Fast optimised ridesharing: Objectives, reformulations and driver flexibility

•General formalisation for sustainable ridesharing schemes with flexible drivers.•Logical reformulations of spatio-temporal constraints of drivers’ intended paths.•Reformulations and state-of-the-art solver show order of magnitude improvement.•Compatibility between maximising mobility services and minimising driven distance. Ridesharing schemes, which match passengers to private car journeys with spare seats, are becoming popular for improving access, and reducing costs, emissions and congestion. Current deployed ridesharing systems offer matches to participants based on trip details and on preferences. They do not optimise for system-wide objectives that generally incur a high computational cost. Academic studies tend to focus on specific single objectives, while stakeholders and policy-makers for practical deployments may have many different, possibly vague, objectives. In this paper, we try to reduce the gap between research and deployed applications, and tackle the problem of computing global plans for a flexible ridesharing scheme, for different objectives. In a flexible scheme, some drivers are willing to leave their cars and become passengers of other drivers. We consider objectives to improve access (maximising served passengers), reduce emissions and congestion (minimising total distance), and to sustain the long-term viability of the system (maximising served users). In the studied scheme, riders reach a meeting point and are picked-up along the intended routes of the drivers. We show that when drivers can change roles and become passengers, a state-of-the-art solver is not able to solve quickly ridesharing schemes optimizing for global sustainable objectives. To handle this issue, we introduce new spatio-temporal constraints, based on the notion of time-consistent sets of riders, from which we derive new logical rules and routing properties. We encode the new properties and the derived logical rules within new ridesharing problem formulations. We show that solving the introduced formulations encoding the routing properties and the logical rules are up to one order of magnitude faster than the basic model, and that even for the larger instances with 1000s of users, achieves results within 2% and 5% of the optimal value within a time limit of 300 seconds. Our study also shows the interaction between the different objectives and to which extent satisfying one objective also satisfies other objectives. This study demonstrates that the introduced met