Algorithms for scheduling problems in semiconductor wafer fabrication

Abstract

In this dissertation, we consider three topics on flowshop scheduling problems in semiconductor wafer fabrication facilities (fabs). We consider two important characteristics of production in the fabs, i.e., existences of re-entrant flows and two classes of jobs with different urgencies. While each job visits each machine once in a typical flowshop, in a re-entrant flowshop, each job should visit the machines two or more times and hence there are re-entrant flows. In the two-machine re-entrant flowshop considered in this thesis, all jobs should be processed two times on each machine, and hence each job should be processed on machine 1 and machine 2, and then on machine 1 and machine 2 again. Also, as in semiconductor manufacturing systems, jobs are classified into two classes according to the urgencies of jobs: normal jobs and urgent jobs. First, we consider a two-machine re-entrant flowshop scheduling problem with sequence-dependent setup times with the objective of minimizing total tardiness of jobs. We give a mathematical formulation, and develop dominance properties and a lower bound for the problem. Then, we propose a branch and bound (B&B) algorithm using these dominance properties and the lower bound. Also, we suggest several heuristics to obtain an initial upper bound for the B&B algorithm. Secondly, we focus on a two-machine flowshop scheduling problem in which there are two classes of jobs with different urgencies, i.e., urgent jobs and normal (not urgent) jobs. The objective of this problem is to minimize a weighted sum of total tardiness of urgent jobs and the maximum completion time of normal jobs. We develop dominance properties, a lower bound and upper bounds for the problem. Then, we suggest a B&B algorithm using these dominance properties and bounds. Finally, we consider a two-machine re-entrant flowshop scheduling problem with two classes of jobs. The objective of this problem is to minimize a weighted sum of total tardiness of urgent jobs a...