The Optimal Two Stages Lot Sizing Problem with An Unreliable Machine

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This paper considers the two-stage lot-sizing problem with an unreliable machine. The production rate at the first stage is greater than that at the second stage and the transfer from the first stage to the second stage is continuous. The problem was classified according to: whether the lot size at the first stage is greater or less than that at the second stage. Lot sizing and batch models often assume reliable manufacturing facilites. But in this paper, we focus on the effects of the breakdown of machine at the stage 2. The machine has an exponentially distributed life time, and the repair time when the machine fails is ignored.

We 1) derive an average cost function, 2) obtain an optimal lot sizes and 3) carry out the analysis to examine the effect of machine paramenter (failure rate) to optimal lot sizes.