Optimizing strategic and operational decisions of car sharing systems under demand uncertainty and substitution

Car sharing is an efficient way to improve mobility, reduce the use of personal vehicles, and lessen the associated carbon emissions. Due to increasing environmental awareness of customers and government regulations, car sharing providers must be careful about the composition of their vehicle fleet to meet diverse customer demand through vehicle types with different carbon emission levels. In this study, for a car sharing company, we consider the problems of determining service regions and purchasing decisions with a mixed fleet of vehicles under budget and carbon emission constraints, and the deployment of these vehicles to service regions under uncertain one-way and round-trip rental requests over a multi-period planning horizon. We further introduce the concept of “substitution” to the car sharing operations that provides customers with alternative vehicle options when their preferred type is unavailable. To address this complex problem, we propose a novel two-stage stochastic mixed-integer program leveraging spatial–temporal networks and multicommodity flows to capture these strategic and operational decisions of this system over the planning horizon while allowing substitution in operations. We further prove that the corresponding second-stage problem of the proposed program has a totally unimodular constraint matrix. Taking advantage of this result, we develop a branch-and-cut-based decomposition algorithm with various computational enhancements. We present an extensive computational study that highlights the value of the proposed models from different perspectives and demonstrates the performance of the proposed solution algorithm with significant speedups. Our case study provides insights for region opening and fleet allocation plans under demand uncertainty and demonstrates the value of introducing substitution to car sharing operations and the importance of integrating strategic and operational decisions and obtaining stochastic solutions.