all trips to their destinations satisfying the requirements. Common requirements of a trip include the source, destination, vehicle capacity, detour distance limit, preferred paths, and time constraints of the trip. Minimizing the total travel distance of the vehicles and minimizing the number of vehicles are major optimization goals. These minimization problems are complex and NP-hard because each trip may have many requirements. We study simplified minimization problems in which each trip's requirements are specified by the source, destination, vehicle capacity, detour distance and preferred path parameters. We show that both minimization problems can be solved in polynomial time if all of the following conditions are satisfied: (1) all trips have the same destination or same source; (2) no detour is allowed and (3) each trip has one unique preferred path. It is known that both minimization problems are NP-hard if any one of the three conditions is not satisfied. Our results and the NP-hard results suggest a boundary between the polynomial time solvable cases and NP-hard cases for the minimization problems.