An optimization model for qualification management in wafer fabs

The individual tools of a tool group need to be qualified to run lots of certain families in wafer fabs. A qualification time window is associated with each family and each tool. This window lasts typically from a couple of days to few weeks. The time window can be re-initialized with separate qualification effort on a need by basis and can be extended by on-time processing of qualifying families. In this paper, we propose a mixed integer programming formulation for this problem assuming a given demand for a planning horizon of several periods. The objective function takes into account qualification costs, backlog costs, and inventory holding costs among others. Results of computational experiments based on randomly generated problem instances are presented that demonstrate that a tradeoff between production objectives and qualification costs can be reached by an appropriate configuration of the model.