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Simultaneous Optimization of Preventive Maintenance and Replacement Policy for Machines: A Modern Control Theory Approach
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In this article, the problem of machine replacement in a changing technological environment is formulated as a problem in modern control theory and the objective is to maximize the present value of all future net profits over a class of infinite chains of machines where each link in the chain represents a uniform length replacement cycle with identical preventive maintenance.Abstract:
In this paper, the problem of machine replacement in a changing technological environment is formulated as a problem in modern control theory. The objective is to maximize the present value of all future net profits over a class of infinite chains of machines where each link in the chain represents a uniform length replacement cycle with identical preventive maintenance. The control is effected by varying (i) the length of the replacement cycle, and (ii) the schedule of preventive maintenance. The optimal control is determined by applying the maximum principle of Pontryagin and resulting influence functions are provided economic interpretations.PDF version: Sethi, S.P. “Simultaneous Optimization of Preventive Maintenance and Replacement Policy for Machines: A Modern Control Theory Approach,” Management Sciences Research Report #223, GSIA, Carnegie-Mellon University, 1971.read more
Citations
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Journal ArticleDOI
A survey of maintenance models: The control and surveillance of deteriorating systems
TL;DR: The literature on maintenance models is surveyed and includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.
Journal ArticleDOI
Optimal maintenance models for systems subject to failure–A Review
Y. S. Sherif,M. L. Smith +1 more
TL;DR: This paper is a state-of-the-art review of the literature related to optimal maintenance models of systems subject to failure and focuses on work appearing since the 1976 survey.
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Reliability analysis : Optimal inspection and maintenance schedules of failing systems
TL;DR: A review of the literature related to optimal inspection and maintenance schedules of failing systems can be found in this article, where the authors present a state-of-the-art review.
Journal ArticleDOI
A mixed optimization technique for the generalized machine replacement problem
Suresh Sethi,Thomas E. Morton +1 more
TL;DR: A mixed optimization technique for optimal machine replacement is presented which allows much more flexibility than previous models and is particularly useful for problems with such asymmetries as an existing initial machine or uneven technological change.
Journal ArticleDOI
Optimal maintenance policies for machines subject to deterioration and intermittent breakdowns
V. V. S. Sarma,Mansoor Alam +1 more
TL;DR: Optimal preventive maintenance policies, for a machine subject to deterioration with age and intermittent breakdowns and repairs, are derived using optimal control theory and are shown to be of bang-bang nature.
References
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Book
Mathematical Theory of Optimal Processes
TL;DR: The fourth and final volume in this comprehensive set presents the maximum principle as a wide ranging solution to nonclassical, variational problems as discussed by the authors, which can be applied in a variety of situations, including linear equations with variable coefficients.
Book
Public Investment, the Rate of Return, and Optimal Fiscal Policy
Kenneth J. Arrow,Mordecai Kurz +1 more
TL;DR: In this paper, a theory of "controllability" is developed and injected into public economics and growth models to analyze optimal public expenditures in the context of modern growth theory, and a model of optimal growth with public capital is proposed.
Journal ArticleDOI
Optimal Maintenance and Sale Age for a Machine Subject to Failure
TL;DR: The necessary conditions for an optimal maintenance policy are shown to be sufficient and the novelty of the approach lies in the explicit distinction between the machine's "natural” failure rate and the actual failure rate resulting from selection of preventive maintenance policy.
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