Implementing Horizontal Cooperation in Public Transport and Parcel Deliveries: The Cooperative Share-A-Ride Problem

The static share-a-ride problem (SARP) consists of handling people and parcels in an integrated way through the same vehicle, which provides a shared trip between an origin and a destination, in response to requests received in advance. When multiple providers compete on the same market (for instance, within the same city or region), horizontal cooperation can be an efficient strategy to consolidate all requests and to optimize the total payoff. This situation gives rise to the cooperative SARP (coop-SARP). In this problem, multiple depots and heterogeneous vehicles must be considered and different cooperation levels may be agreed upon by service providers. In this paper, we propose a new mathematical programming formulation for cooperative SARP along with theoretical bounds. Moreover, through numerical experiments and ad hoc statistics, we analyze the benefits of different levels of horizontal cooperation between service providers. The results show that cooperation leads to reduced travel times and to improved vehicle occupancy rates, service levels, and profits, which make such a cooperative system even more appealing for service providers.