Optimal Scheduling of a Finite Capacity Shuttle under Delayed Information

We consider the optimal scheduling of a nite capacity shuttle in a two node network with imperfect information. When shuttle trips do not depend on the number of passengers carried, we prove optimality and monotonicity of threshold policies. We derive conditions for dispatching which reduce the computational eeort required to compute an optimal threshold policy. We provide a counterexample to the optimality of threshold policies for nite horizon problems where trip lengths increase stochastically in the number of passengers carried. 1 The signiicant role of transportation, communication, and manufacturing networks in today's society motivates the need to develop further insight into the fundamental issues of control and optimization associated with these networks. An open issue for networks is control in the absence of complete state observations. Transportation and communication networks are often characterized by nodes that act individually, each possessing only a local knowledge of its immediate environment. Even when information can be exchanged among nodes, there are propagation and processing delays; also, faults and transmission errors may render the data inaccurate. Thus, an understanding of the eeects of partial information on optimal control policies will be useful for eeectively designing and controlling networks in which incomplete (imperfect) information is a realistic consideration. As a modest step in this direction we focus on the eeect that delayed observations have on an optimal shuttle scheduling policy in a simple two-node transportation network. In discrete time, we examine a two terminal network with a single, nite capacity shuttle providing transportation between the terminals. Passengers arrive at either terminal and must be transported to the other terminal, whereupon they exit the system. At a given terminal at any time t, the controller's (shuttle dispatcher's) decisions are based on the following information: (i) the history of the arrival process to that terminal through time t and (ii) the history of the arrival process of the other terminal through time t ? I. By imposing a holding cost per passenger per unit time held at either terminal, we provide an incentive for prompt service. On the other hand, a dispatching cost is incurred by each shuttle trip, thus discouraging frequent dispatching. The objective is to characterize a shuttle dispatching policy which is a function of the above-mentioned information and minimizes an expected discounted cost due to passenger waiting and the dispatching of the shuttle. Results for this type of network have implications for many existing …