Online Stochastic Planning for Taxi and Ridesharing

In this paper we consider the problem of on-line stochastic ride-sharing and taxi-sharing with time windows. We study a scenario in which people needing a taxi, or a ride, assign their source and destination points plus other restrictions (such as earlier time to departure and maximum time to reach a destination), at the same time, there are taxis or drivers interested in providing a ride (also with departure and destination points, vehicle capacity and time restrictions). We model the time window restrictions as a soft constraint (a reasonable delay might be acceptable in a realistic scenario), and consider the problem as an on-line continual planning problem, in which additional ride requests may arrive while plans for previous ride-matching are being executed. Finally, such new requests may arrive at each time step with some probability. The aim is to maximize the shared trips while minimising the expected travel delay for each trip. In this paper we propose an on-line stochastic optimization planning approach in which instead of myopically optimising for the offered trips and requested trips that are known, incorporate information that partially describes the stochastic future into the model in order to improve the quality of the solution. We prove the effectiveness of the method in a real world scenario using a number of instances extracted from a travel survey in north-eastern Illinois (USA) conducted by the Chicago Metropolitan Agency for Planning.