Chapter 5. (M/M/s/K Model). Leia is responsible for 12 dataunits in the IT offices in a small business called DataWish. Each dataunit runs on an average for 3 weeks andrequires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each dataunit for service andan exponential distribution to the actual service provided, answer the following questions:a. The arrival rate would beunits per week and the service rate would beunits per week.b. Calculate the following operating characteristics for the M/M/S/K system:Utilization Factor (p)%Performance MeasuresPO (probability that sytemis empty)%L (average units in system)unitsLq (average units waitingin queue)unitsW (average time in theweekssystem)Wq (average time in thequeue)weeksc. If we assign a cost of waiting as $400 per week per dataunit and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines?dollarsd. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per week be?dollars.

Answered: a. The arrival rate would be units per…

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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Scenario E.1 SimQuick is being used to simulate the following bank process: Entrance Door Buffer Line Work Station Teller Buffer Served Customers Customer arrivals at the Entrance Door of the bank with an average time between arrivals of 2.5 minutes. The Line Buffer holds 6 customers. If a customer arrives and the buffer line is filled, the customer leaves. The Work Station Teller's processing time per customer is normally distributed, with a mean of 3.0 minutes and a standard deviation of 0.5 minutes. The Served Customer Buffer in the flow chart is used to count the number of customers processed during the period simulated. A 2-hour period was simulated. The SimQuick simulation is run, and the results are as follows: Overall Element Types Element Names Statistics Means Entrance Door Objects entering process 41.80 Objects unable to enter 6.23 Service level 0.87 Buffer Line Objects leaving 37.83 Final inventory 3.98 Minimum inventory 0.00 Maximum inventory 5.85 Mean inventory 3.08 Mean…
11. Leo manages a receiving station for rice. Farmers deliver their loads of rice from 7 am to 7 pm. Leo can process them at a rate of 4.5 tons an hour, and on a heavy day, a total of 96 tons can be expected. The station has room to hold only 15 tons of rice in inventory prior to processing. Once this space is filled, the farmers’ trucks must wait to dump their contents. What is the throughput (flow) rate after 7 pm (in tons/hr)?
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.2 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. (a) Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. (Round your answers to four decimal places. Report time in hours.) λ Wa { é L = P q = || W = W = h h (b) Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? (Round your answer to one decimal place.) W (in minutes) = What action do you recommend? (Select all that apply.) Increase the hours of operation. Increase the mean service rate. Hire another consultant. Decrease the mean service rate. There is no need to change the current operating parameters. min, which is greater ✓than…
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.6 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer. (a) Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. (Round your answers to four decimal places. Report time in hours.) ?=?=Lq=L=Wq= hW= hPw= (b) Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? (Round your answer to one decimal place.) Wq (in minutes) = min, which is than the desired wait time, so the goal met. What action do you recommend? (Select all that apply.) Increase the mean service rate.Decrease the mean service rate.There is no need to change the current operating parameters.Hire another…
Joe’s market is a small grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane at an average rate of 15 customers per hour and that the average order takes 3 minutes to ring up and bag. If Joe does not want the average waiting time in the queue to exceed 5 minutes, what would you tell Joe about his current system? Back up your statement with quantitative information and assumptions.
Customers arrive at the lone check-out desk of a certain convenience store at the average rate of 0.23 per minute. If it takes on average four minutes for the store manager to serve each customer, how many customers will on average find themselves waiting in the queue? A. 10.58 B. 0.00024 C. 3.20 D. 0.00351
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A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.On average, how many parties of truckers are waiting to be seated? Question 1 options: 0.27. 0.52. 0.88. 1.36. 1.75.
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