Optimizing Strategic and Operational Decisions of Car Sharing Systems under Demand Uncertainty and Substitution

Optimizing car sharing systems under demand uncertainty is an emerging problem for ensuring profitable and sustainable operations of these services while taking into account quality of service concerns. With the increasing adoption of electric vehicles and environmental awareness, this problem requires consideration of a mix fleet of vehicles with gasoline-powered and electric, complicating the strategic and operational planning as the demand of each vehicle type are observed. To address this problem, we propose a two-stage stochastic mixed-integer program leveraging spatial-temporal networks that capture the strategic and operational decisions of these systems over a multi-period planning horizon. We optimize the location decisions of regions to serve with purchasing decisions of the vehicles in the first-stage problem under budget and carbon emission considerations in designing the fleet, while considering parking capacities, satisfying one-way and round-trip car rental requests, and relocating cars between open regions under each demand realization in the second-stage problem. We then introduce demand substitution to this problem by extending and generalizing the multi-commodity formulation, and allowing satisfaction of customer demand of each vehicle type with its alternatives. We further prove that the corresponding second-stage problem has a totally unimodular constraint matrix. By benefiting from this result, as our solution approach, we provide a branch-and-cut based decomposition algorithm with enhancements. We present an extensive computational study highlighting the value of the proposed models from different perspectives and demonstrating the performance of the proposed solution algorithm with significant speedups. Introducing substitution to the car sharing operations leads to higher quality of service and flexibility in operations with lower costs under various settings.