On a multi-product model of lot-sizing with quality costs

In this note we consider a multi-product environment where production lot-sizing and investing for quality improvement in several production processes are desired. We develop a mathematical model for addressing this important problem. We use our model to calculate the optimal lot-sizes and the optimal allocation of investment across products in the presence of a budget constraint. We quantify quality loss costs more effectively than the traditionally used Taguchi loss function, in the context of production lot-sizing, by using a modified form of the reflected normal loss function and develop several insights into the nature of the optimal solution. Finally, we show that our model and overall method can be readily adapted to a spreadsheet-based environment and consequently have practical and managerial relevance.