Approximations to production lot sizing with machine breakdowns

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 View the MathML source and upper bound View the MathML source can be obtained to improve some existing results. Finally, numerical examples reveal the lower bound View the MathML source for the optimal lot size is a rather good approximation to the optimal lot size.