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A Renewal Decision Problem

Author

Listed:
  • C. Derman

    (Columbia University)

  • G. J. Lieberman

    (Stanford University)

  • S. M. Ross

    (University of California, Berkeley)

Abstract

A system (e.g., a motor vehicle) must operate for t units of time. A certain component (e.g., a battery) is essential for its operation and must be replaced each time it fails. There are n types of replacement components. A type i replacement costs C i and has a random life with distribution depending on i. There is no salvage value associated with the particular component in use when the system terminates. The problem is to assign the initial component and subsequent replacements from among the n types so as to minimize the total expected cost of providing an operative component for the t units of time. This paper treats this problem when the life distributions are exponential for each type and when t is fixed or has a truncated exponential distribution. Related problems are also considered.

Suggested Citation

  • C. Derman & G. J. Lieberman & S. M. Ross, 1978. "A Renewal Decision Problem," Management Science, INFORMS, vol. 24(5), pages 554-561, January.
    • Handle: RePEc:inm:ormnsc:v:24:y:1978:i:5:p:554-561
    DOI: 10.1287/mnsc.24.5.554
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    Cited by:

    1. Santiago R. Balseiro & David B. Brown, 2019. "Approximations to Stochastic Dynamic Programs via Information Relaxation Duality," Operations Research, INFORMS, vol. 67(2), pages 577-597, March.
    2. Michael Katehakis & Ingram Olkin & Sheldon Ross & Jian Yang, 2013. "On the life and work of Cyrus Derman," Annals of Operations Research, Springer, vol. 208(1), pages 5-26, September.
    3. Chen, Kai & Ross, Sheldon M., 2014. "An adaptive stochastic knapsack problem," European Journal of Operational Research, Elsevier, vol. 239(3), pages 625-635.
    4. Kai Chen & Sheldon M. Ross, 2014. "The burglar problem with multiple options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 359-364, August.
    5. Xiaoqiang Cai & Sean Zhou, 1999. "Stochastic Scheduling on Parallel Machines Subject to Random Breakdowns to Minimize Expected Costs for Earliness and Tardy Jobs," Operations Research, INFORMS, vol. 47(3), pages 422-437, June.
    6. Range, Troels Martin & Kozlowski, Dawid & Petersen, Niels Chr., 2017. "A shortest-path-based approach for the stochastic knapsack problem with non-decreasing expected overfilling costs," Discussion Papers on Economics 9/2017, University of Southern Denmark, Department of Economics.
    7. Brian C. Dean & Michel X. Goemans & Jan Vondrák, 2008. "Approximating the Stochastic Knapsack Problem: The Benefit of Adaptivity," Mathematics of Operations Research, INFORMS, vol. 33(4), pages 945-964, November.
    8. Zuo, Ming J. & Liu, Bin & Murthy, D. N. P., 2000. "Replacement-repair policy for multi-state deteriorating products under warranty," European Journal of Operational Research, Elsevier, vol. 123(3), pages 519-530, June.

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