Operations Management
17th Edition
ISBN: 9781259142208
Author: CACHON, Gérard, Terwiesch, Christian
Publisher: Mcgraw-hill Education,
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Chapter 17, Problem 6PA
Summary Introduction
To determine: The interarrival time for combined lot.
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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?
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?
At the Strathmore University Cafeteria, students seeking to have a meal are observed to arrive at a rate of 16 every 20 min. The service personnel at the cafeteria serve the students at a rate of 19 evevry 20 min.
required:
Assuming M/M/1 setup, deduce
a) the traffic intensity of the strathmore cafeteria
b) the probability of having no students in the queue
c) The probability of having more than 5 students in the system
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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
- The manager of a large group of employees must decideif she needs another photocopying machine. The cost of amachine is $40 per 8-hour day whether or not the machineis in use. An average of 4 people per hour need to use thecopying machine. Each person uses the copier for an averageof 10 minutes. Interarrival times and copying times areexponentially distributed. Employees are paid $8 per hour,and we assume that a waiting cost is incurred when a workeris waiting in line or is using the copying machine. Howmany copying machines should be rented?arrow_forwardAt the Strathmore University Cafeteria, students seeking to have a meal are observed to arrive at a rate of 16 every 20 min. The service personnel at the cafeteria serve the students at a rate of 19 evevry 20 min. required: Assuming M/M/1 setup, deduce the average number of entities in both the system (L)and in the queue (lq)arrow_forwardImagine a small coffee shop with a single counter. On average, 16 customers arrive at the store every hour and stay an average of 30 minutes in the store. Calculate the average number of customers queuing in this coffee shop? Suppose that the average number of customers increased to 30 customers every hour, Describe the consequences, and give a solution.arrow_forward
- A computer processes jobs on a first-come, first served basis in a time-sharing environment. The jobs have Poisson arrival rates, with an average of 5 minutes between arrivals. The objective in processing these jobs is that they spend no more than 8 minutes, on average, in the system. Assuming exponential service times, how fast does the computer have to process jobs (in minutes, rounded to 3 decimal places), on average, to meet this objective?arrow_forwardA small bagel stand known as Andres by the Sea offers drive-thru service to customers in Sants Barbra. Andres by the Sea has two customers arrive every hour on average. Suppose that this bagel stand follows an M/M/1 FIFO queuing system with no limits on queue length. They have one employee working at all times that spends 15 minutes per customer. Assume that the employee is paid $10 per hour and a customer’s waiting cost in queue is estimated to be $12 per hour. The average number of customers in the queue (before rounding up), and the total cost per hour are: a. 0.4; $15. b. 0.8; $18. c. 0.6; $21. d. 0.3; $17. e. 0.5; $16.arrow_forwardPodunk University Operations Research Departmenthas two phone lines. An average of 30 people per hour tryto call the OR Department, and the average length of aphone call is 1 minute. If a person attempts to call whenboth lines are busy, he or she hangs up and is lost to thesystem. Assume that the time between people attempting tocall and service times is exponential.a What fraction of the time will both lines be free?What fraction of the time will both lines be busy? Whatfraction of the time will exactly one line be free?b On the average, how many lines will be busy?c On the average, how many callers will hang up eachhour?arrow_forward
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