A flow shop batch scheduling and operator assignment model with time-changing effects of learning and forgetting to minimize total actual flow time

Abstract

Purpose: This paper aims to investigate simultaneous problems of batch scheduling and operator assignment with time-changing effects caused by learning and forgetting.

Design/methodology/approach: A number of parts will be processed in batches, each of which will be processed through a number of operations where there are alternative operators for each operation bringing different set up and processing times as operators experience different degree of learning and forgetting. A mathematical model is developed for the problems, and the decision variables are operator assignment, the number of batches, batch sizes and the schedule of the resulting batches. A proposed algorithm works by trying different number of batches, starting from one, and increasing the number of batches one by one until the objective function value does not improve anymore.

Findings: We show both mathematically and numerically that the closest batch to the due date always becomes the largest batch in the schedule, and the faster operators learn, the larger the difference between the closest batch to the due date and the other batches, the lower optimal number of batches, and the lower the total actual flow time.

Originality/value: Previous papers have considered the existence of alternative operators but have not considered learning and forgetting, or have considered learning and forgetting but only in a single-stage system and without considering alternative operators.