Optimization of Complete Awaiting Duration of Tasks with Concept of Task Block on Multi-Stage Flow Shop Scheduling

Advancements in technology have broadened the possibility of solving flow-shop scheduling in multi-stations. Completing the waiting period of tasks in multi-stage with a task block is still a challenging job. Therefore, by considering two or more tasks together in one group, as it becomes significant when one task takes priority over another due to some scientific constraints or demand of the contract, it is a favourable domain in multistage flow shop scheduling for the modern era. This research work considers the multi-stage flow-shop scheduling problems with the task block. The objective of the proposed research is to minimize the complete awaiting duration of all the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> tasks on multi-stations, which also includes the equivalent task for a task block. The heuristic methodology has been applied to this study. The proposed algorithm is illustrated with numerical examples that have been implemented by MATLAB. The results demonstrate that the proposed scheme outperforms better, approximately 95 % and above, in comparison to the previous scheme. In addition, the proposed methodology supports industrial managers in better understanding the uncertainties of their selection or decision and provides more reliable and interpretable outcomes among multi-stage flow shop scheduling problems.