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

Alain Bensoussan () and Suresh Sethi
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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

Management Science, 2007, vol. 53, issue 12, 1964-1976

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.

Keywords: optimal control; stochastic control; dynamic programming; variational inequality; maintenance and replacement (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:53:y:2007:i:12:p:1964-1976

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