Get premium membership and access revision papers, questions with answers as well as video lessons.
Cpa Section Iv - Quantitative Analysis. Question Paper
Cpa Section Iv - Quantitative Analysis.
Course:
Institution: Royal Business School question papers
Exam Year:2011
Quantitative Analysis.
Queueing Theory Review Questions.
QUESTION ONE
Cronus Ltd. operates an engineering factory with a very large number of employees. Each employee has to make frequent visits to the firm''s stores to obtain issues of materials for his next job. The issue of one type of material is made in section D at a counter attended by an employee of the stores section. Employees who require issues have to join a single queue and wait until the attendant is available. The average rate of arrival in the stores is 16 per hour and the average rate of service is 20 per hour.
Issues of materials are costed at the cost of materials plus 5% to cover the overhead costs of storage. The overhead costs of storage in section D include £3,000 per annum for wages of the attendant at the issues counter and £600 per annum attributed to the attendant for fixed establishment costs - rent, rates, light and heat and so on - of the service area. Average wages of directly productive employees who visit Section D are £1.60 per hour. The length of the firm''s normal working year is 2,000 hours.
The director of Cronus are considering the desirability of employing an extra man as an attendant at the stores issue counter. His wages and efficiency would be the same as for the existing attendant. It would be necessary to spend £2,000 on capital equipment having a life of ten years. Any savings of the waiting time of directly productive employees would make it possible to reduce the amount of labour time for which the firm pays. The cost of capital of Cronus is 15 percent per annum.
You may assume that arrivals in and departures from the issues section are described by Poisson distributions and that the number of employees is indefinately large. A table of standard formulae is available.
You are required to:
a. Prepare calculations to show whether the additional attendant should be employee and,
b. Explain a techniques of analysis which could be used to study the problem when Poisson distributions and simple queue discipline may not be assumed.
QUESTION TWO
Customers arrive at FirstElias Bank drive-in window at a rate of 10 per hour during regular periods, while the average interarrival time during peak hours is 4 minutes. The average service time is 4.1 minutes.
Determine:
a. The probability a customer is in the system 12 or fewer minutes during a period of regular demand.
b. The probability of finding fewer than 6 customers in the system during a period of regular demand.
c. FirstElias wants to implement a policy that an arriving customer, during peak time, will not have to wait (prior to service), on the average, more than 10 minutes. Is this goal achievable today? If not, determine what service rate is necessary to attain this goal.
d. The operation of the drive-in window costs $20 an hour. The estimated loss due to decreased goodwill, because of the time spent in line, is figured at $1 per hour per customer. Management can expedite the service time to 3 minutes per customer at a cost of $15 per hour. Would you recommend it for the regular hours? For the peak hours? Why or why not?
QUESTION THREE
A mechanic repairs four machines. The mean time between service requirements is 5 hours for each machine and forms an exponential distribution. The mean repair time is 1 hour and also follows the same distribution pattern. Machine downtime costs Rs. 25 per hour and the mechanic costs Rs. 55 per day.
a. Find the expected number of operating machines.
b. Determine the expected downtime costs per day.
c. Would it be economical to engage two mechanics, each repairing only two machines?
QUESTION FOUR
At a railway station only one train is handled at a time. The railway yard is sufficient only for two trains to wait while other is given signal to leave the station. Trains arrive at the station at an average rate of 6 per hour and the railway station can handle them on an average of 12 per hour. Assuming Poisson arrivals and exponential service distribution, find the steady state probabilities of the various number of trains in the system. Also find the average number of trains in the system.
QUESTION FIVE
At what average rate must a clerk at a supermarket work in order to ensure a probability of 0.90 that the customer will not wait longer than 12 minutes? It is assumed that there is only one counter at which customers arrive in a Poisson fashion at an average rate of 15 per hour. The service by the clerk has an exponential distribution.
More Question Papers
Popular Exams
Return to Question Papers