Assume you are sequencing jobs using Johnson's rule.There are three jobs called A, B and C.The first step in 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

To apply Johnson's rule, we need to find which job should be done first in the first step and which job should be done last in the second step. To do this, we need to calculate the "forward" and "backward" time for each job.

Forward time for a job is the time it takes to complete the first step and the partial second step if the job is done first in the first step. Backward time for a job is the time it takes to complete the partial second step and the second step if the job is done last in the second step.

So, for job A, forward time = 3 hours (assemble) + 6 hours (paint) = 9 hours. Backward time = 6 hours (paint) + 3 hours (assemble) = 9 hours.

For job B, forward time = 7 hours (assemble) + 2 hours (paint) = 9 hours. Backward time = 2 hours (paint) + 7 hours (assemble) = 9 hours.

For job C, forward time = 4 hours (assemble) + 1 hour (paint) = 5 hours. Backward time = 1 hour (paint) + 4 hours (assemble) = 5 hours.

According to Johnson's rule, we should schedule the job that has the smallest "backward time" first in the first step, and the job that has the smallest "forward time" last in the second step. In this case, job C has the smallest backward time and should be scheduled first in the first step, while job A has the smallest forward time and should be scheduled last in the second step.

So the sequence should be: C -> B -> A.

The completion time of the last job in the second step (painting) is the sum of the time it takes to paint all three jobs, minus the time it takes to paint the job that was done last in the first step.

The total time to paint all three jobs is 6 (paint A) + 2 (paint B) + 1 (paint C) = 9 hours.

Since job C was done first in the first step, it was already painted and we don't need to subtract any time. Since job A was done last in the second step, we need to subtract the time it takes to paint job A, which is 6 hours.

So the completion time of the last job in the sequence in the second step (painting) is 9 - 6 = 3 hours after job A is done in the second step, which is a total of 15 hours.

Therefore, the answer is B) 15.

Assume You Are Sequencing Jobs Using Johnson's Rule