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Two accountants, John and Debby, have an office, and each has a secretary. The accountants are...

Two accountants, John and Debby, have an office, and each has a secretary. The accountants are considering pooling their secretaries to gain efficiency in office operations. Currently, John gives a task to his secretary on the average of once every 20 minutes. It takes an average of 10 minutes to complete the task. Currently, Debby gives a task to her secretary on the average of once every 12 minutes. It takes an average of 10 minutes to complete the task. On the basis of available data, the interarrival times and processing times of tasks are exponentially distributed. What effect will the pooling of secretaries have on task turn-around time and secretary utilization?

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Answer #1

Turn-around time is the time taken to complete a task by a secretary. It is calculated by difference between the time of submission and time of completion of a task. At present, before pooling of secretaries, the turn-around time is 10 mins.

Secretary utilization: It is the time utilized for productive work. So, if the secretary is working only 10 mins on 1 task out of the 20 mins till the next task comes so the utilization is 50%.

John's secretary Debby's secretary
Arrival time (Time to get 1 task) 20 mins 12 mins
Service time (Time to complate 1 task) 10 mins 10 mins
no. of tasks in 1 hour 3 (60/20) 5 (60/12)

When we pool the resources, total no. of tasks in 1 hour is 8 (3+5 of both secretaries)

So now the Arrival time = total time / no. of tasks = 60mins/8 = 7.5 mins

Servicing time is still same = 10 mins but now there are two secretaries so in 10 mins- 2 tasks can be completed

No. of tasks completed in 1 hour = 60/10*2 =12

So the pooling will help in decreasing the wait around time. In hour , 8 tasks can be assigned and 12 tasks can be completed.

The turnaround time of task remains the same as 10 mins but now 4 tasks are completed each for John and Debby instead of 3 (33% increase of performance) in 1 hour.

Secretary utilization - in 1 hour 2people are completing 8 tasks = 80/2/60 = 67%

so, Secretary utilization increases from 50 to  67%

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