An asymptotically optimal algorithm for pickup and delivery problems

Abstract

Abstract-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 operations. One particular 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 a route optimization problem behind several transportation systems, e.g., Transportation-On-Demand (TOD) systems. The SCP is NP-Hard and the best know approximation algorithm only provides a 9/5 approximation ratio. We present an algorithm for the stochastic SCP which: (i) is asymptotically optimal, i.e., it produces a solution approaching the optimal one as the number of pickups/deliveries goes to infinity; and (ii) has computational complexity O(n 2+ ), where n is the number of pickup/delivery pairs and is an arbitrarily small positive constant. Our results leverage a novel connection between the Euclidean Bipartite Matching Problem and the theory of random permutations.

Dynamic traffic congestion pricing mechanism with User-Centric considerations

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Cost bounds for Pickup and Delivery Problems with application to large-scale transportation systems

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Simulation Framework for Rebalancing of Autonomous Mobility on Demand Systems

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“…The review is built upon work discussed in [5,[11][12][13][14]. [3,4] is published in continuance of [2,5,9,11].…”

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