Problem 16-8: The Following Table Shows Orders To Be Process ✓ Solved
Problem 16-8 The following table shows orders to be processed
Problem 16-8 The following table shows orders to be processed at a machine shop as of 8:00 a.m. Monday. The jobs have different operations they must go through. Processing times are in days. Jobs are listed in order of arrival.
a. Determine the processing sequence at the first work center using each of these rules: (1) First come, first served, (2) Slack per operation.
Sequence for First come, first served
Sequence for Slack per operation
b. Compute the effectiveness of each rule using each of these measures: (1) average completion time, (2) average number of jobs at the work center. (Round your answers to 2 decimal places.)
First Come, First Served
Slack per Operation
Average completion time
What will be the average job tardiness? (Round your answer to 2 decimal places.)
Average job tardiness new average job tardiness is [removed] minutes.
Paper For Above Instructions
This analysis addresses the processing of jobs at a machine shop using two scheduling rules: First Come, First Served (FCFS) and Slack per Operation (SPO). Understanding these methodologies will help optimize the workflow and efficiency of operations within the workshop.
Understanding the Job Processing Environment
At any machine shop, numerous jobs arrive to be processed, each having varying processing times and due dates. Scheduling becomes critical in determining the order of job processing, which can significantly impact completion times and job tardiness.
Processing Sequences
The orders displayed in the hypothetical table can be analyzed based on the arrival times of the jobs. Utilizing the rules set forth, the following sequences can be deduced:
1. First Come, First Served (FCFS)
The principle of FCFS schedules jobs in the order they arrive at the work center. This means that the first job in the queue gets processed first, the second job follows, and so forth. This method is straightforward and ensures that no job is skipped over, but it may not always be efficient, particularly if the jobs have significantly varied processing times.
Assuming the table indicated various jobs A, B, C, D, and E with respective processing times and due dates, the FCFS sequence would align directly with their order of arrival.
2. Slack per Operation (SPO)
In contrast, Slack per Operation calculates the slack time for each job where slack is defined as the difference between the time remaining until the due date and the total processing time required for the job. The job with the least amount of slack is processed first, promoting on-time completion. To determine this sequence, we must analyze the processing times and due dates of each job. The job providing the least slack time would be prioritized.
Effectiveness of Each Scheduling Rule
To gauge the effectiveness of the two scheduling rules, we calculate the average completion time and the average number of jobs still present at the work center at the end of each period.
Average Completion Time
For FCFS, the average completion time can be computed by taking the sum of completion times for all jobs and dividing it by the total number of jobs. For instance, if job A completes at day 2, job B on day 4, job C at day 6, and so forth, the average will reflect the efficiency of this method's ordering.
Conversely, for SPO, the average completion time would depend on the calculated slacks and whether the sequence allowed for shorter processing times, thereby facilitating earlier job completions.
Average Number of Jobs at the Work Center
This figure can be assessed by summing the number of jobs present at the work center at different checkpoints (days) throughout the job processing. A continuous flow of jobs indicates a well-optimized scheduling approach, while peaks can indicate bottlenecks or inefficiencies.
Calculating Average Job Tardiness
Job tardiness refers to the delay a job experiences beyond its due date. This measure is crucial for evaluating the operational efficiency, as high tardiness can affect customer satisfaction and overall workflow. The average job tardiness is determined by the sum of all tardy days divided by the number of jobs processed. For example, if a job due on day 3 is completed on day 5, it contributes 2 tardy days to the total count.
After implementing both scheduling methods, the results should provide insight into which rule yields more favorable average job tardiness. A significant reduction in tardiness when employing the SPO method can highlight its effectiveness in meeting project deadlines compared to FCFS.
Conclusion
In conclusion, the scheduling of jobs within machine shops is paramount in optimizing both operational efficiency and meeting customer deadlines. Evaluating the different methodologies such as FCFS and SPO reveals varying strengths and weaknesses regarding job completion times and tardiness. Data analysis from actual job processing can further inform best practices in managing workloads effectively.
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