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Random Review Production/Inventory Systems with Compound Poisson Demands and Arbitrary Processing Times

Author

Listed:
  • Mandyam M. Srinivasan

    (Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2117)

  • Hyo-Seong Lee

    (Department of Industrial Engineering, Kyung Hee University, Kiheung, Yongin-goon, Kyunggi-do, 449-900, Korea)

Abstract

A production/inventory system is considered in which a single production facility produces items of a given type. The demand for the item is assumed to arrive according to a compound Poisson process. The time required to produce an item is assumed to follow an arbitrary distribution. An (s, S) policy is considered in which production stops at the instant that the inventory level is raised to S and production resumes at an inspection point when the inventory level is observed to have dropped to or below s for the first time. The time interval between two successive inspection points during a nonproduction period is a random variable which follows an arbitrary distribution. Under a cost structure which includes a set-up cost, a linear holding cost and a linear backorder cost, an expression for the expected cost per unit time is obtained for given control values. The operating cost during a cycle is shown to be convex in S for a given value of S-s. For the continuous review simple Poisson demand system, as well as some other special cases of the system considered here, it is shown that the expected cost per unit time is unimodal. Based on these properties, a procedure to find the optimal (s, S) policy is presented.

Suggested Citation

  • Mandyam M. Srinivasan & Hyo-Seong Lee, 1991. "Random Review Production/Inventory Systems with Compound Poisson Demands and Arbitrary Processing Times," Management Science, INFORMS, vol. 37(7), pages 813-833, July.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:7:p:813-833
    DOI: 10.1287/mnsc.37.7.813
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    Cited by:

    1. Dieter Fiems & Eline De Cuypere & Koen De Turck & Dieter Claeys, 2020. "Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production," Mathematics, MDPI, vol. 8(11), pages 1-16, November.
    2. repec:dgr:rugsom:10005 is not listed on IDEAS
    3. Gillen, David & Hasheminia, Hamed, 2013. "Estimating the demand responses for different sizes of air passenger groups," Transportation Research Part B: Methodological, Elsevier, vol. 49(C), pages 24-38.
    4. Nicky D. Van Foreest & Jacob Wijngaard, 2014. "On Optimal Policies for Production-Inventory Systems with Compound Poisson Demand and Setup Costs," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 517-532, May.
    5. Foreest, N. D. van & Wijngaard, J., 2010. "On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity," Research Report 10005, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. Wenhui Zhou & Dongmei Wang & Weixiang Huang & Pengfei Guo, 2021. "To Pool or Not to Pool? The Effect of Loss Aversion on Queue Configurations," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4258-4272, November.

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