Vehicle repositioning for a ride-sourcing network system providing differentiated services

The increasing trend on adopting ride-sourcing services has brought obvious benefits to short-haul transportation systems. In this paper, we investigate a dynamic ride-sourcing system, where, in each period, a constant number of vehicles (fixed system capacity) is used to satisfy random customer demands or is reallocated within an under-investigation network. To save resources, our objective is to deploy the smallest number of vehicles to satisfy the network system with differentiated service levels. Unlike the common approaches that achieve an equilibrium solution to match supply and demand by implementing a proper pricing and waging policies, based on the fixed vehicle capacity, we need to explicitly confront the region-to-region imbalance in the system by using appropriate reallocation strategies. We first formulate a framework for this type of ride-sourcing system and investigate the lower and upper bounds for the optimal vehicle capacity. Then, we discuss the conditions of obtaining the lower bound and the optimality of the upper bound. Based on the proposed model, we further design some heuristics to appropriately reallocate the vehicles. In particular, we introduce a benchmark heuristic that robustly performs between the lower and upper bounds. A variety of experiments are conducted to validate this benchmark for a wide choice of potential settings. Finally, besides satisfying the differentiated service levels, we generalize the model by incorporating the operation costs of maintaining the vehicle fleet, route dependent costs, and unequal travel times to adapt some common real-world situations.