What is the optimum job sequence for the jobs listed below using Johnsons Rule

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A.e-g-f-dB.d-g-f-eC.d-f-g-eD.e-d-f-gE.f-e-d-gAccessibility: Keyboard NavigationDifficulty: MediumLearning Objective: 16-03 Discuss and use common priority rules and performance measures for sequencing; and perform sequencing forfour types of problems.Topic: 16-08 Sequencing Jobs through Two Work Centres/Machines69. The Theory of Constraints focuses on ________.

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Accessibility: Keyboard NavigationDifficulty: EasyLearning Objective: 16-06 Describe some of the approaches used for staff scheduling; including scheduling tow consecutive days off; shiftscheduling; and airline crew scheduling.Topic: 16-20 Shift Scheduling

The sequencing problem deals with determining an optimum sequence of performing a number of jobs by a finite number of service facilities [machine] according to some pre-assigned order so as to optimize the output. The objective is to determine the optimal order of performing the jobs in such a way that the total elapsed time will be minimum.

Consider there are jobs 1,2,3,…….,n to be processed through m machines. [Machine A, Machine B, Machine C, ……, Machine n]. The objective is to find a feasible solution, such that the total elapsed time is minimum. We can solve this problem using Johnson’s method.  This method provides solutions to n job 2 machines, n job 3 machines, and 2 jobs m machines.

Johnson’s Algorithm:

Johnson’s rule in sequencing problems is as follows:

1. Find the smallest processing time on Machine 1 and Machine 2.
2. a] If the smallest value is in Machine 1 process that job first.
   b] If the smallest value is in the Machine 2  process that job last.
3. a] if the minimum time for both Machine 1 and Machine 2 is equal, then perform the job of Machine 1 first and then the job of Machine 2.
        b] if there is a tie for a minimum time among jobs in Machine 1, select the job corresponding to the minimum of Machine 2 and process it first.
        c] if there is a tie for a minimum time among jobs in Machine 2, select the job corresponding to the minimum of Machine 1 and process it last.
4. And then calculate the total elapsed time[ the time interval between starting the first job and completing the last job] and Idle time[ the time during which the machine remains idle during the total elapsed time.

In this article, we will understand this problem through n job 2 machines. We have to find the sequence of jobs to be executed in different machines to minimize the total time.

Example:

 Solution: The smallest time is 1 for Machine 1, process it first.

Next, the smallest time is 2 for Machine 2, process it last

The next smallest time is 3 of job 5 but Job 5 is already being processed by Machine 2. Discard it.

Next, the smallest time is 4 for Machine 2, process it last just before J5.

The next smallest time is 5 for job 2  but job 2 is already being processed by Machine 2. Discard it. 

Next, the smallest value is 7 for Machine 2, process it last just before J2.

Next, the smallest value is for Machine 1 & Machine 2, J1 of Machine 1 is already being processed on Machine 2 . So, take J3 of Machine 2 and process it last just before J3.

So, the final sequence of processing the jobs is J4, J3, J1, J2, and J5. 

Total Elapsed Time = 28
Idle time of Machine 1 = 0
Idle time of Machine 2 = 1 [Machine 2 has to wait for Machine 1 for 1 unit during the execution of Job 4.

What is Johnson's rule for sequencing?

Is the process of deciding on the job order on same machine or at same work Centre?