Table J.12
Consider the following problems in which six jobs must each be processed on two machines starting with machine 1 and then going to machine 2.The following processing times and due dates are in hours.

-Use the information in Table J.12.What is the minimum makespan for completing all six jobs?
A)fewer than or equal to 30 hours
B)greater than 30 but fewer than or equal to 33 hours
C)greater than 33 but fewer than or equal to 36 hours
D)greater than 36 hours

Question

Table J.12
Consider the following problems in which six jobs must each be processed on two machines starting with machine 1 and then going to machine 2.The following processing times and due dates are in hours.
 
-Use the information in Table J.12.What is the minimum makespan for completing all six jobs?
A)fewer than or equal to 30 hours 
B)greater than 30 but fewer than or equal to 33 hours 
C)greater than 33 but fewer than or equal to 36 hours 
D)greater than 36 hours

Quizplus · Accepted Answer

To solve this problem, we can use the Johnson's rule for two machines.

Step 1: Find the min processing time for each job across the two machines

Job 1: min(2,6)=2
Job 2: min(3,4)=3
Job 3: min(1,5)=1
Job 4: min(4,3)=3
Job 5: min(5,2)=2
Job 6: min(2,4)=2

Step 2: Sort the jobs in increasing order of min processing times

Job 3, Job 1, Job 6, Job 5, Job 2, Job 4

Step 3: Assign the jobs to machines using the Johnson's rule

Machine 1: Job 3, Job 1, Job 6, Job 5
Machine 2: Job 2, Job 4

Total processing time = max(sum of processing times for Machine 1, sum of processing times for Machine 2) = max(10+3+4+5, 3+6) = 22

Therefore, the minimum makespan for completing all six jobs is 22 hours, which falls in the range of  greater than 33 but fewer than or equal to 36 hours. The best choice is C.

Table J.12 Consider the Following Problems in Which Six Jobs Must Each