Heuristic algorithms to solve the capacity allocation problem in photolithography area (CAPPA)

Abstract

Wafer fabrication is one of the most complex and high competence manufacturing. How to fully utilize the machine capacity to meet customer demand is a very important topic. In this paper, we address the capacity allocation problem for photolithography area (CAPPA), which belongs to a capacity requirement planning scheme, with the process window and machine dedication restrictions that arise from an advanced wafer fabrication technology environment. Process window means that a wafer needs to be processed on machines that can satisfy its process capability (process specification). Machine dedication means that once the first critical layer of a wafer lot is processed on a certain machine, the subsequent critical layers of this lot must be processed on the same machine to ensure good quality of final products. We present six modified heuristics and a linear-programming-based heuristic algorithm (LPBHA) to solve the problem efficiently. The performance of the proposed algorithms is tested using real-world CAPPA cases taken from wafer fabrication photolithography area. Computational results show that LPBHA is the most effective one, and with a least average and a least standard deviation of deviation ratio of 0.294 and 0.085% compared to the lower bound of the CAPPA.