Concept explainers
Sequence the jobs shown below by using a Gantt chart. Assume that the move time between machines is on” hour. Sequence” the jobs in priority order 1, 2, 3, 4.
JobWork | Center/Machine Hours | Due Date (days) |
1 | A/3, B/2, C/2 | 3 |
2 | C/2, A/4 | 2 |
3 | B/6, A/1, C/3 | 4 |
4 | C/4, A/1, B/2 | 3 |
- a. What is the make span?
- b. How much machine idle time is there?
- c. When is each job delivered compared with its due date?
- d. How much idle time (waiting time) is there for each job?
- e. Devise a better job sequence for processing.
a)
To determine: The makespan.
Introduction:
Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.
Answer to Problem 3P
The makespan is 18 hours.
Explanation of Solution
Given information:
Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:
Construct the Gantt chart:
Hence, the total makespan is 18 hours (refer the Gantt chart).
b)
To determine: The machine idle time.
Introduction:
Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.
Answer to Problem 3P
The machine idle time is 24 hours.
Explanation of Solution
Given information:
Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:
Construct Gantt chart:
Determine the idle time for Machine A:
It can be determined that subtracting the sum of machine hours from the total makespan.
Determine the idle time for Machine B:
It can be determined that subtracting the sum of machine hours from the total makespan.
Determine the idle time for Machine C:
It can be determined that the subtracting the sum of machine hours from the total makespan.
Determine the machine idle time:
It can be calculated by adding the idle time of Machine A, Machine B, and Machine C.
Hence, the total machine idle time is 24 hours.
c)
To determine: The delivery time of each job compared to due dates.
Introduction:
Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.
Answer to Problem 3P
The delivery time does not exist due date.
Explanation of Solution
Given information:
Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:
Construct Gantt chart:
Determine the delivery time:
Due date is given in days. It must be converted to hours by considering working hours per day is 8 hours.
Job | Due date (hours) | Delivery time (hours) |
1 | 24 | 9 |
2 | 16 | 7 |
3 | 32 | 18 |
4 | 24 | 14 |
Delivery time is taken from the Gantt chart. Example: Job 1 is on its 9th hour at last. After that there is no Job 1.
d)
To determine: The idle time of the jobs.
Introduction:
Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.
Answer to Problem 3P
The job idle time is 11 hours.
Explanation of Solution
Given information:
Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:
Construct Gantt chart:
Determine the idle time of the jobs
There is no idle time for Job 1 and Job 2. However, Job 3 has the idle time of 6 hours in Machine C from 9th hour to 15th hour (Refer Gantt chart). Job 4 has the idle time of 5 hours in Machine A from 8th hour to 13th hour (Refer Gantt chart).
Hence, the total idle time is 11 hours.
e)
To determine: The better sequence for processing.
Introduction:
Gantt chart is the tool used to allocate the resources and schedule the tasks of projects.
Answer to Problem 3P
The makespan is 14 hours and the better sequence is 3, 2, 4, and 1.
Explanation of Solution
Given information:
Moving time between the machines is one hour and sequence is given as 1, 2, 3, and 4. In addition to this, the information is given below:
Construct the Gantt chart:
Hence, the total makespan is 14 hours (refer the Gantt chart).
Determine the idle time for Machine A:
It can be determined that subtracting the sum of machine hours from the total makespan.
Determine the idle time for Machine B:
It can be determined that subtracting the sum of machine hours from the total makespan.
Determine the idle time for Machine C:
It can be determined that subtracting the sum of machine hours from the total makespan.
Determine the machine idle time:
It can be calculated by adding the idle time of Machine A, Machine B, and Machine C.
Hence, the total machine idle time is 12 hours.
Determine the delivery time:
Due date is given in days. It must be converted to hours by considering the working hours per day as 8 hours.
Job | Due date (hours) | Delivery time (hours) |
1 | 24 | 14 |
2 | 16 | 7 |
3 | 32 | 12 |
4 | 24 | 12 |
Delivery time is taken from the Gantt chart. Example: Job 2 is on its 7th hour at last. After that there is no Job 2.
Hence, the sequence 3, 2, 4, and 1 is better in makespan and idle time.
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Chapter 12 Solutions
OPERATIONS MANAGEMENT IN THE SUPPLY CHAIN: DECISIONS & CASES (Mcgraw-hill Series Operations and Decision Sciences)
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