A finite-state semi-Markov process (SMP) with penalties is considered. A property which is similar to an increasing-hazard-rate property for a Markov chain is defined for an SMP. The SMP is controlled by shifts from the state E i to immediately after a transition has occurred. Conditions are given which guarantee that the optimal stationary Markovian policy belongs to a subclass of control-limit policies.
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I. Gertsbach (1976) studied this question.
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