Optimizing batch-processing operations with batch-position-based learning effects

Motivated by applications in porcelain-making companies, we consider a type of optimization problems for batch-processing operations. In production, single machine with fixed capacity is used to process jobs. Several jobs can be processed together if their total size no more than the capacity. Batch-position-based learning effects are considered because workers become skillful gradually after they perform processing task repeatedly. The actual time batch decreasing function its position production. objective minimize makespan and three different problems. first problem, have identical sizes present an algorithm which find optimal solutions polynomial time. second times show problem NP-hard strong sense. We propose approximation absolute performance guarantee 1.5 asymptotic 1.223. third non-identical simultaneously. 2. Besides, evolution provide managerial insights decision makers manufacturing companies.