A scatter simulated annealing algorithm for the bi-objective scheduling problem for the wet station of semiconductor manufacturing

This paper studies a single-machine scheduling problem where flexible maintenance is required in the planning horizon. The problem observed is in the clean operation of semiconductor manufacturing, where jobs are associated with release times, processing times, due dates, penalty weight of tardy jobs and the amount of dirt left on the machine during processing. The machine, named the wet station, should be stopped for cleaning or maintenance before a maximum amount of dirt has accumulated; the cleaning time is fixed and is known in advance. However, the starting point of each maintenance activity is a decision variable. Preemptive operation is not allowed. The bi-objective of minimizing total weighted tardiness and total completion time is considered in this paper. An intuitive threshold method and a dynamic programming approach are proposed for scheduling jobs and PMs under a given job sequence. A mixed-integer programming formulation is developed to obtain all efficient solutions for the small-size problems. In addition, this paper also develops a scatter simulated annealing (SSA) algorithm in which a scatter-search mechanism leads SSA to explore more potential solutions. Computational experiments are conducted to examine the efficiency of the SSA algorithm. For the small-size problems, SSA could obtain all non-dominated solutions except for a tiny fraction of the instances. For the large size problems, SSA performs considerably well compared with SMOSA and NSGA-II, demonstrating its potential to efficiently solve bi-objective single problems with flexible maintenance activities.