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The Machine Maintenance and Sale Age Model of Kamien and Schwartz Revisited

Author

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  • Alain Bensoussan

    (International Center for Decision and Risk Analysis, School of Management, The University of Texas at Dallas, Richardson, Texas 75080)

  • Suresh P. Sethi

    (Center for Intelligent Supply Networks, School of Management, The University of Texas at Dallas, Richardson, Texas 75080)

Abstract

In this paper, we revisit and clarify the celebrated machine maintenance and sale age model of Kamien and Schwartz (KS) involving a machine subject to failure. KS formulate and solve the problem as a deterministic optimal control problem with the probability of the machine failure as the state variable. Thus, they obtain deterministic optimal maintenance and sale date. We study two underlying stochastic models with known and random machine modes, and clarify the relationship between the resulting value functions to that of KS. In particular, our maintenance and sale date decisions, when the machine is in operation, are precisely the ones obtained from the deterministic solution of KS. We explain why that is so. Moreover, we provide a sufficient condition for an optimal maintenance and sale date policy that is missing in KS. We describe many applications of the KS model in areas other than that of machine maintenance. We conclude the paper with extensions of the KS problem that are stochastic control problems not easily solvable or not at all solvable as deterministic problems.

Suggested Citation

  • Alain Bensoussan & Suresh P. Sethi, 2007. "The Machine Maintenance and Sale Age Model of Kamien and Schwartz Revisited," Management Science, INFORMS, vol. 53(12), pages 1964-1976, December.
    • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:12:p:1964-1976
    DOI: 10.1287/mnsc.1060.0666
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    References listed on IDEAS

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    Cited by:

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    6. A. Bensoussan & Q. Feng & S. P. Sethi, 2022. "Integrating equipment investment strategy with maintenance operations under uncertain failures," Annals of Operations Research, Springer, vol. 317(2), pages 353-386, October.
    7. Rubel, Olivier, 2018. "Profiting from product-harm crises in competitive markets," European Journal of Operational Research, Elsevier, vol. 265(1), pages 219-227.
    8. Kurata, Hisashi & Nam, Seong-Hyun, 2013. "After-sales service competition in a supply chain: Does uncertainty affect the conflict between profit maximization and customer satisfaction?," International Journal of Production Economics, Elsevier, vol. 144(1), pages 268-280.
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    10. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.

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