) FIVE JOBS ARE SCHEDULED IN TWO MACHINES IN A MANUFACTURING SHOP. AL FIVE JOBS ARE TO UNDERGO PROCESSING IN BOTH THE MACHINES SEQUENTIALLY

Question

) FIVE JOBS ARE SCHEDULED IN TWO MACHINES IN A MANUFACTURING SHOP. AL FIVE JOBS ARE TO UNDERGO PROCESSING IN BOTH THE MACHINES SEQUENTIALLY

PROCESSING TIMES IN MINUTES
JOB NO MACHINES1 MACHINE 2
1 4 7
2 6 3
3 2 3
4 7 7
5 8 6

A) IDENTIFY THE BEST SEQUENCE USING JOHNSON’S RULE
B) DEVELOP A GANTT CHART FOR SCHEDULE AND COMPUTE FLOW TIMES

Answer 1

To identify the best sequence using Johnson's rule, we need to follow these steps:

Step 1: Find the minimum processing time for each job in both machines.
Step 2: Identify whether the minimum processing time is in Machine 1 or Machine 2.
Step 3: Sort the jobs in the ascending order of the minimum processing time.

Let's go through the steps one by one:

Step 1: Find the minimum processing time for each job in both machines.

JOB NO MACHINES 1 MACHINE 2
1 4 7
2 6 3
3 2 3
4 7 7
5 8 6

For Job 1, the minimum processing time is 4 minutes.
For Job 2, the minimum processing time is 3 minutes.
For Job 3, the minimum processing time is 2 minutes.
For Job 4, the minimum processing time is 7 minutes.
For Job 5, the minimum processing time is 6 minutes.

Step 2: Identify whether the minimum processing time is in Machine 1 or Machine 2.

For Jobs 1, 2, and 3, the minimum processing time is in Machine 1.
For Jobs 4 and 5, the minimum processing time is in Machine 2.

Step 3: Sort the jobs in the ascending order of the minimum processing time.

According to Johnson's rule, we first schedule the jobs with the minimum time on Machine 1 and then the jobs with the minimum time on Machine 2.

Job 3 (2 minutes) is scheduled first on Machine 1.
Job 2 (3 minutes) is scheduled second on Machine 1.
Job 1 (4 minutes) is scheduled third on Machine 1.
Job 5 (6 minutes) is scheduled fourth on Machine 2.
Job 4 (7 minutes) is scheduled last on Machine 2.

So, the best sequence using Johnson's rule is: Job 3, Job 2, Job 1, Job 5, Job 4.

Now, let's develop a Gantt chart for the schedule and compute flow times.

Gantt chart:

Job 3 | Job 2 | Job 1 | Job 5 | Job 4
______|_______|_______|________|_______
2 5 9 15 22
|_________|________|________|________|

Flow time calculation:

For Job 1, the flow time is 9 minutes.
For Job 2, the flow time is 5 minutes.
For Job 3, the flow time is 2 minutes.
For Job 4, the flow time is 22 minutes.
For Job 5, the flow time is 15 minutes.

I hope this helps! Let me know if you have any further questions.