Heuristic algorithms for the operator-based relocation problem in one-way electric carsharing systems

•Economic sustainability of E-VReP in one way carsharing systems was addressed.•Computational complexity and APX-hardness is addressed.•Heuristics were designed to overcome the drawback of the high CPU times of the MILP.•Variable revenues associated with requests satisfied were also considered.•Sensitivity analysis was carried out on the number of requests and the revenue.

This paper addresses an Electric Vehicle Relocation Problem (E-VReP), in one-way carsharing systems, based on operators who use folding bicycles to facilitate vehicle relocation. In order to calculate the economic sustainability of this relocation approach, a revenue associated with each relocation request satisfied and a cost associated with each operator used are introduced. The new optimization objective maximizes the total profit. To overcome the drawback of the high CPU time required by the Mixed Integer Linear Programming formulation of the E-VReP, two heuristic algorithms, based on the general properties of the feasible solutions, are designed. Their effectiveness is tested on two sets of realistic instances. In the first, all the requests have the same revenue, while, in the second, the revenue of each request has a variable component related to the user's rent-time and a fixed part related to customer satisfaction. Finally, a sensitivity analysis is carried out on both the number of requests and the fixed revenue component.