Question

RideShare offers short-term rentals of vehicles that are kept in small lots in urban neighborhoods with plenty of potential customers. With one lot, it has eight cars. The interarrival time of potential demand for this lot from its base of customers is 40 minutes. The average rental period is five hours. If a customer checks availability of vehicles in this lot online and finds that they are all rented for the desired time, the customer skips renting and finds alternative arrangements. However, because customers pay a monthly fee to subscribe to this service, RideShare does not want customers to be disappointed too often.

b. What is the implied utilization?

• A. 0.87
• B. 0
• C. 0.54
• D. 0.94

c. What is the capacity of the process (rentals per hour)?

• A. 3.6
• B. 1.6
• C. 2.6
• D. 4.6

d. What is the probability that all eight cars are rented at the same time?

• A. 0.207
• B. 0.107
• C. 0.307
• D. 0.407

Answer 1

Answer:-

Given That:-

RideShare offers short-term rentals of vehicles that are kept in small lots in urban neighborhoods with plenty of potential customers. With one lot, it has eight cars. The interarrival time of potential demand for this lot from its base of customers is 40 minutes. The average rental period is five hours. If a customer checks availability of vehicles in this lot online and finds that they are all rented for the desired time, the customer skips renting and finds alternative arrangements. However, because customers pay a monthly fee to subscribe to this service, RideShare does not want customers to be disappointed too often.

b. What is the implied utilization?

Demand rate =total cars per 5 kms/40 minutes time

= 60/40

= 1.5 cars/hr

implied utilization = Demand rate/offered load

= 1.5/1.6

= 0.9375

= 0.94

implied utilization = 0.94

Answer is option D.

c. What is the capacity of the process (rentals per hour)?

capacity of the process = 1 lot/5 hours

= 8/5

capacity of the process = 1.6  rentals per hour

Answer is option B.

d. What is the probability that all eight cars are rented at the same time?

Let,

eight cars are rented at the same time is :

(1 - 0.9375) * (0.9375)8

= (0.0625) * (0.5967)

= 0.0372

Therefore,

The probability that all eight cars are rented at the same time is 0.037

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