Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 12, Problem 52P
Summary Introduction
To determine: The number of copying machines that must be rented.
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
Trending nowThis is a popular solution!
Students have asked these similar questions
BOBO Van is a start-up company which develops an app to receive orders from customers and provide delivery service. It owns one single vehicle. Two workers form a crew. The whole crew, which includes both workers working as a team, is needed to complete the delivery service. On average, an order arrives every 20 minutes while it takes 15 minutes on average to complete the order. If an order arrives while the crew is working on another order, the arriving order needs to join the waiting line for service. Assume the app provide adequate quota to accommodate essentially any number of orders waiting in the line.
What is the average number of orders in the waiting line?
Group of answer choices
0.1227
0.0333
3
0.5
2.25
Consider two identical queuing systems except for the service time distribution. In the first system the service time is random and Poisson distributed. The service time is constant in the second system. How would the waiting time differ in the two systems?
Explain the concept of queue and queue theory or waiting line theory and its importance in business
A bank has only one counter for its customers. Suppose that the customers to the bank arrive at random with exponential inter arrival time and their mean inter arrival time is 10 minutes. Suppose the counter takes on an average 15 minutes to serve the customer and this also follow an exponential distribution.
What percentage of time the bank counter is busy?
On the average, how many customers are in the system?
On the average, how many customers are in the queue waiting for the service?
How long a customer will take to be out of the service system after being served?
How long a customer to wait before being served?
What is the probability that there are at most three customers in the system?
Chapter 12 Solutions
Practical Management Science
Ch. 12.3 - Prob. 1PCh. 12.3 - Explain the basic relationship between the...Ch. 12.3 - Prob. 3PCh. 12.3 - Prob. 4PCh. 12.4 - Prob. 5PCh. 12.4 - Prob. 6PCh. 12.4 - Prob. 7PCh. 12.4 - Prob. 8PCh. 12.5 - Prob. 9PCh. 12.5 - Prob. 10P
Ch. 12.5 - Prob. 11PCh. 12.5 - Prob. 12PCh. 12.5 - Prob. 13PCh. 12.5 - Prob. 14PCh. 12.5 - Prob. 15PCh. 12.5 - Prob. 16PCh. 12.5 - Prob. 17PCh. 12.5 - Prob. 18PCh. 12.5 - Prob. 19PCh. 12.5 - Prob. 20PCh. 12.5 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.5 - On average, 100 customers arrive per hour at the...Ch. 12.5 - Prob. 24PCh. 12.5 - Prob. 25PCh. 12.5 - Prob. 26PCh. 12.5 - Prob. 27PCh. 12.5 - Prob. 28PCh. 12.5 - Prob. 29PCh. 12.5 - Prob. 30PCh. 12.5 - Prob. 31PCh. 12.5 - Prob. 32PCh. 12.5 - Prob. 33PCh. 12.5 - Prob. 34PCh. 12.5 - Prob. 35PCh. 12.5 - Two one-barber shops sit side by side in Dunkirk...Ch. 12.5 - Prob. 37PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 54PCh. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61P
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
- Customer interarrival times at a store are exponentially distributed with rate 8 customers per hour. Customers are served by a single customer service representative (CSR), at a rate of 10 customers per hour. Service times are also exponentially distributed. Which of the following statements are true? O The probability of having exactly three customers in the store is 0.128. O None of the answers are correct. The store has customers waiting for a CSR 80.0% of the time. The average number of customers in the store is 3.2. O The average wait time for the CSR is 24 minutes.arrow_forwardA server operates with 80 % utilization. Coefficient of variation of service process is 0.5. Coefficient of variation of arrival process is 0.9. Average processing fime is 3 minutes. What is the average time a customer spends in the system using the single server queueing model 7 Show all formulas used, calculations and results.arrow_forwardA supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customer is four minutes. Interarrival times and servicetimes are exponentially distributed, and the system can be modeled as an M/M/s system. (In contrast to the situation at most supermarkets, we assume that all customers wait in a single line.) It costs $20 per hour tooperate a cash register, and a cost of $0.25 is assessed for each minute the customer spends in the cash register area (in line or being served). How many registers should the store open to minimize the expected hourly cost?arrow_forward
- True or False? The average number of customers in queue plus the number of servers equals the average number of customers in the system. The main cause of delay at Logan Airport was overbooking, and building a new runway solved the delay problem. If a company hopes to increase the capacity of a process, the company needs to try to shorten the process’s cycle time. Little’s Law only applies to an M/M/1 queue, which is a special case of a G/G/C queue. If a queuing system has deterministic arrival rate λ and service rate μ, and λ < μ, then Lq = 0 in this queue.arrow_forwardTown 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. 12. What percentage of time only one dispatcher is busy? ° 56.27% 27.27% 45.35% 15.89%arrow_forwardA large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 35 calls per hour. The service rate per line is 19 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0)=P(1)=P(2)=P(3)= (b) What is the probability that an agent will be denied access to the…arrow_forward
- A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 29 calls per hour. The service rate per line is 19 calls per hour. (a) What is the probability that 0, 1, 2, and 3 access lines will be in use? (Round your answers to four decimal places.) P(0) = P(1) = P(2) = P(3) = (b) What is the probability that an agent will be denied access to the…arrow_forwardTown 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. 11. What percentage of time all dispatchers are idle? 25.58% 15.58% 45.75% 8.65%arrow_forwardTown 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 minsarrow_forward
- The organizers of a conference in the Houston Convention Center are evaluating the possibility of setting up a computer area where attendees can check their e-mail on computers provided by the organization. There will be one common queue for all computers and only one person uses a computer at a time. On average there are 20 attendee arrivals per hour and the average time a person spends on the computer is 15 minutes To ensure that waiting times are not too long, the organizers want to ensure that the utilization of the computers doesn’t exceed 80 percent. At least how many computers do they need to have? The organizers of the conference have decided to buy 6 computers. Assume that the standard deviation of arrivals is equal to the average inter-arrival time, and the standard deviation of processing times is equal to the average processing time. What is the average waiting time to check e-mails?arrow_forwardA supermarket is trying to decide how many cashregisters to keep open. Suppose an average of 18customers arrive each hour, and the average checkouttime for a customer is four minutes. Interarrival timesand service times are exponentially distributed, andthe system can be modeled as an MyMys system.(In contrast to the situation at most supermarkets,we assume that all customers wait in a single line.)It costs $20 per hour to operate a cash register,and a cost of $0.25 is assessed for each minute thecustomer spends in the queue. How many registersshould the store open to minimize the expectedhourly cost?arrow_forwardA chemical plant stores spare parts for maintenance in a large warehouse. Throughout the working day, maintenance personnel go to the warehouse to pick up supplies needed for their jobs. The warehouse receives a request for supplies, on average, every 2 minutes (Poisson distributed). The average request requires 1.7 minutes to fill (exponential service times). Maintenance employees are paid $20 per hour, and warehouse employees are paid $12 per hour. The warehouse is open 8 hours each day. What is the optimal number of warehouse employees to hire? (Hint: Time spent by maintenance workers waiting in line for supplies should be considered an expense.) What is the total cost per hour (waiting plus warehouse employee labor cost) of your solution?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,