A small local grocery store has one checkout counter. Shoppers arrive at the che
ID: 456888 • Letter: A
Question
A small local grocery store has one checkout counter. Shoppers arrive at the checkout lane at an average rate of 15 customers per hour and the average order takes 3 minutes to ring up and bag. What information would you develop to help the manager analyze the current operation? If the manager does not want the average time waiting for service to exceed 5 minutes, what would you tell him about the current system? After reviewing the analysis, the manager felt it would be desirable to hire a full-time person to assist in the checkout operation. The manager believed that if this employee assisted the cashier, average scrvicc time could be reduced to 2 minutes. However, the manager was also considering installing a second checkout lane, which could be operated by the new person. This would provide a two-server system with the average service time of 3 minutes for each customer. Should the manager use the new employee to assist on the current checkout counter or to operate a second counter? Justify your recommendation.Explanation / Answer
The average rate of the shopper arrival at the customer counter is 15 (per hr)
Let the arrival rate at the counter be 'A' and the time taken for the average order be 'B'
Thus, A = 1/15 = 0.06 per hour
B = 1/ 3 = 0.33
The probability of the average time the order takes on the counter is calculated for 15 customers. Some assumptions that are taken into consideration are -
1) The arrival at each counter follows the poisson probability distribution with arrival rate as A.
2) The service times follow an exponential probability distribution with service rate as B
If the manager does not want the average time for waiting for the service as 5 mins, then a new counter has to be installed with a new person in the new counter. Then the average service time reduces.
The manager should use new employee to assist a new counter. That way, the old counter can be looked after him.
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