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Single‐stage, multi‐product production/inventory systems with lost sales

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  • Tayfur Altiok
  • Goang An Shiue

Abstract

A production/inventory system consisting of a single processor producing three product types and a warehouse is considered. For each product type, the demand process is assumed to be Poisson and the processing time is phase‐type. Excess demand is lost. Products have a priority structure and the processor's attention is shared by all the products according to a switching rule. Production of a product continues until its target level is reached. Then, a switch‐over takes place if another product needs the processor's attention. A set‐up process takes place every time a switch‐over occurs. An (R, r) continuous‐review inventory control policy is used to start and stop the production of each product. The underlying Markov chain is studied and its steady‐state distribution is obtained recursively. Through the recursive procedure, the steady‐state balance equations to be dealt with are significantly reduced to a manageable set. The procedure is implemented on a supercomputer and examples are provided to show its efficiency and stability for a range of model parameters. We analyzed the joint behaviors of the inventory levels of the three products as their demand rates increase. Finally we introduced a cost minimizing objective function to guide design efforts. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • Tayfur Altiok & Goang An Shiue, 1995. "Single‐stage, multi‐product production/inventory systems with lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 889-913, September.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:6:p:889-913
    DOI: 10.1002/1520-6750(199509)42:63.0.CO;2-1
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    References listed on IDEAS

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    1. Matthew J. Sobel, 1969. "Optimal Average-Cost Policy for a Queue with Start-Up and Shut-Down Costs," Operations Research, INFORMS, vol. 17(1), pages 145-162, February.
    2. Martin Eisenberg, 1972. "Queues with Periodic Service and Changeover Time," Operations Research, INFORMS, vol. 20(2), pages 440-451, April.
    3. B. Avi-Itzhak & W. L. Maxwell & L. W. Miller, 1965. "Queuing with Alternating Priorities," Operations Research, INFORMS, vol. 13(2), pages 306-318, April.
    4. Jack S. Sykes, 1970. "Simplified Analysis of an Alternating-Priority Queuing Model with Setup Times," Operations Research, INFORMS, vol. 18(6), pages 1182-1192, December.
    5. Daniel P. Heyman, 1968. "Optimal Operating Policies for M / G /1 Queuing Systems," Operations Research, INFORMS, vol. 16(2), pages 362-382, April.
    6. Bezalel Gavish & Stephen C. Graves, 1980. "Technical Note—A One-Product Production/Inventory Problem under Continuous Review Policy," Operations Research, INFORMS, vol. 28(5), pages 1228-1236, October.
    7. Tayfur Altiok, 1989. "( R , r ) Production/Inventory Systems," Operations Research, INFORMS, vol. 37(2), pages 266-276, April.
    8. Colin E. Bell, 1971. "Characterization and Computation of Optimal Policies for Operating an M / G /1 Queuing System with Removable Server," Operations Research, INFORMS, vol. 19(1), pages 208-218, February.
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