Optimization for a Joint Predictive Maintenance and Job Scheduling Problem With Endogenous Yield Rates

Abstract

While job scheduling problems have been studied extensively, scheduling problems with endogenous yield rates that may be affected by predictive maintenance is not thoroughly investigated. In this study, we consider the optimization of a joint predictive maintenance and job scheduling problem for the minimization of total shortage penalty. As maintenance may be conducted to raise machine yield rates, machine production rates and job processing times become endogenous, and the optimization problem is different from traditional scheduling problems. We formulate a mixed integer program for this problem and develop a heuristic algorithm based on Tabu search. We demonstrate the effectiveness of our algorithm through numerical experiments and a way of estimating the yield declining rate with industry defect and maintenance records. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the real need of our industry collaborator, red electronics manufacturer. Every morning, the manufacturer chooses up to three out of eleven photolithography machines to conduct maintenance. Conducting maintenance helps raise machine yield rates to decrease the number of defects in expectation. However, the production schedule of some jobs must be postponed, and delay and shortage may arise. The decision is thus to schedule jobs as well as maintenance to find a balance between yield loss and shortage loss. We help the manufacturer by formulating an optimization model and develop an algorithm to solve the model. The algorithm may be applied to similar cases when one needs to schedule maintenance and production processes at the same time.