Abstract
In general, the study of the convexity (concavity) of the total annual cost function (the annual net profit function) should be one of the main research topics about the inventory model. This paper first shows that the long-run average cost function per unit of time for the case of exponential failures is unimodal. However, it is neither convex nor concave. Second, the better lower bound Q ℓ ∗ and upper bound Q u ∗ can be obtained to improve some existing results. Finally, numerical examples reveal the lower bound Q ℓ ∗ for the optimal lot size is a rather good approximation to the optimal lot size. Scope and purpose In 1992, Groenevelt, Pintelon and Seidmann focused on the effects of machine breakdowns and corrective maintenance on the economic lot sizing decisions. They indicate that the economic manufacturing quantity (EMQ) is a good approximation to the optimal lot size. The main purpose of this paper is to provide a better approximation to the optimal lot size than EMQ.
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