An improved formulation for scheduling an automated wet-etch station

Abstract

Wet-etching is a key step in wafer fabrication. An automated wet-etch process involves a complex interplay of zero wait and no-intermediate-storage policies, and a shared robot; and poses a challenging scheduling problem. In this paper, we reformulate a previously reported mixed integer linear programming (MILP) model for minimizing the makespan in an automated wet-etch station. Extensive numerical evaluation shows that the reformulations outperform their predecessors by a significant margin. Interestingly, this improvement in performance arises merely from a slightly redefined binary variable. We also present an effective empirical formula for ranking MILP models in a situation where assessing alternate models is difficult due to the absence of an outright winner, and problem- as well as machine-dependent relative performances of models.