Optimal Dispatching of a Finite Capacity Shuttle

Rajat K. Deb
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Rajat K. Deb: Stanford University

Management Science, 1978, vol. 24, issue 13, 1362-1372

Abstract: We consider the problem of determining the optimal operating policy of a two terminal shuttle with fixed capacity Q \le \infty . The passengers arrive at each terminal according to Poisson processes and are transported by a single carrier operating between the terminals. The interterminal travel time is a positive random variable with finite expectation. Under a fairly general cost structure, we show that the policy which minimizes the expected total discounted cost over infinite time horizon has the following form: Suppose the carrier is at one of the terminals with x passengers waiting there and y passengers waiting at the other terminal. Then the optimal policy is to dispatch the carrier if and only if x \ge G(y), where G(y) is a monotone decreasing control function. Furthermore, G(y) is always less than or equal to the carrier capacity Q. This control function can be approximated by the linear function G(y) = K - \betay.

Keywords: queues: batch service; dynamic programming: Markov; infinite state (search for similar items in EconPapers)
Date: 1978
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:24:y:1978:i:13:p:1362-1372

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