Assume you are sequencing jobs using Johnson's rule. There are three jobs called A, B, and C. The first step is assembling and the second step is painting. Job A requires 3 hours to assemble and 6 hours to paint. Job B requires 7 hours to assemble and 2 hours to paint. Job C requires 4 hours to assemble and 1 hour to paint. The objective is to minimize the total processing time of all jobs, using Johnson's rule. What is the completion time of the last job in the sequence in the second step (painting)?
A) 14
B) 15
C) 9
D) 12
E) 10

Question

Quizplus · Accepted Answer

1. First, we need to calculate the processing times for both the assembling and painting steps for all the jobs:

Job A: Assembling time = 3 hours, Painting time = 6 hours, Total processing time = 9 hours
Job B: Assembling time = 7 hours, Painting time = 2 hours, Total processing time = 9 hours
Job C: Assembling time = 4 hours, Painting time = 1 hour, Total processing time = 5 hours

2. Next, we need to apply Johnson's rule to sequence the jobs:

Step 1: Identify the job with the shortest processing time for the first step (assembling).
Job C has the shortest assembling time, so we assign it to be the first job.

Step 2: Identify the job with the shortest processing time for the second step (painting).
Job B has the shortest painting time, so we assign it to be the last job.

Step 3: Sequence the remaining job based on their processing time for the first step (assembling).
Job A has a shorter assembling time than Job B, so it should be assigned to the second job.

Therefore, the optimal sequence is: C-A-B.

3. Finally, we need to calculate the completion time of the last job in the sequence in the second step (painting):

Job B: Assembling time = 7 hours, Painting time = 2 hours, Total processing time = 9 hours
C-A-B: Assembling time = 4+3+7 = 14 hours, Painting time = 1+6+2 = 9 hours, Total processing time = 23 hours

The completion time of the last job (Job B) in the second step (painting) is 9 hours. Therefore, the best choice is B.

Assume You Are Sequencing Jobs Using Johnson's Rule