Simulated-annealing heuristics for the single-machine scheduling problem with learning and unequal job release times

In scheduling of batch processing machines in the diffusion and oxidation areas of a wafer fabrication facility, it can be found that the processing times of these batching operations can be extremely long (10 h) when compared to other operations (1-2 h) in a wafer fab. Moreover, the jobs to be processed may have different priorities/weights, due dates and ready times. In the presence of unequal ready times, it would be better to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, repeated processing of similar tasks improves workers’ skills. Motivated by these observations, we consider a single-machine problem with the sum of processing times based learning effect and release times. The objective is to find a schedule to minimize the total completion times. We first develop a branch-and-bound algorithm for the optimal solution. Then we propose a simulated-annealing heuristic algorithm for a near-optimal solution. Finally, we conduct a computational experiment to evaluate the performances of the proposed algorithms. The results show that the branch-and-bound algorithm can solve instances up to 24 jobs, and the average error percentage of the simulated-annealing algorithm is less than 0.1482%.