A new surgical facility called Cut & Sew is opening in neighborhoods throughout the United States. They are job shops that handle a variety of outpatient surgical procedures. Their process is set up so that one doctor cuts and the other sews. They have five patients to sequence for tomorrow. Since the weather forecast is for a cool and sunny day, they would also like to play golf tomorrow. They want to sequence their patients with the objective of minimizing the time from the beginning of the first job until the finish of that job. The patients and estimated times are as follows: Patient Cut Time (hours) Sew Time (hours)
A 2.3 2.8
B 2.5 3
C 2 1.5
D 0.6 1
E 3.6 2.6

Sequence the patients using Johnson's Method, state the schedule for each operation, and determine the minimum makespan.

Sequence: D| A| B| E| C|

Makespan = 14.1 hours.

Explanation:

Solution: We are asked to use Johnson's Method to sequence the patients and to determine the minimum makespan.

In Johnson's Method of sequencing, there are some conditions which must be met in order to solve this questions which are as follows:

1. Constant time for jobs, no variation.

2. No job priorities.

3. Jobs will go through from machine 1 to machine 2.

Keeping all those conditions in mind, let's start sequencing by Johnson's method.

Sequence:

                                    D| A| B| E| C|

Hence, this is the sequence to reduce the total time efficiently to perform all the jobs.

Rules to do sequencing:

First of check the number of jobs, here in our case, we have 5 jobs. So create a line of 5 boxes.

Secondly, you have check the data, check for the job and the machine which gives minimum time. If machine 1 (which is  Patient cut) gives minimum job time, then write it on the left most box and proceed towards right if other minimum times are also from machine 1. Otherwise, if machine 2 gives minimum job time for a particular job then write in the right most box and so on. Here you can see, Job C and Machine 2 gives the minimum job time, that is why I have put it on the right most box. Now, after including C, you cannot repeat job C. Moreover, you can see, Job D machine 1 gives minimum time, that is why wrote it in the left most box.

Hope, you have understood the method.

Let's Calculate the Makespan for this.    

Makespan: It is basically the total elapsed time from the start of job 1 to the end of job 5.

I have attached a table showing the starting and ending of each job and hence calculating the makespan. Please refer to the attachment.

Makespan = 14.1 hours.

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