Abstract
This research addresses a batch scheduling model for a single machine with learning effect leading to a situation where as the operator becomes experienced in processing similar tasks sequentially, the processing time for a job will be shorter if the job is processed in latter position in the production schedule. The objective for the models is to minimize the so-called total actual flow time of all parts in the shop, defined as the total interval times between the respective arrival times of all parts in all batches which is processed by the machine and their common due date. The problem is formulated as a non-linear programming model for which a relaxation is applied by considering variable N (the number of batches) to be a parameter, i.e., setting several values of N for the model, started from N = 1 and increased by 1 iteratively until a stopping rule is satisfied. Numerical experiments to show the effectiveness of the methods are also provided.