Fleet sizing for one-way electric carsharing services considering dynamic vehicle relocation and nonlinear charging profile

This study aims to determine the electric vehicle fleet size for one-way carsharing services by maximizing the profit of carsharing operators while taking into account the vehicle relocation operations and nonlinear electric vehicle charging profile. We formulate a set partitioning model for the considered problem. A tailored branch-and-price (B&P) approach is proposed to find the exact optimal solution of the model. In particular, an effective multi-label correcting method is developed to solve the pricing problem (i.e., generate columns) within the B&P approach. A novel non-dominated charging strategy is put up to avoid the exponential growth of labels caused by the allowance of partial charging with a nonlinear charging profile. In addition to the B&P approach, two heuristic methods are put forward for solving the large-scale problems or reinforcing the B&P approach. Numerical experiments with randomly generated instances and a case study based on a one-way carsharing operator in Singapore are conducted to further assess the efficiency and applicability of the proposed solution methods. The effects of several key parameters, i.e., the fixed cost of EV, relocation cost, electricity cost, service charge, EV driving range, the charging efficiency, and the number of rentals on the performance of a one-way electric carsharing system are also examined.