Question

In the ABC retail store customers arrive at an average 50 per shift. The store manager wants to calculate whether he should hire 1, 2, 3 or 4 salespeople.He has deter- mined that average waiting times will be 6 minutes with one salesperson, 3 minutes with two salespeople, 2 minutes with three salespeople, and 1 minute with four salespeople.He has estimated the cost per minute that customer wait at $1. The cost per salesperson per shift (including fringe benefits) is $70. How many sales people should be hired?

Answer 1

Given that,

Cost per salesperson, Cs = $ 70 per shift

Cost of waiting, Cw = $ 1 per minute

Arrival rate, a = 50 per shift

For Number of salesperson, n = 1, Average waiting time, Wq = 6 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 1*70 + 50*6*1 = $ 370

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For Number of salesperson, n = 2, Average waiting time, Wq = 3 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 2*70 + 50*3*1 = $ 290

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For Number of salesperson, n = 3, Average waiting time, Wq = 2 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 3*70 + 50*2*1 = $ 310

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For Number of salesperson, n = 4, Average waiting time, Wq = 1 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 4*70 + 50*1*1 = $ 330

Total cost per shift is lowest with 2 salespeople.

Therefore 2 sales people should be hired.