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 six cars. The interarrival time of potential demand for this lot from its base of customers is 20 minutes. The average rental period is 4 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.

Required:
a. What is the offered load?
b. What is the implied utilization?
c. What is the capacity of the process (rentals per hour)?
d. What is the probability that all eight cars are rented at the same time?

Answer 1

a. Offered load = 1 lot / 4 hours = 6 cars/4 hours = 1.5 cars/hours

b. Demand rate = Total cars per 4 hours/20 minutes time

Demand rate = 6*4 / 20

Demand rate = 24/20

Demand rate = 1.2 cars/hours

Implied utilization = Demand rate / Offered load

Implied utilization = 1.2/1.5

Implied utilization = 0.8

Implied utilization = 80%

c. Capacity of the process = 1 lot / 5 hours

Capacity of the process = 6 / 5

Capacity of the process = 1.2 rentals per hours

d. Probability that all eight cars are rented at the same time

=> (1 - 0.8) * (0.8)^8

=> 0.2 * 0.1678

=> 0.03356

=> 3.36