Lot sizing in the forging industry considering lot size dependent tool wear

Lot sizing is an important task of production planning and control: basis of lot sizes are order change costs and costs for storage. Models for lot sizing do not consider lot size dependent maintenance costs. However, for a forging company the tool wear is very important, because the tooling costs represent a major part in the production cost. In this article, the deterministic lot size model of Andler is extended with lot size dependent maintenance costs. For this purpose, the correlation between lot size and the tool wear is first derived in order to develop a lot size dependent wear function. The linking of a lot size dependent wear function with maintenance costs results in a lot size dependent maintenance cost function, which can be integrated into existing lot size models with a customized total cost function. The validation of the extended lot size model consists of two parts. In the first part, the functionality of the extended lot size model is validated. In the second part, a sensitivity analysis of the lot size is carried out with regard to lot size dependent costs and unit costs.