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This paper addresses a batch loading and scheduling problem of minimizing the makespan on parallel batch processing machines. For batch loading, jobs with compatible families can be assigned to the same batch process even if they differ in size; however, batches can only be formed from jobs within the same family, and the batch production time is determined by the family. During the batch scheduling, the deterioration effects are continuously added to batches processed in each parallel machine so that the batch production times become deteriorated. The deteriorated processing time of batches can be recovered to the original processing times of batches by a maintenance or cleaning process of machines. In this problem, we sequentially determine the batching of jobs and the scheduling of batches. Due to the complexity of the problem, we proposed a three-stage ant colony optimization algorithm. The proposed algorithm found an optimal solution for small-sized problems and achieved near-optimal solutions and better performance than a genetic algorithm or a particle swarm optimization for large-sized problems.

A Three-Stage ACO-Based Algorithm for Parallel Batch Loading and Scheduling Problem with Batch Deterioration and Rate-Modifying Activities