Robust production control policies considering WIP balance and setup time in a semiconductor fabrication line

This paper discusses the problem of determining workload in a semiconductor fabrication line for providing robust production control. A mathematical model is proposed to determine the amount of wafers to be processed on equipment in a photolithography process where the setup time is incurred if the type of wafers is changed on the equipment. The objective of the model is to control the fabrication line by maintaining the target work-in-process (WIP) level as close as possible for the purpose of short cycle time and by minimizing the setup time loss for maximal throughput. The proposed model is formulated using mixed integer programming (MIP) to minimize the weighted sum of two objective functions. A heuristic approach is suggested using linear relaxation and its adjustment. Performances are evaluated for the optimal solution with computational cost and for the heuristics. It is shown that the heuristics give good solutions which are 10% away, on average, from the optimal solution, but which can be obtained in a few seconds.