Suppose we are interested in estimating the average number of customers in the s

Question

Suppose we are interested in estimating the average number of customers in the supermarket. On average, there are 15 customers entering the supermarket every 5 minutes. And on average, a typical customer spends about 20 minutes in the supermarket (from entering to exiting the market).

a. Calculate the average number of customers in the supermarket.

b. About 20% of customers leave without making a purchase. On average, a customer spends about 5 minutes in the checkout area. Estimate the average number of customers in the checkout area.

Explanation / Answer

This problem will be solved using principles of Little’s law.

As per Little’s law ,

Rate of Arrival in the system ( R ) x Throughput time in the system ( T) = Inventory in the system ( I )

Answer to question a:

In the given case :

R = Rate of arrival of customers in the super market = 15/5 = 3 per minute

T = Amount of time customer spends in the supermarket = 20 minutes

Therefore ,

Average number of customers in the supermarket = I = 3 X 20 = 60

AVERAGE NUMBER OF CUSTOMERS IN THE SUPERMARKET = 60

Answer to question b :

Since 20% of customers leave without making a purchase, 80% of customers make purchases and go to checkout area

Therefore ,

R = Rate at which customers go to checkout area = 80% of arrival in the supermarket = 80% of 3 / minute= 2.4 / minute

T = Throughput time in the checkout area = 5 minutes

Therefore , average number of customers in the checkout area = R X T = 2.4 X 5 = 12

AVERAGE NUMBER OF CUSTOMERS IN THE CHECKOUT AREA = 12

AVERAGE NUMBER OF CUSTOMERS IN THE SUPERMARKET = 60

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