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Optimal Control of a Single Stage Production System Subject to Random Process Shifts

Author

Listed:
  • Raman K. Nurani

    (Carnegie Mellon University, Pittsburgh, Pennsylvania)

  • Sridhar Seshadri

    (New York University, New York, New York)

  • J. George Shanthikumar

    (University of California, Berkeley, California)

Abstract

We consider a single stage production system with Poisson demand and exponential processing times. After producing a good item, the production process can shift to an “out-of-control” state with a given probability and start producing bad items. The state of the process is known only when the next stage (or customer) receives the item. Once an out-of-control process is detected, process correction is instantaneous. Customers arriving to an empty system get backlogged. In this framework, we examine FIFO (First In First Out) and LIFO (Last In First Out) issuing policies. The objective is to minimize the total expected discounted or average costs over an infinite time horizon. We characterize the structure of the optimal production policy for FIFO and LIFO, show that LIFO is better than FIFO and, in general, better than a large class of issuing policies. A numerical example illustrates that savings up to 20 percent can be obtained from using LIFO over FIFO. We also derive conditions under which maintaining zero inventory is optimal, and show that zero inventory is more likely to be optimal when either the backlogging cost or arrival rate of customers is small, and when the inventory carrying cost or the processing rate or the probability of getting a good item is large.

Suggested Citation

  • Raman K. Nurani & Sridhar Seshadri & J. George Shanthikumar, 1997. "Optimal Control of a Single Stage Production System Subject to Random Process Shifts," Operations Research, INFORMS, vol. 45(5), pages 713-724, October.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:5:p:713-724
    DOI: 10.1287/opre.45.5.713
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    Citations

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    Cited by:

    1. Vickson, Raymond G. & Hassini, Elkafi, 2006. "Lot streaming for quality control in two-stage batch production," European Journal of Operational Research, Elsevier, vol. 170(3), pages 824-843, May.
    2. Armero, Carmen & Conesa, David, 2004. "Statistical performance of a multiclass bulk production queueing system," European Journal of Operational Research, Elsevier, vol. 158(3), pages 649-661, November.
    3. Wai Ki Ching, 2001. "Markovian approximation for manufacturing systems of unreliable machines in tandem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 65-78, February.
    4. Albert Y. Ha, 2000. "Stock Rationing in an M/E k /1 Make-to-Stock Queue," Management Science, INFORMS, vol. 46(1), pages 77-87, January.
    5. C. Roger Glassey & Sridhar Seshadri & J. Shanthikumar, 1997. "Using information about machine failures to control flowlines," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(3), pages 455-481, October.
    6. Thomas Sloan, 2008. "Simultaneous determination of production and maintenance schedules using in‐line equipment condition and yield information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 116-129, March.
    7. R.E. Lillo, 2001. "Optimal control of an M/G/1 queue with impatient priority customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 201-209, April.

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