On the approximability and energy-flow modeling of the electric vehicle sharing problem

• Published in: Computers & industrial engineering Vol. 192; p. 110181
• Main Authors: Silva, Welverton R., Usberti, Fábio L., Schouery, Rafael C.S.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-06-2024
• Subjects: Electric vehicle; Mixed-integer linear programming; One-way car-sharing; One-way car-sharing; Electric vehicle; Mixed-integer linear programming
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2024.110181

The electric vehicle sharing problem (EVSP) arises from the planning and operation of one-way electric car-sharing systems. It aims to maximize the total rental time of a fleet of electric vehicles while ensuring that all the demands of the customer are fulfilled. In this paper, we first show that the EVSP is NP-hard to approximate to within a factor of n1−ϵ in polynomial time, for any ϵ>0, where n denotes the number of customers. In addition, we also show that the problem does not have a monotone structure, which can be detrimental to the development of heuristics employing constructive strategies. Moreover, we propose a novel approach for modeling the EVSP based on energy flows. Based on this new model, we propose a relax-and-fix strategy and an exact algorithm. Our computational results show that our formulation outperforms the previous best-performing formulation in the literature in the number of optimal solutions obtained, optimality gaps, and computational times. Previously, 32.7% of the instances remained unsolved (within a time limit of one hour), while our formulation obtained optimal solutions for all instances. To stress our approaches, two more challenging new sets of instances are generated, for which we can solve 49.5% of the instances, with an average optimality gap of 2.91% for those not solved optimally.
•We study the approximability of the electric vehicle sharing problem (EVSP).•A new formulation is proposed, considering energy flows in the network.•A relax-and-fix heuristic is developed, aiming high-quality solutions in short time.•An exact algorithm with reduced-cost variable-fixing is shown effective for large instances.•Extensive computational experiments are conducted on new benchmark instances.