Question

A retail store is trying to decide how many clerks to hire for the Christmas shopping season. Customers arrive during the big sales at a rate of 180 per hour. 5 clerks can check out an average customer every 15 seconds. 8 clerks can check out an average customer every 10 seconds. The cost to hire each clerk is $10 per hour and they work 9 hours on big shopping days. If customers stand in line too long they will leave and go on to another store. The cost of having a customer standing around is $150. How many clerks should be hired?

Answer 1

Arrival rate lambda= 180

Service rate mu with 5 clerks= 60*60/15 = 240 per hour

Waiting time= lambda /mu*(mu-lambda)

Wq= 180/240*(240-180) = 1/80 hours

Total waiting time per hour = lambda*wq = 180/80 hours.

Cost of waiting= 150*180/80 = 337.5

Total cost = 10*5+337.5 = 387.5 per hour.

Service rate with 8 clerks = 60*60/10= 360

Waiting time ,= 180/360*(360-180) = 1/360 hours

Total hourly waiting time = 180/360=0.5 hours

Total cost of waiting = 0.5*150=75

Total cost = 8*10+75 = 155.

8 clerks should be hired because the total cost is low.