Practical Management Science
5th Edition
ISBN: 9781305734845
Author: WINSTON
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 13.5, Problem 20P
Summary Introduction
To determine: The number of tellers that the bank should hire.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A small bank is trying to determine how many tellers toemploy. The total cost of employing a teller is $100 per day,and a teller can serve an average of 60 customers per day.An average of 50 customers per day arrive at the bank, andboth service times and interarrival times are exponential. Ifthe delay cost per customer-day is $100, how many tellersshould the bank hire?
Using an M/M/1 queuing system as an example demonstrate how the event list in a simulation model would evolve over 5 discrete steps if the first part will arrive at time zero, the time between the next four arrivals are 3, 5, 6, and 4 minutes and that the machining times for the first five parts are 6, 4, 3, 5, and 4 minutes. The performance metrics of interest are the average queue length and the number of items processed.
A crew of mechanics at the Transylvania Department of Motor Vehicles garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. Approximately how many vehicles are in the garage, waiting for or being repaired?
Chapter 13 Solutions
Practical Management Science
Ch. 13.3 - Prob. 1PCh. 13.3 - Prob. 2PCh. 13.3 - Prob. 3PCh. 13.3 - Prob. 4PCh. 13.4 - Prob. 5PCh. 13.4 - Prob. 6PCh. 13.4 - Prob. 7PCh. 13.4 - Prob. 8PCh. 13.5 - Prob. 9PCh. 13.5 - Prob. 10P
Ch. 13.5 - Prob. 11PCh. 13.5 - Prob. 12PCh. 13.5 - Prob. 13PCh. 13.5 - Prob. 14PCh. 13.5 - Prob. 15PCh. 13.5 - Prob. 16PCh. 13.5 - Prob. 17PCh. 13.5 - Prob. 18PCh. 13.5 - Prob. 19PCh. 13.5 - Prob. 20PCh. 13.5 - Prob. 21PCh. 13.5 - Prob. 22PCh. 13.5 - Prob. 23PCh. 13.5 - Prob. 24PCh. 13.5 - Prob. 25PCh. 13.5 - Prob. 26PCh. 13.5 - Prob. 27PCh. 13.5 - Prob. 28PCh. 13.5 - Prob. 29PCh. 13.5 - Prob. 30PCh. 13.5 - Prob. 31PCh. 13.5 - Prob. 32PCh. 13.5 - Prob. 33PCh. 13.5 - Prob. 34PCh. 13.5 - Prob. 35PCh. 13.5 - Prob. 36PCh. 13.5 - Prob. 37PCh. 13 - Prob. 46PCh. 13 - Prob. 47PCh. 13 - Prob. 48PCh. 13 - Prob. 49PCh. 13 - Prob. 50PCh. 13 - Prob. 51PCh. 13 - Prob. 52PCh. 13 - Prob. 54PCh. 13 - Prob. 58PCh. 13 - Prob. 59P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, operations-management and related others by exploring similar questions and additional content below.Similar questions
- A small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $10 per hour, and a teller can serve an average of 50 customers per day. An average of 40 customers per day arrive at the bank, and both service times and interarrival times are exponential. If the delay cost per customer- hour is $10 and bank is working 8 hours per day, how many tellers should the bank hire?arrow_forwardMarty's Barber Shop has one barber. Customers have an arrival rate of 1.1 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? Round your answer to four decimal places.P3 = What is the probability that more than two customers are waiting? Round your answer to four decimal places.P(More than 2 waiting) = What is the average time a customer waits for service? Round your answer to four decimal places.Wq = minutesarrow_forwardA post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. What is the average length of the line?arrow_forward
- A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $500, how many tellers should the bank hire? (The “MMs Template with Economic Analysis” is attached for you to do the calculation. Report your input and final answer in the exam template file.)arrow_forwardA small bank is trying to determine how many tellers to employ. The total cost of employing a teller is $10 per hour, and a teller can serve an average of 120 customers per day. An average of 100 customers per day arrive at the bank, and both service times and interarrival times are exponential. If the delay cost per customer- hour is $10 and bank is working 8 hours per day, how many tellers should the bank hire?arrow_forwardConsider a system with Poisson distributed arrival rate with average of 10 clients per day. The service time is exponentially distributed with 8 clients per day. If the cost for operating each server is $20 per day and the cost of holding a client in the system is $200 per day, What is the total cost of operating with 5 servers? Answer is $350.65 please explain.arrow_forward
- Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hoursarrow_forwardA post office has a single line for customers waiting for the next available postal clerk. There are two postal clerks who work at the same rate. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. The average arrival rate is three per minute and the average service rate is two per minute for each of the two clerks. How long does the average person spend waiting for a clerk? 1.143 minutes 3.429 minutes 1.929 minutes 0.643 minutearrow_forwardYou are considering to invest in a franchise for a coffee shop in your neighborhood. To understand the revenue potential, you decide to visit a coffee shop from the same chain next to your neighborhood. In the next few months, you visit this coffee shop at random times between 6am and 9am. You observe that the line (queue) averages about 9 customers and it takes about 3 minutes to get in and out of the coffee shop. Assuming this is a typical experience and each customer spends about $5 per visit, what is the revenue potential per hour of this coffee shop? Hint: Calculate the number of customers arriving per minute (i.e., λ). Convert this to customers per hour. Then, calculate the revenue from these customers (each customer spends about $5, on average)arrow_forward
- In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle? What is the probability of having exactly 4 customers in the system? What is the probability of having 4 or fewer customers in the system?arrow_forwardThe manager of a bank wants to use an MyMys queueingmodel to weigh the costs of extra tellers against the costof having customers wait in line. The arrival rate is 60customers per hour, and the average service time is fourminutes. The cost of each teller is easy to gauge at the$11.50 per hour wage rate. However, because estimatingthe cost per minute of waiting time is difficult, the bankmanager decides to hire the minimum number of tellersso that a typical customer has probability 0.05 of waitingmore than five minutes in line.a. How many tellers will the manager use, given thiscriterion?b. By deciding on this many tellers as “optimal,” themanager is implicitly using some value (or some range of values) for the cost per minute of wait-ing time. That is, a certain cost (or cost range) would lead to the same number of tellers as sug-gested in part a. What is this implied cost (or cost range)?arrow_forwardFor a single-server queue of 10 customers whose arrival and service time is given below in the table. Complete the below given table. Customer Arrival Time ti Inter Arrival Time Ai=ti—ti-1 Service Begins (Sb) Delay Time (Di) Service Time (Si) Calculate Ci=ti+Di+Si 1 7:00 7:02 6 2 7:08 7:12 4 3 7:11 7:16 1 4 7:13 7:19 5 5 7:18 7:25 10 6 7:36 7:39 2 7 7:40 7:44 3 8 7:45 7:48 3 9 7:49 7:52 4 10 7:55 7:57 3 Find the average service time and average delay time. Average Service Time= Average Delay Time=arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,
Practical Management Science
Operations Management
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:Cengage,