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Production/Clearing Models Under Continuous and Sporadic Reviews

Author

Listed:
  • Oded Berman

    (University of Toronto)

  • Mahmut Parlar

    (McMaster University)

  • David Perry

    (University of Haifa)

  • M. J. M. Posner

    (University of Toronto)

Abstract

We consider production/clearing models where random demand for a product is generated by customers (e.g., retailers) who arrive according to a compound Poisson process. The product is produced uniformly and continuously and added to the buffer to meet future demands. Allowing to operate the system without a clearing policy may result in high inventory holding costs. Thus, in order to minimize the average cost for the system we introduce two different clearing policies (continuous and sporadic review) and consider two different issuing policies (“all-or-some” and “all-or-none”) giving rise to four distinct production/clearing models. We use tools from level crossing theory and establish integral equations representing the stationary distribution of the buffer’s content level. We solve the integral equations to obtain the stationary distributions and develop the average cost objective functions involving holding, shortage and clearing costs for each model. We then compute the optimal value of the decision variables that minimize the objective functions. We present numerical examples for each of the four models and compare the behaviour of different solutions.

Suggested Citation

  • Oded Berman & Mahmut Parlar & David Perry & M. J. M. Posner, 2005. "Production/Clearing Models Under Continuous and Sporadic Reviews," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 203-224, June.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1483-1
    DOI: 10.1007/s11009-005-1483-1
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    References listed on IDEAS

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    1. Shaler Stidham, 1977. "Cost Models for Stochastic Clearing Systems," Operations Research, INFORMS, vol. 25(1), pages 100-127, February.
    2. Shaler Stidham, 1986. "Clearing Systems and ( s , S ) Inventory Systems with Nonlinear Costs and Positive Lead Times," Operations Research, INFORMS, vol. 34(2), pages 276-280, April.
    3. Serfozo, Richard & Stidham, Shaler, 1978. "Semi-stationary clearing processes," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 165-178, January.
    4. Stidham, Shaler, 1974. "Stochastic clearing systems," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 85-113, January.
    5. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
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