Trip pricing of one-way station-based carsharing networks with zone and time of day price variations

• The proposed metaheuristic is applicable to different problem sizes.
• Bounds can be defined for the profit maximization problem.
• Trip pricing seems to be a good option to balance one-way carsharing vehicle stocks.
• Implementing trip pricing greatly increases profitability.

One-way station-based carsharing systems provide short term car rentals in which users can take a car from the initial station and return it to any other station. They are more flexible than round-trip carsharing, where the vehicle can only be returned to the station where it was picked up, and can be used for daily commuting trips as well. This flexibility, however, comes at a cost of vehicle stock imbalance within the network. Several solutions and strategies have been suggested to counter this problem, one of which is variable trip pricing. By charging high prices for the trips that increase imbalance and lowering prices for trips that help improve the balance, it has been hypothesized, but never demonstrated, that the clients’ behavior could be used to balance the vehicle stocks and thus make carsharing systems more manageable and profitable. In this paper, we develop a mixed integer non-linear programming (MINLP) model, defined as the Trip Pricing Problem for One-Way Carsharing Systems (TPPOCS), which sets these prices in order to maximize profit. An iterated local search (ILS) metaheuristic is proposed for solving it. The method is applied to the theoretical case-study of a network of 75 stations distributed across the city of Lisbon (Portugal). Although the implemented metaheuristic is tuned for the Lisbon example, the generic nature of its operators makes the model applicable elsewhere. The results demonstrate that the trip pricing strategy can be used to increase profit through a more balanced system. If no price-based balancing strategies are applied, operating this service results in a daily deficit of €1161. When the trip pricing policy is applied, profits of 2068 €/day are possible. The optimal prices are on average 23% higher than the base price, and 18% less demand is served, but the enhanced performance leads to lower expenses with the fleet of vehicles and number of parking spaces.