Abstract-One-way carsharing systems allow travelers to pick up a car at one station and return it to a different station, thereby causing vehicle imbalances across the stations. In this paper, realistic ways to mitigate that imbalance by relocating vehicles are discussed. Also presented are a new mathematical model to optimize relocation operations that maximize the profitability of the carsharing service and a simulation model to study different real-time relocation policies. Both methods were applied to networks of stations in Lisbon Portugal. Results show that real time relocation policies, and these policies when combined with optimization techniques, can produce significant increases in profit. In the case where the carsharing system provides maximum coverage of the city area, imbalances in the network resulted in an operating loss of 1160 €/day when no relocation operations were performed. When relocation policies were applied, however, the simulation results indicate that profits of 854 €/day could be achieved, even with increased costs due to relocations. This improvement was achieved through reductions in the number of vehicles needed to satisfy demand and the number of parking spaces needed at stations. This is a key result that demonstrates the importance of relocation operations for sustainably providing a more comprehensive network of stations in one-way carsharing systems, thus reaching a higher number of users in a city. IndexTerms-Mathematical programming, one-way carsharing, relocation operations, simulation.

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Car-sharing systems are an alternative to private transportation whereby a person may use an automobile without having to own the vehicle. The classical systems in Europe are organized in stations scattered around the city where a person may pick up a vehicle and afterward return it to the same station (round trip). Allowing a person to drop off the vehicle at any station, called one-way system, poses a significant logistics problem because it creates a significant stock imbalance at the stations, which means that there will be times when users will not have a vehicle available for their trip. Previous mathematical programming formulations have tried to overcome this limitation by optimizing trip selection and station location in a city in order to capture the best trips for balancing the system. But there was one main limitation: The users were assumed to be inflexible with respect to their choice of a station, and held to use only the one closest to their origin and destination. If the user is willing to use the second or even the third closest station the user could benefit from using real-time information on vehicle stocks at each station and be able to select the one with available capacity. In this article we extend a previous model for trip selection and station location that takes that aspect into account by considering more vehicle pick-up and drop-off station options and then apply it to a trip origin-destination matrix from the Lisbon region in Portugal. Through the extended formulation we were able to conclude that user flexibility allied with having information on vehicle stocks increases the profit of the company, as people will go directly to a station with a vehicle available, thus making the use of the fleet more efficient. Observing the size of the stations resulting from the model, we also concluded that the effect of information is enhanced by large car-sharing systems consisting of many small stations.

a b s t r a c tAlthough one-way carsharing is suitable for more trip purposes than round-trip carsharing, many companies in the world operate only in the round-trip market. In this paper, we develop a method that optimizes the design of a one-way carsharing service between selected origin-destination pairs of an existing round-trip carsharing system. The goal is to supplement the established round-trip services with new one-way services and increase profitability. We develop an integer programming model to select the set of new one-way services and apply it to the case study of Boston, USA, considering only trips with one endpoint at a station in the round-trip Zipcar service network and the other endpoint at Logan Airport. The airport was chosen as a necessary endpoint for a one-way service because it is a very significant trip generator for which the round-trip carsharing is not suitable. Results show that these supplemental one-way services could be profitable. Enabling relocation operations between the existing round-trip stations and the Airport greatly improves the demand effectively satisfied, leads to an acceptable airport station size (in terms of the number of parking spots required), and is profitable; however, these benefits come with the need to manage relocation operations.

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