The Friendly Neighbor Grocery Store has a single checkout stand with a full-time cashier. Customers arrive randomly at the stand at a mean rate of 30 per hour. The service-time distribution is exponential, with a mean of 1.5 minutes. This situation has resulted in occasional long line complaints from customers. Therefore, because there is no room for a second checkout stand, the manager is considering the alternative of hiring another person to help the cashier by bagging the groceries. This help would reduce the expected time required to process a customer to 1 minute, but the distribution still would be exponential. In response to complaints from customers, the manager now has adopted three guidelines for providing a satisfactory level of service to the customers. In particular, she would like to have the percentage of time that there are more than two customers at a checkout stand down below 25 percent. She also would like to have no more than 5 percent of the customers needing to wait at least five minutes before beginning service, or at least seven minutes before finishing service. a) Use the formulas for the M/M/1 Model to calculate L, W, Wq, Lq, P0, P1, P2, for the current mode of operation. What is the probability of having more than two customers at the checkout stand? b) Use the excel template for this model to check your answers in part a. Also, find the probability that the waiting time for beginning service exceeds five minutes, and the probability that the waiting time before finishing service exceeds seven minutes. c) Repeat part a for the alternative being considered by the manager. d) Repeat Part b for this alternative. e) Which approach should the manager use to satisfy her guidelines as closely as possible?

Name: Homework Chapter 11Solve the following Problems. Be sure to use Excel
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Description: Homework Chapter 11Solve the following Problems. Be sure to use Excel and Word for your work. All work needs to be shown.Problem 1) The Friendly Neighbor Grocery Store has a single checkout stand with a full-time cashier. Customers arrive randomly at

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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Homework Chapter 11 Solve the following Problems. Be sure to use Excel and Word for your work. All work needs to be shown. Problem 1) The Friendly Neighbor Grocery Store has a single checkout stand with a full-time cashier. Customers arrive randomly at the stand at a mean rate of 30 per hour. The service-time distribution is exponential, with a mean of 1.5 minutes. This situation has resulted in occasional long line complaints from customers. Therefore, because there is no room for a second checkout stand, the manager is considering the alternative of hiring another person to help the cashier by bagging the groceries. This help would reduce the expected time required to process a customer to 1 minute, but the distribution still would be exponential. In response to complaints from customers, the manager now has adopted three guidelines for providing a satisfactory level of service to the customers. In particular, she would like to have the percentage of time that there are more than two customers at a checkout stand down below 25 percent. She also would like to have no more than 5 percent of the customers needing to wait at least five minutes before beginning service, or at least seven minutes before finishing service. a) Use the formulas for the M/M/1 Model to calculate L, W, Wq, Lq, P0, P1, P2, for the current mode of operation. What is the probability of having more than two customers at the checkout stand? b) Use the excel template for this model to check your answers in part a. Also, find the probability that the waiting time for beginning service exceeds five minutes, and the probability that the waiting time before finishing service exceeds seven minutes. c) Repeat part a for the alternative being considered by the manager. d) Repeat Part b for this alternative. e) Which approach should the manager use to satisfy her guidelines as closely as possible? Problem 2) The Centerville International Airport has two runways, one used exclusively for takeoffs and the other exclusively for landing. Airplanes arrive randomly in the Centerville airspace to request landing instructions at a mean rate of 10 per hour. The time required for an airplane to land after receiving clearance to land has an exponential distribution with a mean of three minutes, and this process must be completed before giving clearance to land to another airplane. Airplanes waiting clearance must circle the airport. The Federal Aviation Administration has a number of criteria regarding the safe level of congestion of airplanes waiting to land. These criteria depend on a number of factors regarding the airport involved, such as the number of runways available for landing. For Centerville, the criteria are (1) the average number of airplanes waiting to receive clearance to land should not exceed one, (2) 95 percent of the time the actual number of airplanes waiting to receive clearance to land should not exceed four, (3) for 99 percent of airplanes, the amount of time spent circling the airport before receiving clearance to land should not exceed 30 minutes (since exceeding this amount of time often would require rerouting the airplane to another airport for an emergency landing before fuel runs out). a) Evaluate how well these criteria are currently being satisfied. b) A major airline is considering adding this airport as one of its hubs. This would increase the mean arrival time to 15 airplanes per hour. Evaluate how well the above criteria would be satisfied if this happens. c) To attract additional business (including the major airline mentioned in Part b), airport management is considering adding a second runway for landings. It is estimated that this eventually would increase the mean arrival time to 25 planes per hour. Evaluate how well the above criteria would be satisfied if this happens.

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