Tool capacity planning in semiconductor manufacturing

The demand for distinct wafer types in semiconductor manufacturing is an explicit function of the electronic components in which those wafers are used. Given that the component demands vary not only by the product type but also over time, it is obvious that wafer demands are also lumpy and time varying. In this paper, we discuss strategic level investment decisions on procuring new equipment and aggregate level capacity planning. In this context, we examine the problem of planning wafer production over multiple time periods within a single facility assuming that a demand forecast for each wafer type for each period is known. To address this problem, we develop a multi-period mixed-integer programming model to minimize the machine tool operating costs, new tool acquisition costs, and inventory holding costs. Given that production of wafers requires a large number of operations with multiple tools capable of performing each operation, tool operating costs are explicitly minimized by integrating the assignment of specific operations to tools in our model. Since our model is computationally intractable, we propose a Lagrangean-based relaxation heuristic to find efficient tool procurement plans.