**Barber Shop Operations Analysis**Robert Olney's Barbershop is a well-known hair cutting and styling salon near the University of New Haven. It employs four full-time barbers, each spending an average of 15 minutes on every customer. The customer arrival rate is 12 per hour, following a Poisson distribution, and service times are negatively exponentially distributed. This setup allows us to explore the following questions using the given quantitative module.a) **Probability of the Shop Being Empty** Calculate the probability that the shop is empty. *(Round your response to four decimal places).*b) **Average Number of Customers in the Barber Shop** Determine the average number of customers present in the shop. *(Round your response to two decimal places).*c) **Average Time Spent in the Shop** Find out the average time customers spend in the shop. *(Round your response to three decimal places).*d) **Average Waiting Time** Analyze the average time a customer waits before being called to the barber chair. *(Round your response to three decimal places).*e) **Average Number Waiting to be Served** Estimate the average number of customers waiting to be served. *(Round your response to two decimal places).*f) **Utilization Rate with a Fifth Barber** Consider adding a fifth barber and calculate the new utilization rate of the shop. *(Round your response to four decimal places).*This educational exercise can help in understanding queue management and efficiency in service-oriented businesses.

Answered: Robert Olney's Barbershop is a popular…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

See similar textbooks

Similar questions

A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 9 customers per hour and an average service rate of 13 customers per hour. The probability of 6 customers in the system is : a. 0.9661 b. 0.8899 c. 0.3077 d. 0.03388
Forecasting and Queuing model List three positive and three negative outcomes for each of these application of management science
Please try to solve it with in 40 minutes please i need help
Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.
Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?
Please help me answer this question
Consider the table attached below:Assuming an M/M/1 setup, a service rate of 18 customers every 10 minutes, and a traffic intensity of 0.90.Assume a probability density function characterized by the exponential distribution.i). Compute the corresponding variates.ii). How robust is the above derived density function?
4. The problem: In a queueing problem modelled as (M/M/2), if L (number of units in the system) 0.75 units and service rate for each s (server) is 3 units per hour, what is the arrival rate? To answer the problem or question, you were given the following data/statements: = (1) The average time a unit spends in the queue is 2.5 mins. (2) The average time a unit spends in the system is 22.5 hours. Which of the following appropriately describes the data/statements provided? Select the corresponding letter and support your answer. A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient. B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 mins
A car mechanic, Carlos, can install new mufflers at an average rate of 3 every hour (following an exponential distribution). Customers needing this service arrive at the shop (following a Poisson distribution) on an average of 2 per hour. They are served on a first-in, first-out basis and come from the very large (almost infinite) population of possible buyers. Calculate the following operating characteristics of the service system: a. The probability there are no cars in the system. b. The average number of cars waiting in line. c. The average number of cars in the system. d. The average time a car spends waiting in line. e. The average time a car spends in the system.
3 The M/M/1 Queue During peak time, customers arrive at a bank teller window (with a single teller) at a rate of 23 per hour, where the teller can serve 25 per hour. This problem will allow you to investigate (via a simple extension of the mean queue size formula) the effect of highly-variable service times on our familiar queuing metrics. The diagram below stylizes the queuing system: Waiting Service Calculate the marginal probability P (T > oT). a. O b. 0.25 O c. 0.63 O d. 0.75 Calculate the mean time a customer spends at the bank (waiting time plus service time) in minutes. O a. 30 minutes O b. 27.6 minutes O c. 2.4 minutes O d. 7 minutes

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Business in Action

Operations Management

ISBN:

9780135198100

Author:

BOVEE

Publisher:

PEARSON CO

Purchasing and Supply Chain Management

Operations Management

ISBN:

9781285869681

Author:

Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson

Publisher:

Cengage Learning

Production and Operations Analysis, Seventh Editi…

Operations Management

ISBN:

9781478623069

Author:

Steven Nahmias, Tava Lennon Olsen

Publisher:

Waveland Press, Inc.

SEE MORE TEXTBOOKS