Topic: Waiting Line Models
Problem 1: Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute.
a. What is the mean or expected number of customers that will arrive in a five-minute period?
b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. If required, round your answers to four decimal places.
c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your answer to four decimal places.
Problem 2: Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.6 customers arrives each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 12 minutes with each customer.
a. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. If required, round your answers to four decimal places.
b. Service goals dictate that an arriving customer should not wait for service more than an average of 4 minutes. Is this goal being met? If not, what action do you recommend? (See attached screenshot to question #b)
c. If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean service rate? If required, round your answer to one decimal place.
Will the service goal be met? Yes or No for question c.
Problem 3: (Algorithmic) Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to eight. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.05 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.5 machines per hour.
a. Compute the operating characteristics if the company retains the single-employee repair operation. If required, round your answers to four decimal places.
b. Compute the operating characteristics if a second employee is added to the machine repair operation. If required, round your answers to four decimal places.
c. Each employee is paid $25 per hour. Machine downtime is valued at $75 per hour. From an economic point of view, should one or two employees handle the machine repair operation? Explain. If required, round your answers to two decimal places.
From an economic point of view--------- should handle the machine repair operation.
Option for question c one employee or two?
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Attachment:- Waiting Line Models.rar