Applied Stochastic Models in Business and Industry

Optimal decision procedure for an operation‐dependent deteriorating system

Journal Article

Highly flexible and integrated systems can perform one of several operations at a time, which allows the decision‐maker to select which operation to perform in the safest and most effective way. There are strong dynamic interactions between a system's deterioration and the operations it performs. In this research, optimal decision‐making was investigated for operation‐dependent deteriorating systems under variable operations while formulating the problem as a Markov decision process with the operation as a parameter. The decision‐maker selects the operation that will minimize the total expected cost over an infinite horizon on the basis of the current state. The properties of the resulting optimal expected cost function were examined, and the optimal decision procedure was found to be given by a monotone procedure under certain conditions. This research provides a generalization of the ‘keep, inspection, and replacement’ problem that was initially introduced by Derman (Mathematical Optimization Techniques: 201–210, 1963) and has been studied extensively since then. Copyright © 2014 John Wiley & Sons, Ltd.

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