Abstract
A well-known formula gives the optimum length of a production series by balancing change-over costs against inventory costs. This formula can no longer be considered as optimum in the case of a high breakdown rate of the tools. We can often reduce our costs in such situations by ending the production series when a breakdown occurs. This introduces a variability in the lot-sizes, which in turn causes higher stock levels.
A production policy was developed, based on two limits, Ql and Q2. Production is stopped either at the first break-down after Q1 units have been produced, or at Q2. Optimum values of Q1 and Q2 were derived and can be read off from a set of graphs.
One assumption of this theory is that tools are always available, which theoretically requires an infinite stock of these tools.
A Monte Carlo programme was set up to study the situation, in which the number of tools was limited. The number of tools, and the reorder-level for the products, required for a desired probability of stock-out, can be derived by the programme.
The theoretical values of Q1 and Q2 could be considered optimum for practical purposes in the cases under consideration.
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Muyen, A. Optimum Lot-Size Policy if Tools Break Down Frequently. J Oper Res Soc 12, 41–53 (1961). https://doi.org/10.1057/jors.1961.4
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DOI: https://doi.org/10.1057/jors.1961.4