Note—A Remark on Optimality of Control Limit Rules

Abstract

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Optimality of control limit policies in replacement models

“…39 (1992) Therefore, g, can be computed by calculating C,(i) and T'(i) recursively using (8) and (9), starting from i = M . Using Corollary 3.5(b), the following simple bisection procedure can be used to determine the optimal n-policy .…”

“…LeSanovsky [8] conjectured that Conditions A and K are also sufficient for the unimodality of the average cost under control limit policies. Using Theorem 5.1, we have shown that these two conditions are indeed sufficient for this unimodality property, and we have thus provided an affirmative answer to this conjecture.…”

“…Consider any fixed n , 1 i : n 5 M. The average cost under the n-policy is given by g, , = C,(O)/T,(O) with and Naval Research Logistics, Vol. 39 (1992) Therefore, g, can be computed by calculating C,(i) and T'(i) recursively using (8) and (9), starting from i = M . Using Corollary 3.5(b), the following simple bisection procedure can be used to determine the optimal n-policy .…”

A survey of preventive maintenance models for stochastically deteriorating single-unit systems

“…The difference between the immediate and delayed replacement models is that the first takes action at the time of a shock, while the latter takes action at the next shock time. LeSanovskq [61] presents a counterexample to invalidate Kolesar's assertions of an optimal controllimit policy. LeSanovsky [60] compares the immediate and delayed replacement policies, proving that the immediate replacement policy generally yields lower long-run expected cost per unit time when a control-limit policy is optimal.…”

Comparison of two replacement policies

“…It is proved in [3] that if the rule R, is optimal in the model M 1 then the sequences {«p"}~=o and {«Pn}~=k are respectively non-increasing and non-decreasing. On the other hand, the sequence {CPn}~=0 does not generally have the analogous property (see [6]).…”