## 4 MIU Methodology and Its Computations  
In this section, the proposed MIU approach is introduced as a heuristic framework to address the scheduling problem. The methodology combines multiple dispatching rules to improve scheduling efficiency and adaptability in dynamic environments. The implementation details, including rule selection and their integration into the scheduling algorithm, are explained in depth. Computations were made by applying the steps in the flow chart given in Figure 4.  
The flowchart represents a decision-making framework for scheduling and rescheduling processes. It begins with selecting an initial strategy by management, followed by creating an initial schedule using MIU (details given in Figure 5). The manufacturing process runs for a set period, after which the system evaluates whether rework is required for completed jobs. If rework is needed, the jobs are added to the unstarted job list. Figure 4: Predictive–reactive rescheduling using MIU. If there are still unstarted jobs, machine availability is assessed, and an objective function target may be updated by management at this moment. Management may define the objective function at the outset of the scheduling process and update it at the beginning of each period if necessary. The unstarted job list is then rescheduled using MIU, and the cycle repeats with another manufacturing period. This iterative process continues until all jobs are completed, at which point the process concludes. Figure 5 illustrates the procedure of MIU. The proposed scheduling approach begins by reading the data set and generating a list of upcoming tasks. If the list is empty, the process moves directly to performance evaluation. Otherwise, the algorithm determines machine availability and sets the scheduling time T as the minimum available time among all machines. At this point, a scheduling list is created, including all tasks with a release time less than or equal to T. The selected dispatching rule is then applied to determine the task order, and the first task in the ordered list is assigned to an available machine. Once assigned, the machine's availability is updated by adding the task's processing time to the current time. The task is then recorded in the job list with its relevant parameters, including the dispatching rule name, task number, assigned machine number, starting and finishing times, tardy time, and weighted tardy time. Afterward, the scheduled task is removed from the upcoming task list, and the process continues iteratively until all tasks are scheduled. Upon completing the scheduling process, the algorithm evaluates performance by calculating the total weighted tardiness (TWT) and the number of tardy jobs (NTJ). These metrics are stored for each dispatching rule, and if all 13 predefined dispatching rules have not yet been tested, the algorithm switches to the next rule and repeats the process. Once all dispatching rules have been evaluated, the results are sorted,  
Figure 5: MIU procedure. and the best-performing rule--based on the lowest TWT value--is selected as the optimal scheduling approach. Finally, the selected rule and its corresponding job sequence are presented as the final output. It is accepted that the periodic meeting is held once a month, each day is two units of time, each week has 5 days, each month has 4 weeks. This calculation makes the period length 40 units. The machine availability time is calculated based on the expected values of the planned jobs in the previous period. If only the rework process remains after the main transactions are completed in the last period, this process is completed without waiting for the periodic meeting. The rework process of the delayed job is considered late even if the main process is completed on time. If rework is needed within a period, no complete or partial rescheduling should be conducted without a periodic meeting and a decision should be waited after the meeting.