A BRKGA-DE algorithm for parallel-batching scheduling with deterioration and learning effects on parallel machines under preventive maintenance consideration

This paper introduces a parallel-batching scheduling problem with deterioration and learning effects on parallel machines, where the actual processing time of a job is subject to the phenomena of deterioration and learning. All jobs are first divided into different parallel batches, and the processing time of the batches is equal to the largest processing time of their belonged jobs. Then, the generated batches are assigned to parallel machines to be processed. Motivated by the characteristics of machine maintenance activities in a semiconductor manufacturing process, we take the machine preventive maintenance into account, i.e., the machine should be maintained after a fixed number of batches have been completed. In order to solve the problem, we analyze several structural properties with respect to the batch formation and sequencing. Based on these properties, a hybrid BRKGA-DE algorithm combining biased random-key genetic algorithm (BRKGA) and Differential Evolution (DE) is proposed to solve the parallel-batching scheduling problem. A series of computational experiments is conducted to demonstrate the effectiveness and efficiency of the proposed algorithm.