Exam 10: Managing Customer and Work Flows

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand. -What is the probability that exactly 10 customers will arrive in 1 hour, when the mean arrival rate is 3 customers per hour, and interarrival times are exponentially distributed?

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60. -Calculate the total expected profit with 32 reservations (which means 2 overbookings).

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand. -What is the probability that exactly 30 calls arrive at a call center in an hour, when the mean arrival rate is 30 customer calls per hour, and interarrival times are exponentially distributed?

A street noodle vendor in Singapore can service an average of 10 customers per hour. Given an average arrival rate of 8 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand. -What is the probability that more than 4 customers will arrive in 1 hour, when the mean arrival rate is 4 customers per hour, and interarrival times are exponentially distributed?

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour. -What is the probability of exactly 2 customers arriving within 1 hour?

Leyland Motors can service an average 5 cars per hour, and the owner of Leyland Motors wants to know the probability of various customer arrival rates. Given the average arrival rate of 4 customers per hour, the owner uses the Poisson distribution to calculate the probabilities of various customer arrivals per hour. -What is the probability of exactly 5 customers arriving within 1 hour?

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand. -Calculate the mean waiting time in the queue.

Use the following information to determine the optimal overbooking policy for a motel at a rural town in South Carolina. The motel's capacity is 30 rooms. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per room is $110, and the cost of lost goodwill per guest due to overbooking is approximately $60. -Calculate the total expected profit with 33 reservations (which means 3 overbookings).

A street noodle vendor (one server) in Singapore can service an average of 20 customers per hour. Given an average arrival rate of 12 customers per hour, use the Poisson distribution to calculate the probability that the vendor can handle the demand. -What is the probability that there is no customer in the system at any given time?

Use the following information to determine the optimal overbooking policy for a spa center at downtown Marquette. The center's capacity is 12 guests. The historic number of no-shows for a typical day, along with the probability of occurrence, is shown in the following table. The average profitability per guest is $80, and the cost of lost goodwill per guest due to overbooking is approximately $40. -Based on the total expected profits obtained in Questions 41 through 43, which policy should be selected?