The machine maintenance and sale age model of Kamien and Schwartz revisited

• 成果类型: Article
• 署名作者: Bensoussan, Alain; Sethi, Suresh P.
• 署名单位: University of Texas System; University of Texas Dallas; University of Texas System; University of Texas Dallas
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1060.0666
• 发表日期: 2007
• 页码: 1964-1976
• 关键词: Optimal control; stochastic control; dynamic programming; Variational Inequality; maintenance and replacement

摘要

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.