In this paper, we discuss a general ordering policy in which a spare delivered is put into inventory until a prespecified allowed inventory time unless an original unit fails, and further two special cases; 1) the spare is put into inventory until the original one fails; 2) the spare delivered takes over the operation immediately; introducing non-linear running and salvage costs. For the latter case 2), we also discuss the ordering policy including negative ordering time. We show that under certain conditions there exists a finite and unique optimum policy minimizing the expected total discounted cost, respectively, and present the relationships between the results in this paper and earlier contributions.
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