Granos, Inc. purchased new automated coffee vending machines, the Preso 2000. This Preso2000 requires a constant 45 seconds to produce a coffee. It has been estimated that customerswill arrive at the vending machine according to a Poisson distribution at an average of one every50 seconds. To help determine the amount of space needed for the line in front of the vendingmachine, Granos, Inc. would like to know the expected average time in the system, the averageline length (in costumers), and the average number of costumers in the system (both in line andat the vending machine).

Answered: Granos, Inc. purchased new automated…

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...

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13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.
(a) Determine the utilization of each of the copy centers. (b) Determine the average waiting time at each of the copy centers. (c) What is the annual cost of the administrative assistants’ average waiting time using the current system? (d) Determine the utilization of the combined copy center with two copiers. (e) Determine the average waiting time at the combined copy center. (f) What would be the annual cost of the administrative assistants’ average waiting time using the combined two copier setup? (g) What would be the utilization of the combined copy center with three copiers? (h) What would be the annual cost of the administrative assistants’ average waiting time using the combined three-copier setup? (i) What would you recommend to Catherine
Which of the following is not a valid queuing model based on the Kendall notation? Select one: A. M/M/0 B. M/M/3 C. D/M/1 D. G/D/1- E. D/D/2
Consider an M/M/1/4 queuing system with arrival rate A=24 per hour and service rate p=12 per hour. The probability that the system is full is closest to a. None of these b. 0.03 c. 0.97 d. 0.52
Define the following terms with an example Constant service time model Queuing theory Critical path analysis Sensitivity analysis Hungarian method
Suppose the cross-price elasticity of demand between goods X and Y is -5. How much would the price of good Y have to change in order to change the consumption of good X by 40 percent?
A drive-through at a Fast Food serves 424 customers over a 10-hour day. On average, a customer spends 3 minutes waiting in line, 7 minutes placing the order, and 4 minutes completing the order before leaving the drive-through. How many customers on average are "in" the drive-through (i.e., from the time they enter to the time they exit the drive-through) on a typical day? (Specify your answer in two decimal points)
A fast-food restaurant offers a variety of products: from pre-made packaged sandwiches to milkshakes with different flavors. Many customers order one item time, other customers order multiple items. Sometimes customers buy the pre- made items, and some customers actually ask the restaurant to cook their food while they wait. The restaurant manager has kept careful records of some queuing statistics over several weeks. According to this data, the staff needs 4 minutes on average to serve a random customer. On average, the restaurant served 120 customers on a given day. This restaurant is open from 9 AM to 9 PM every day, and has a single service counter. If you want to help the manager measure this restaurant's waiting line performance, which of the following should you use? Exponential Service Rate Model The Finite Source Model Constant Service Rate Model O The multi phase single channel model
Suppose the waiting time at a certain checkout counter is bi-modal. With probability 0.85, the waiting time follows an exponential distribution with a mean waiting time of four minutes. With probability 0.15, the waiting time equals 20 minutes. a) Compute the mean and median waiting time at the checkout counter. b) Compute the variance of the waiting time at the checkout counter. c) Compute the probability that an individual customer waits longer than 5 minutes at the checkout counter.
How many years (t) can we expect to do business with a customer? Thetotal number of years is denoted by T.
The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?
Ashley’s department store in Kansas City maintains a successful catalog sales department in which four clerk takes orders by telephone. If four clerks are occupied on four-lines, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon as the clerk is free, the party that has waited for the longest is transferred and answered first. Calls come in an average of 3 minutes. The clerk is capable of taking an order in an average of 10 minutes. Calls tend to follow a Poisson distribution, and service times tend to be exponential. a. λ= μ= b. Calculate P0 c. How many callers, on average, are waiting to place an order under the current operating system?

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