Coupon Accepted Successfully!



Scheduling specifies the order in which the given tasks should be performed. In other words, it gives the precedence relationship among the tasks—which task will be done first, which task will be done second and so on. In a production environment, scheduling becomes very critical owing to the cost constraint and the offerings of the competitor. Even at B-Schools, scheduling constitute a substantial part of the course curriculum.
For the sake of CAT preparation, CAT has asked scheduling problems quite a few times in the last couple of years. We will now learn the methods of scheduling through some typical problems.

Example 1- Go through the following passage and solve the questions based on it.
Heartkare hospital is specialized in heart related surgeries. Hospital boasts of the following facilities and conditions of surgery:
  1. Surgery is performed by one of the 12 senior doctors assisted by one of the seven junior doctors. Senior doctors generally take about one hour to prepare for and perform each surgery, and they operate on four patients per day.
  2. Senior doctors day ends at 4 p.m., although they can be asked to come every 14th night and every 10th weekend.
  3. Each patient goes through a series of tests and reporting before going for surgery. Tests are done between 9 a.m. to 3.30 p.m. (Monday to Friday), 10 a.m. to 2 a.m. (on Saturday).
  4. Patients come to hospital between 1 p.m. to 3 p.m. the day before their surgery.
  5. 1st operation begins at 7.30 a.m.
  6. The hospital is having five operating rooms, a patient recovery room, a laboratory, and five test examination rooms. Hospital performs 150 surgeries per week on an average with patients staying at the hospital for three days. Although surgeries are performed only five days a week, hospital is needed to be in operation for whole of the week to take care of recovering patients. Table above gives the current scenario of number of beds required in the hospital:
Current Scenario Beds required: Operations with 90 beds (30 patients per day)*
* - Patients stay in the hospital for three days requiring beds.
Check in day Monday Tuesday Wesnesday Thrusday Friday Saturday Sunday
Monday 30 30 30        
Tuesday   30 30 30      
Wesnesday     30 30 30    
Thrusday       30 30 30  
Sunday 30 30         30
Total 60 90 90 90 60 30 30


For example, 30 patients checked in the hospital on Tuesday and they stayed on Tuesday–Wednesday–Thursday. On Thursday, they were discharged from the hospital.
Hospital management is seriously considering now to expand its number of surgeries to generate more revenue.
There are two options before the management right now:
  1. Start surgeries on one more day (Saturday) ⇒ Leading to a flat 20% rise in surgeries done.
  2. Add one more premises to increase the number of beds by 50%.
    Assume that there is sufficient demand of the facilities of the hospital.

What is the ‘bed’ utilization of the hospital?
Hospital is not able to use its beds on all the days at its maximum level. Only on three days of the week—Tuesday, Wednesday and Thursday—all the beds in the hospital are utilized. For two of the remaining days of the week, only 30 beds are utilized and for the left two days 60 beds are utilized.
Hence ‘bed’ utilization for the whole week = 450/(90×7) = 450 / 630 = 71.4%
How would the above given table look like if management decides to perform surgery on Saturday too (assume 30 surgeries per day still)? What will be the ‘bed’ utilization in that case?
Following will be the occupancy table in the new case:
Proposed Scenario
Check in day Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Monday 30 30 30        
Tuesday   30 30 30      
Wednesday     30 30 30    
Thursday       30 30 30  
Friday         30    
Saturday           30  
Sunday 30 30         60
Total 60 90 90 90 90 60 60

New ‘bed’ utilization for the whole week = 540/(90×7) = 540 / 630 = 85.7%
What problems can occur, if any, if management decides to add another floor to expand the operation (Assume that in one operating room, only one surgery can be done at one point of time)?
If the capacity of the number of beds in the hospital is increased by 50%, then on an average 45 operations should have been done using the existing resources.
The resources are:
Operation room, senior doctors and junior doctors.
Now, Operation starts at 7.30 a.m. and goes till 4 p.m.

In this period of 8.30 hours × 5 operation room, a maximum of 40 operations can be done. And this lack of available operating room is the bottleneck. Hence to fully utilize the beds, we need to increase the operating hours by 30 mins making it 9 hours per day (from 7.30 a.m. to 4.30 p.m. for example), and then we can do 45 operations daily on an average.

After increasing 30 mins of operating time per day, new bed utilization chart will look like:
Check in day Monday Tuesday Wednesday Thursday Friday Saturday
Monday 45 45 45      
Tuesday   45 45 45    
Wednesday     45 45 45  
Thursday       45 45 45
Sunday 45 45        
Total 90 135 135 135 90 45

‘Bed’ utilization percentage for the whole week now = 675 /(135×7) = 71.4%

Example 2- 
Read the following passage and answer the questions based on it.
‘Noodles’ the fast food joint at North Campus, Delhi is famous for its value-for-money Chinese food. To understand and expand their business, management at ‘Noodles’ analyzed its processes and came out with following:
Customer enters Process 1 Process 2  Process 3  Process 4  Customer leaves

Any customer order has to go through all the four processes as given above.

Following is the time taken to do the processes:
Process 1 – 1 minute/order
Process 2 – 4 minutes/order
Process 3 – 3 minutes/order
Process 4 – 2 minutes/order

Noodles is open for 8 hours per day. A particular employee can work only in one process.

What is the maximum number of customers that ‘Noodles’ can service daily?
Total number of customers that can be serviced per day through different processes:
Process 1 – 480
Process 2 – 120
Process 3 – 160
Process 4 – 240
Since process 2 can service only 120 customers, hence total number of customers serviced = Min (480, 120, 160, 240) = 120.
It has been found that only one new employee can be added to ‘Noodles’ looking upon cost-benefit analysis. Which process the employee should be added to? How many customers can be serviced after this addition of new employee?
Obviously process 2 is the bottleneck, so the new employee should be added to process 2. After adding new employee, total number of customers serviced/day = 160.

Test Your Skills Now!
Take a Quiz now
Reviewer Name