Midterm Planning to Minimize Deviations From Daily Target Outputs in Semiconductor Manufacturing

This paper presents a new model for production planning in a high volume fab that uses quarterly commitments to define daily target outputs. Rather than relying on due dates and priority rules to schedule lot starts and move work-in-process through the facility, processing at each step in a route is determined with the objective of minimizing the sum of the deviations between the target outputs and finished goods inventory. The model takes the form of a large-scale linear program that is intractable for planning horizons beyond a few days. To find solutions, we first tried several standard iterative techniques, including Lagrangian relaxation and Benders' decomposition, but each proved ineffective. As a consequence, it was necessary to design a solution methodology that was more tailored to the problem's structure. This involved creating weekly subproblems that were myopic but could be solved to optimality within a few minutes, and then post-processing the results with a decomposition algorithm to fully utilize excess machine time. The heart of the post-processor consists of a rescheduling algorithm and a dispatching heuristic. Extensive testing using data provided by Texas Instruments showed that realistic size instances spanning 4-13 weeks could be solved within a fraction of a day.