The objective of this work is to provide analytical guidelines and financial justification for the design of shared-vehicle mobility-on-demand systems. Specifically, we consider the fundamental issue of determining the appropriate number of vehicles to field in the fleet, and estimate the financial benefits of several models of car sharing. As a case study, we consider replacing all modes of personal transportation in a city such as Singapore with a fleet of shared automated vehicles, able to drive themselves, e.g., to move to a customer's location. Using actual transportation data, our analysis suggests a shared-vehicle mobility solution can meet the personal mobility needs of the entire population with a fleet whose size is approximately 1/3 of the total number of passenger vehicles currently in operation.

Pickup and delivery problems (PDPs), in which objects or people have to be transported between specific locations, are among the most common combinatorial problems in real-world logistical operations. A widely-encountered type of PDP is the Stacker Crane Problem (SCP), where each commodity/customer is associated with a pickup location and a delivery location, and the objective is to find a minimum-length tour visiting all locations with the constraint that each pickup location and its associated delivery location are visited in consecutive order. The SCP is NP-Hard and the best known approximation algorithm only provides a 9/5 approximation ratio. The objective of this paper is threefold. First, by embedding the problem within a stochastic framework, we present a novel algorithm for the SCP that: (i) is asymptotically optimal, i.e., it produces, almost surely, a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; and (ii) has computational complexity O(n 2+ε ), where n is the number of pickup/delivery pairs and ε is an arbitrarily small positive constant. Second, we asymptotically characterize the length of the optimal SCP tour. Finally, we study a dynamic version of the SCP, whereby pickup and delivery requests arrive according to a Poisson process, and which serves as a model for large-scale demand-responsive transport (DRT)systems. For such a dynamic counterpart of the SCP, we derive a necessary and sufficient condition for the existence of stable vehicle routing policies, which depends only on the workspace geometry, the stochastic distributions of pickup and delivery points, the arrival rate of requests, and the number of vehicles. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations, and, for the dynamic setting, exhibit novel features that are absent in traditional spatially-distributed queueing systems.

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