Flexibility and product variety in lot-sizing models

This paper seeks insight into the role of process flexibility and product variety in the capacitated multiproduct lot-sizing model. The variety of the product line is defined in terms of the number of products and the relative value of their demand rate, setup time, and unit cost of production. Process flexibility is defined as a property of operating costs: one process is more flexible than another if an increase in product variety yields a relatively smaller increase in operating costs. In this context, flexibility is seen to depend not only on commonly understood factors, such as setup time and setup cost, but also on the capacity of the machine. The analysis yields new insights and formulas for the evaluation of product mix, process design and process improvement decisions. The approach can be viewed as an exercise in aggregate sensitivity analysis: instead of focusing on variations in individual scalar data, the analysis considers variations in aggregate measures which are themselves defined as functions of the original problem data.