The following set of jobs must be processed serially through a two-step system.The times at each process are in hours.If Johnson's Rule is used to sequence the jobs then the makespan time (in hours)for all jobs is
A)42 hours.
B)53 hours.
C)90 hours.
D)95 hours.

Question

The following set of jobs must be processed serially through a two-step system.The times at each process are in hours.If Johnson's Rule is used to sequence the jobs then the makespan time (in hours)for all jobs is 
A)42 hours. 
B)53 hours. 
C)90 hours. 
D)95 hours.

Quizplus · Accepted Answer

Using Johnson's Rule, we first find the minimum processing time (in hours) for each job across both steps:

A: 2 + 3 = 5
B: 3 + 5 = 8
C: 4 + 6 = 10
D: 6 + 4 = 10

So the sequence based on Johnson's Rule would be A-B-C-D. The total processing time for this sequence is 2 + 3 + 5 + 4 + 6 + 4 = 24 hours.

However, the question asks for the makespan time, which is the total time taken for all jobs to be processed from start to finish. In this case, we need to consider that each job cannot start processing in Step 2 until it has finished processing in Step 1. This means that the makespan time is equal to the total processing time for the sequence, plus the maximum time taken to complete Step 1 or Step 2 for any job.

To find the maximum time taken for Step 1, we add up the Step 1 processing times for each job:

2 + 3 + 4 + 6 = 15

To find the maximum time taken for Step 2, we add up the Step 2 processing times for each job:

3 + 5 + 6 + 4 = 18

Therefore, the makespan time is 24 + 18 = 42 hours, which is the total time taken for all jobs to be processed sequentially through the two-step system. However, we must also note that there is an error in the answer choices, as the makespan time calculated here is not equal to any of the options provided.

The Following Set of Jobs Must Be Processed Serially Through