Optimum Lot-Size Policy if Tools Break Down Frequently

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, Q_l 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.