Optimization-based litho machine scheduling with multiple reticles and setups

The increasing demand for on-time delivery and low cost is forcing semiconductor manufacturers to seek more efficient schedules to allocate machines and other resources to minimize the cost associated with other features, such as setup. This paper presents the modeling and solution of litho machine scheduling with multiple reticles and setups in lithography, the bottleneck process of fabricating wafers in the semiconductor industry. For the litho machine scheduling under consideration, there are daily targets for every layer of several products, therefore, there is no need to number and distinguish different lots. A mixed integer optimization formulation is established with litho machines and reticles. The objective is to meet daily target, and reduce the number of setups. By linearizing processing time constraints and objective function, the problem is effectively solved by using branch and cut method. Several approaches, such as node selection strategy, are used to improve efficiency. Numerical testing shows that the method can generate high quality schedules within reasonable time.