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.

Delays and disruptions in airline operations annually result in billions of dollars of additional costs to airlines, passengers, and the economy. Airlines strive to mitigate these costs by creating schedules that are less likely to get disrupted or schedules that are easier to repair when there are disruptions. In this paper, we present a robust optimization model for the crew pairing problem, which generates crew schedules that are less likely to get disrupted. Our model allows adding robustness without requiring detailed knowledge of the underlying delay distributions. Moreover, our model allows us to capture in detail the delay propagation through crew connections and the complex cost structure of the pay-and-credit crew salary scheme, thus enabling us to find a good trade-off between the deterministic component of the planned costs on the one hand and the expected delay and disruption costs on the other hand. Our robust crew pairing model is based on a deterministic crew pairing model formulated as a mixed-integer linear program. The robust version that we propose retains the linearity of the constraints and objective function and thus can be handled by commercial solvers, which facilitates its implementation in practice. We propose and implement a new solution algorithm for solving our model to optimality. Several optimal solutions with varying robustness levels are compared for the network of a moderate-size airline in the United States. We test the model’s solutions in a simulation environment using real-world delay data. Our simulation results show that the robust crew pairing solutions lead to lower delays and fewer instances of operational infeasibilities, thus requiring fewer recovery actions to address them. We find that, with the inclusion of robustness, it is possible to generate crew pairing solutions that significantly reduce the delay and disruption costs with only a small increase in planned costs.