RentAPhone is a new service company that provides European mobile phones to American visitors to Europe. The company currently has 80 phones available at Charles de Gaulle Airport in Paris. There are, on average, 25 customers per day requesting a phone. These requests arrive uniformly throughout the 24 hours the store is open. The corresponding coefficient of variation is 1. Customers keep their phones on average 72 hours. The standard deviation of this time is 100 hours. Given that RentAPhone currently does not have a competitor in France providing equally good service, customers are willing to wait for the telephones. Yet, during the waiting period, customers are provided a free calling card. Based on prior experience, RentAPhone found that the company incurred a cost of $1 per hour per waiting customer, independent of day or night.
a. What is the average number of telephones the company has in its store?
b. How long does a customer, on average, have to wait for the phone?
c. What are the total monthly (30 days) expenses for telephone cards?
d. Assume RentAPhone could buy additional phones at $1,000 per unit. Is it worth it to buy one additional phone? Why?
e. How would waiting time change if the company decides to limit all rentals to exactly 72 hours? Assume that if such a restriction is imposed, the number of customers requesting a phone would be reduced to 20 customers per day.

- m = 80

a = 24 hours / 25 customers = 0.96 hours

p = 72 hours

u = p/(m x a) = 72 /(80×0.96)=0.9375

On average 93.75% of the phones are in use. 0.9375 x 80 = 75 phones are in use. Thus, 5 phones are available on average.

From above it is clear that 93.75%% of total phones are in use therefore total number of cell phones in use = 0.9375*80=75

So only 5 phones are available.

- CVa =1, CVp = 100/72 = 1.3889

Tq =( 72/80*[(0.9375 √2*80+1)-1]/(1-0.9375) * (12+1.88892)/2) = 9.89 hour

Thus average waiting time = 9.89 hours

Explanation:

- m = 80

a = 24 hours / 25 customers = 0.96 hours

p = 72 hours

u = p/(m x a) = 72 /(80×0.96)=0.9375

On average 93.75% of the phones are in use. 0.9375 x 80 = 75 phones are in use. Thus, 5 phones are available on average.

From above it is clear that 93.75%% of total phones are in use therefore total number of cell phones in use = 0.9375*80=75

So only 5 phones are available.

- CVa =1, CVp = 100/72 = 1.3889

Tq =( 72/80*[(0.9375 √2*80+1)-1]/(1-0.9375) * (12+1.88892)/2) = 9.89 hour

Thus average waiting time = 9.89 hours

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