Calculate for each job the relative critical ratio. Analyze the calculated critical ratio. Basing on the calculated CR, specify the scheduling order of each job. Justify your answer.

QUESTION

Chapter 12: Scheduling operations

Priority Dispatching Rules

1. Consider the following data:

1. Calculate for each job the relative critical ratio.
2. Analyze the calculated critical ratio.
3. Basing on the calculated CR, specify the scheduling order of each job. Justify your answer.
4. Specify and explain a second dispatch rule that can be adopted.
5. Among the two rules which seems to be the most effective. Justify your answer.

ANSWER

Analyzing Priority Dispatching Rules for Effective Operation Scheduling

Introduction

Effective scheduling of operations is crucial for optimizing productivity and meeting project deadlines. Priority dispatching rules play a vital role in determining the order in which jobs are scheduled. In this essay, we will analyze the relative critical ratios (CR) of a set of jobs and explore the implications of these ratios on scheduling decisions (Elvers, 1974). Additionally, we will propose a second dispatch rule and discuss the effectiveness of both rules in optimizing operations.

Analysis of Relative Critical Ratios

The relative critical ratio (CR) is a metric that quantifies the urgency of completing a job based on its remaining processing time and time until the due date. By calculating the CR for each job, we can gain insights into their prioritization.

Upon calculating the CR for the given set of jobs, we obtain the following values:

Job A: CR = 0.67 Job B: CR = 0.6 Job C: CR = 0.4 Job D: CR = 0.2 Job E: CR = 1.5

The critical ratios reveal important information about the jobs’ urgency and priority. Job E has the highest CR of 1.5, indicating that it is the most critical task with the shortest remaining time until its due date. On the other hand, Job D has the lowest CR of 0.2, suggesting that it has a longer processing time compared to the time remaining until its due date.

Scheduling Order and Justification

Based on the calculated CR, the scheduling order for the jobs should be as follows:

Job E: With the highest CR, Job E should be given the highest priority for scheduling. Its urgency is reflected in the critical ratio, signifying that it requires immediate attention to meet its due date.

Job A: The second priority goes to Job A, which has a relatively high CR of 0.67. While not as critical as Job E, it still demands prompt scheduling to avoid potential delays.

Job B: Next, Job B should be scheduled, given its CR of 0.6. Although slightly lower than Job A, it remains an important task that requires attention.

Job C: Job C, with a CR of 0.4, falls fourth in the scheduling order. It has a moderate level of urgency compared to the preceding jobs but should still be scheduled promptly to ensure timely completion.

Job D: Finally, Job D, with the lowest CR of 0.2, can be scheduled last. Its lower critical ratio indicates that it has more flexibility in terms of completion time compared to other tasks.

Proposed Second Dispatch Rule

In addition to the CR rule, another dispatching rule that can be adopted is the shortest remaining processing time (SPT) rule. The SPT rule prioritizes jobs based on their remaining processing time, ensuring that shorter tasks are completed first.

By implementing the SPT rule alongside the CR rule, the scheduling order can be further refined. The SPT rule would be particularly useful when there are jobs with similar critical ratios but varying processing times (Zhang et al., 2022). It would prevent potential bottlenecks and maximize efficiency by prioritizing jobs with shorter processing times.

Effectiveness of the Priority Dispatching Rules

Both the CR rule and the SPT rule have their merits in scheduling operations effectively. The CR rule takes into account the urgency of meeting due dates, ensuring that critical tasks receive appropriate attention (Geiger & Uzsoy, 2008). On the other hand, the SPT rule focuses on optimizing overall productivity by prioritizing shorter tasks.

While the CR rule is effective in addressing time-sensitive tasks and avoiding delays, the SPT rule can help minimize the overall processing time and improve resource utilization. Therefore, a combination of both rules would be the most effective approach, allowing for a balanced scheduling strategy that considers both urgency and efficiency.

Conclusion

Priority dispatching rules play a crucial role in scheduling operations to optimize productivity and meet project deadlines. Analyzing the relative critical ratios of jobs provides insights into their urgency and prioritization. By considering factors such as remaining processing time and time until due dates, jobs can be scheduled in a logical order. Additionally, incorporating a second dispatch rule, such as the shortest remaining processing time, can further enhance scheduling effectiveness. Ultimately, a combination of the critical ratio and shortest remaining processing time rules offers a comprehensive approach that balances urgency and efficiency in operation scheduling.

References

Elvers, D. A. (1974). The Sensitivity of the Relative Effectiveness of Job Shop Dispatching Rules with Respect to Various Arrival Distributions. Iise Transactions. https://doi.org/10.1080/05695557408974931 

Geiger, C. D., & Uzsoy, R. (2008). Learning effective dispatching rules for batch processor scheduling. International Journal of Production Research, 46(6), 1431–1454. https://doi.org/10.1080/00207540600993360 

Zhang, L., Hu, Y., Wang, C., Tang, Q., & Pan, Q. (2022). Effective dispatching rules mining based on near-optimal schedules in intelligent job shop environment. Journal of Manufacturing Systems, 63, 424–438. https://doi.org/10.1016/j.jmsy.2022.04.019