Abstract: The problem of scheduling batch processing machines is considered in this study. Batch processing machines are encountered in various manufacturing environment and the study is motivated by burning-in operation in semiconductor manufacturing while time-of-use electricity price is considered as well. In the problem under study, jobs seizes are non-identical and machines are batch processing machines which can process several jobs simultaneously as a batch.Since the electricity price is time related, the objectives of electrical cost and makespan is influenced by start processing time of each batch. These two objectives were minimized simultaneously on single batch processing machine with non-identical job sizes. Two pareto ant colony optimization algorithms were designed to solve the problem. One is J-PACO (Job-based Pareto Ant Colony Optimization) algorithm and the other is B-PACO (Batch-based Ant Colony Optimization) algorithm. This problem is different from traditional batch scheduling problems. As the price is related to the time, the start processing time of jobs should be determined after the sequence of batches are fixed. In the two algorithms proposed, jobs and batches are scheduled on time line separately. Random job instances are generated in the simulation experimentation to evaluate the performance of algorithms proposed. The experiment results indicate that B-PACO, which group jobs into batches using FFLPT(First Fit Longest Processing Time), outperforms J-PACO in computational time, numbers of non-dominated solution and hypervolume. The study will be helpful in the application of ACO involving multi objectives. And, the idea of allocating jobs in a time line before they are grouped into batches can also be used in scheduling batch processing machines.

Key words: multi-objective, scheduling, ant colony optimization, batch processing machine, TOU price