Lot sizing and machining economics: The multi-item, multi-stage cost minimization case

This paper presents models for multi-item, multi-stage machining systems. The first model presented extends the manufacturing lead time expression developed for single-item, single-stage machining systems to multi-item, multi-stage machining systems through the introduction of the appropriate auxiliary variables. Application of Little’s law to the manufacturing lead time expression results in the development of a lot sizing model. Then, the lot-size value minimizing inventory costs is derived analytically. Finally a model is presented for the simultaneous determination of the optimal cutting speed and lot-size values. It is shown that the total cost function is dominated by its machining cost component. Based on this property, an efficient search technique is developed for quickly locating the optimal cutting-speed-lot-size point in machining systems constrained by the time allocated to processing an item on a machine. Computational experience with the algorithm verifies its quick convergence (after only a few iterations) to the optimal point.