Question
Nine jobs need to be completed within eight weeks. The number of weeks required to complete each job is given in the file P08_21.xlsx. For
Nine jobs need to be completed within eight weeks. The number of weeks required to complete each job is given in the file P08_21.xlsx. For example, job 2 requires five weeks. Each job requires 40 hours of labor per week. Each week, 160 hours of regular time labor are available. Up to 40 hours of overtime labor can be purchased each week at a cost of $18 per hour. Additional overtime hours cost $22 per hour.
a. Determine how to minimize the overtime cost incurred in completing the jobs within eight weeks.
b. The same file also lists the due date for each job.
For example, job 1 should be completed by the end of week 6. A penalty of $500 is incurred for each day a job is late. Determine how to minimize the sum of overtime and due date penalties.
part a
| Completing jobs | ||||||||||||||
| Weekly hour availabilties | | |||||||||||||
| Available | Hourly cost | |||||||||||||
| Reg time | 160 | |||||||||||||
| Overtime, up to | 40 | $10 | ||||||||||||
| Overtime, over | 40 | $20 | ||||||||||||
| Hours per job per week | 40 | |||||||||||||
| Deadline (weeks) | 8 | |||||||||||||
| Data on jobs | Times for jobs | |||||||||||||
| Job | Weeks | Job | Start | Finish | Weeks over deadline | |||||||||
| 1 | 4 | 1 | 5 | 8 | 0 | |||||||||
| 2 | 3 | 2 | 6 | 8 | 0 | |||||||||
| 3 | 5 | 3 | 1 | 5 | 0 | |||||||||
| 4 | 4 | 4 | 1 | 4 | 0 | |||||||||
| 5 | 4 | 5 | 1 | 4 | 0 | |||||||||
| 6 | 2 | 6 | 7 | 8 | 0 | |||||||||
| 7 | 3 | 7 | 1 | 3 | 0 | |||||||||
| 8 | 2 | 8 | 5 | 6 | 0 | |||||||||
| 9 | 5 | 9 | 4 | 8 | 0 | |||||||||
| Hours used, week by week, by jobs | ||||||||||||||
| Job/Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | ||||||
| 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | ||||||
| 2 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | ||||||
| 3 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | ||||||
| 4 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | ||||||
| 5 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | ||||||
| 6 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | ||||||
| 7 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | ||||||
| 8 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | ||||||
| 9 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | ||||||
| Total hours | 160 | 160 | 160 | 160 | 160 | 160 | 160 | 160 | ||||||
| Overtime hours | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ||||||
| Overtime cost | $0 | $0 | $0 | $0 | $0 | $0 | $0 | $0 | ||||||
| Total cost (including penalty for being past deadline) | $0 | |||||||||||||
part b
| Completing jobs | |||||||||
| Weekly hour availabilties | |||||||||
| Available | Hourly cost | ||||||||
| Reg time | 160 | ||||||||
| Overtime, up to | 40 | $10 | |||||||
| Overtime, over | 40 | $20 | |||||||
| Hours per job per week | 40 | ||||||||
| Weekly penalty cost | $500 | ||||||||
| Data on jobs | Times for jobs | ||||||||
| Job | Weeks | Due date | Job | Start | Finish | Weeks late | |||
| 1 | 4 | 7 | 1 | 4 | 7 | 0 | |||
| 2 | 3 | 6 | 2 | 5 | 7 | 1 | |||
| 3 | 5 | 5 | 3 | 1 | 5 | 0 | |||
| 4 | 4 | 4 | 4 | 1 | 4 | 0 | |||
| 5 | 4 | 5 | 5 | 3 | 6 | 1 | |||
| 6 | 2 | 4 | 6 | 1 | 2 | 0 | |||
| 7 | 3 | 4 | 7 | 1 | 3 | 0 | |||
| 8 | 2 | 4 | 8 | 1 | 2 | 0 | |||
| 9 | 5 | 5 | 9 | 3 | 7 | 2 | |||
| Hours used, week by week, by jobs | |||||||||
| Job/Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
| 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | |
| 2 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | |
| 3 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | |
| 4 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 5 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | |
| 6 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 7 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 8 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 9 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | |
| Total hours | 200 | 200 | 200 | 200 | 200 | 160 | 120 | 0 | |
| Overtime hours | 40 | 40 | 40 | 40 | 40 | 0 | 0 | 0 | |
| Overtime cost | $400 | $400 | $400 | $400 | $400 | $0 | $0 | $0 | |
| Total cost (including penalties for being past due dates) | $4,000 | ||||||||
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Materiality In Financial Reporting An Integrative Perspective
Authors: Francesco Bellandi
1st Edition
178743737X, 9781787437371
