2. Little\'s Law (12 points) a) (6 points) Little Claw Pet Hospital takes in str

Question

2. Little's Law (12 points)

a) (6 points) Little Claw Pet Hospital takes in stray pets as part of its service to the community at large. The Hospital receives 200 stray pets per month , 40% of which are cats and the rest are dogs. The average stay of a cat is 15 days and the average stay of a dog is 10 days. The hospital has enough boarding facilities to hold a maximum of 50 dogs and 30 cats ( a dog cannot be housed in a cat kennel and vice versa). Is the boarding house at Little Claw big enough to accomodate the demand on its facilities? Assume 30 days per month.

b) (6 points) Little Claw's Famous diner remains open 24 hours per day, 365 days per year. The total number of customers served in the restaurant during 2008 was 12% greater than the total for 2007. In each year, the number of customers in the restaurant was recorded at a large number of randomly selected times, and the average of those numbers in 2008 was 16% greater than the average in 2007. By how much did the average duration of a customer visit to the diner increase or decrease?

Explanation / Answer

Answer a:

80 cats, 120 dogs

Average stay cats = 15days, average stay dogs= 10days

Capacity 50 dogs, 30 cats

According to little’s law:

I= R*T

Through put rate R = 80 cats/30days

Flow time T= 15 days per cat

Inventory I or how many cats that cats be accommodated= 15*(80/30)= 40 cats

But the capacity for cats is 30. Therefore, boarding house cannot accommodate all the cats

Through put rate R = 120 dogs/30days

Flow time T= 10 days per dog

Inventory I or how many cats that dogs be accommodated= 10*(120/30)= 40 dogs

The capacity for dogs is 50. Therefore, boarding house can accommodate all the dogs

Answer b: let the total customers in 2007= x, therefore customers in 2008= 1.12x

Inventory in 2007= I, Inventory in 2008= 1.16*I…… (this is no. of customers in restaurant at a random time)

throughput rate 2007=R1= x/(24*365), throughput rate 2008= R2= 1.12x/(24*365)……….. (average customers per hour)

Flow time in 2007= T1=duration of customer in restaurant= inventory /throughput rate= I/[x/(24*365)]……….. (using Little’s law T= I/R)

Flow time in 2008= T2=duration of customer in restaurant= inventory /throughput rate= 1.16I/[1.12x/(24*365)]

Now, ratio of T2/T1= 1.16/1.12= 1.035 that is increase of 3.5% over 2007

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