In this work, we address a scheduling problem arising in the photolithography stage of semiconductor wafer fabrication. Photolithography is a well-known bottleneck in wafer fabs because stepper machines are extremely expensive and significantly costlier than most other tools. As a result, efficient scheduling at this stage is central for improving overall fab performance. Although stepper scheduling has been widely studied, the combined integration of qualification constraints and send-ahead wafers has received far less attention. The present study builds on these contributions by explicitly incorporating re-qualification mechanisms via send-ahead wafers and modeling secondary resource constraints associated with mask availability. We model this problem as a integer linear extended formulation and propose a column generation algorithm to solve its relaxation and to obtain feasible solutions. Preliminary results show that the linear relaxation by the column generation is much tighter than the the one by a compact model.

