15.7 Chapter Problems
Chapter Problems
- Define job scheduling. Explain its significance in both manufacturing and service operations.
- List and describe four common job scheduling rules. Discuss the advantages and disadvantages of each.
- Consider the following jobs with their processing times and due dates:
| Job | Processing Time (Hours) | Due Date (Hours) |
| A | 16 | 36 |
| B | 8 | 30 |
| C | 40 | 100 |
| D | 10 | 39 |
| E | 35 | 90 |
- Apply the following scheduling rules to the jobs in Question 3:
- First-Come, First-Served (FCFS)
- Shortest Processing Time (SPT)
- Earliest Due Date (EDD)
For each rule, calculate:
- Average Flow Time
- Average Lateness
- Maximum Tardiness
- Based on your calculations in Question 4:
- Which rule would you recommend to minimize average flow time?
- Which rule would you recommend to minimize maximum tardiness?
- Justify your recommendations.
- What is the Critical Ratio (CR) rule?
- Calculate the CR for each job in Question 3.
- Sequence the jobs using the CR rule.
- Calculate the average tardiness for this sequence.
- Explain the concept of “makespan.”
- How is it calculated?
- Why is it an important metric in job scheduling?
- A manufacturing company has five jobs to be processed on two machines (Machine 1 and Machine 2). The processing times are as follows:
| Job | Machine 1 (Hours) | Machine 2 (Hours) |
| 1 | 5 | 6 |
| 2 | 6 | 8 |
| 3 | 5 | 6 |
| 4 | 7 | 4 |
- Determine a job sequence that minimizes the makespan for the jobs in Question 8. (Hint: This may require applying Johnson’s Rule or another advanced scheduling technique.)
- A construction company needs to assign four cranes to four construction sites. The cost matrix for assigning each crane to each site is given below:
| Crane | Site A | Site B | Site C | Site D |
| 1 | 13 | 5 | 7 | 7 |
| 2 | 2 | 11 | 6 | 5 |
| 3 | 7 | 7 | 3 | 8 |
| 4 | 2 | 4 | 7 | 9 |
- Use the Hungarian Algorithm (or another appropriate method) to determine the optimal assignment of cranes to sites that minimizes total cost.
- Discuss the limitations of the scheduling rules presented in this chapter. What real-world factors are often not considered by these rules?
- How can technology improve job scheduling in practice? Discuss the role of tools such as scheduling software, real-time data, and automation in enhancing scheduling accuracy and responsiveness.
