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Optimal Dispatching of a Finite Capacity Shuttle

Author

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  • Rajat K. Deb

    (Stanford University)

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.

Suggested Citation

  • Rajat K. Deb, 1978. "Optimal Dispatching of a Finite Capacity Shuttle," Management Science, INFORMS, vol. 24(13), pages 1362-1372, September.
  • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:13:p:1362-1372
    DOI: 10.1287/mnsc.24.13.1362
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    Cited by:

    1. Hall, Randolph W. & Sabnani, Vikas C., 2002. "Control of vehicle dispatching on a cyclic route serving trucking terminals," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(3), pages 257-276, March.
    2. Papadaki, Katerina P. & Powell, Warren B., 2002. "Exploiting structure in adaptive dynamic programming algorithms for a stochastic batch service problem," European Journal of Operational Research, Elsevier, vol. 142(1), pages 108-127, October.
    3. Katerina P. Papadaki & Warren B. Powell, 2003. "An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 742-769, October.
    4. Song, Dong-Ping & Earl, Christopher F., 2008. "Optimal empty vehicle repositioning and fleet-sizing for two-depot service systems," European Journal of Operational Research, Elsevier, vol. 185(2), pages 760-777, March.
    5. Menachem Berg & Frank van der Duyn Schouten & Jorg Jansen, 1998. "Optimal Batch Provisioning to Customers Subject to a Delay-Limit," Management Science, INFORMS, vol. 44(5), pages 684-697, May.

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