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Optimal Dispatching of a Finite Capacity Shuttle

Rajat K. Deb
Management Science
Vol. 24, No. 13 (Sep., 1978), pp. 1362-1372
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/2630642
Page Count: 11
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Optimal Dispatching of a Finite Capacity Shuttle
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Abstract

We consider the problem of determining the optimal operating policy of a two terminal shuttle with fixed capacity Q ≤ ∞. 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 ≥ G(y), where G(y) is a monotone decreasing control function. Futhermore, 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 - βy.

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