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an introduction to management science

Questions and Answers of An Introduction to Management Science

=a. Use the random numbers in cells C17:C26 of Figure
=12.4. The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to the next. Suppose for a certain location that this probabilistic evolution
=E*e. Repeat part d with 800 replications.
=E*d. Use this spreadsheet to generate a data table with eight replications of the simulation. Compare this frequency distribution of the number of heads with the probability distribution of the
=E*c. Formulate a spreadsheet model for performing a computer simulation of three flips of the coin and recording the number of heads. Perform one replication of this simulation.
=C5:C13 of Figure 12.5 to simulate the flips specified in part a and record the information indicated in part a.
=b. Use random numbers in the order in which they are given in column C of Figure 12.4 and then in cells
=a. Using your own coin, flip it 24 times divided into eight groups of three flips each, and record the number of groups with no head, with one head, with two heads, and with three heads.
=12.3. Each time an unbiased coin is flipped three times, the probability of getting 0, 1, 2, and 3 heads is 1⁄8, 3⁄8, 3⁄8, and 1⁄8, respectively. Therefore, with eight groups of three flips
=E*d. Repeat part c with 1,000 replications (like Figure 12.3).
=E*c. Use this revised spreadsheet model to generate a data table with 14 replications like Figure 12.2.
=E*b. Revise the spreadsheet model in Figure 12.1 by using Excel’s VLOOKUP function instead of the IF function to generate each simulated flip of the coin. Then perform a computer simulation of
=12.1 and analyzed with computer simulation in Figures 12.1, 12.2, and 12.3.a. Simulate one play of this game by repeatedly flipping your own coin until the game ends. Record your results in the
=12.2. Reconsider the coin-flipping game introduced in Section
=c. The color of a traffic light found by a randomly arriving car when it is green 40 percent of the time, yellow 10 percent of the time, and red 50 percent of the time.
=b. A baseball pitcher who throws a strike 60 percent of the time and a ball 40 percent of the time.
=a. Throwing an unbiased coin.
=12.1 to generate six random observations for each of the following situations.
=12.1.* Use the random numbers in cells C13:C18 of Figure
=8. What are the two ways in which a management science team usually presents its recommendations to management?
=7. What kinds of estimates are obtained from simulation runs?
=3. What is the difference between a general-purpose simulation language and an applicationsoriented simulator?
=1. When beginning a computer simulation study, with whom should a management science team meet to address some key questions and then to learn the details of how the system would operate?
=6. What is the state of the system for Herr Cutter’s barber shop?
=4. What is a simulation clock?
=1. What is the decision facing Herr Cutter?
=4. What is a random number? For what purpose is it used?
=7. Outline the steps of a major computer simulation study.
=6. Describe and use the building blocks of a simulation model for a stochastic system.
=5. Use the Queueing Simulator to perform computer simulations of basic queueing systems and interpret the results.
=4. Use Excel to perform basic computer simulations on a spreadsheet.
=3. Use random numbers to generate random events that have a simple discrete distribution.
=2. Describe the role computer simulation plays in many management science studies.
=1. Describe the basic concept of computer simulation.
=d. Make your recommendations for reducing the average level of in-process inventory at the inspection station and at the group of machines. Be specific in your recommendations, and support them
=c. Determine the effect of proposal 2. Make specific comparisons to the results from parta. Explain this outcome to Jerry Carstairs.
=b. What would be the effect of proposal 1? Why? Make specific comparisons to the results from parta. Explain this outcome to Jerry Carstairs.
=a. To provide a basis of comparison, begin by evaluating the status quo. Determine the expected amount of in-process inventory at the presses and at the inspection station. Then calculate the
=e. Mark realizes that queueing theory helps him only so much in determining the number of representatives needed. He realizes that the queueing models will not provide accurate answers if the inputs
=d. Mark tells you that he is not happy with the number of representatives required to achieve a high customer service level.He therefore wants to explore alternatives to simply hiring additional
=c. Each representative receives an annual salary of $30,000, and Mark tells you that he simply does not have the resources available to hire the number of representatives required to achieve the
=b. Mark tells you that he will not be satisfied unless 95 percent of the customers wait only one minute or less for a representative to answer the call. Given this customer service level and the
=a. You ask Mark to describe the demand and service rate. He tells you that calls are randomly received by the call center and that the center receives an average of 70 calls per hour.The computer
=E11.35. The Garrett-Tompkins Company provides three copy machines in its copying room for the use of its employees. However, due to recent complaints about considerable time being wasted waiting
=E11.34.* Jim McDonald, manager of the fast-food hamburger restaurant McBurger, realizes that providing fast service is a key to the success of the restaurant. Customers who have to wait very long
=E11.33. When describing economic analysis of the number of servers to provide in a queueing system, Section 11.9 introduces a cost model where the objective is to minimize TC Css CwL. The purpose
=11.31. The County Hospital emergency room always has one doctor on duty. In the past, having just a single doctor there has been sufficient. However, because of a growing tendency for emergency
=d. Determine the average number of hours per day that the ticket agent is busy.
=c. What is the expected waiting time before service begins for first-class customers as a fraction of this waiting time for coach-class customers?
=Eb. Find the main measures of performance—L, Lq, W, and Wq—for both first-class passengers and coachclass passengers.
=a. What kind of queueing model fits this queueing system?
=11.30.* Southeast Airlines is a small commuter airline. Its ticket counter at one of its airports is staffed by a single ticket agent. There are two separate lines—one for first-class passengers
=11.29. The Southern Railroad Company has been subcontracting for the painting of its railroad cars as needed. However, management has decided that the company can save money by doing this work
=E11.28. People’s Software Company has just set up a call center to provide technical assistance on its new software package. Two technical representatives are taking the calls, where the time
=E*11.27. In the Blue Chip Life Insurance Company, the deposit and withdrawal functions associated with a certain investment product are separated between two clerks. Deposit slips arrive randomly
=E11.25. Consider the M/M/s model with a mean arrival rate of 10 customers per hour and an expected service time of five minutes. Use the Excel template for this model to print out the various
=c. Determine how many tellers will be needed a year from now to completely satisfy these guidelines.
=b. Evaluate how well the guidelines will be satisfied a year from now if no change is made in the number of tellers.
=a. Use the M/M/s model to determine how well these guidelines are currently being satisfied.
=E11.23. The Security & Trust Bank employs four tellers to serve its customers. Customers arrive randomly at a mean rate of two per minute. However, business is growing and management projects that
=11.22.* The production of tractors at the Jim Buck Company involves producing several subassemblies and then using an assembly line to assemble the subassemblies and other parts into finished
=11.21. Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section 11.6. Briefly describe how queueing theory was
=11.19. Consider the following statements about the M/G/1 queueing model, where 2 is the variance of service times. Label each statement as true or false, and then justify your answer.a. Increasing 2
=11.18. Consider the M/G/1 model with 0.2 and 0.25.Ea. Use the Excel template for this model to generate a data table that gives the main measures of performance—L, Lq, W, Wq—for each of the
=11.17.* Consider the M/G/1 model. What is the effect on Lq and Wq if 1/ , 1/ , and are all reduced by half? Explain.
=E11.16. The Centerville International Airport has two runways, one used exclusively for takeoffs and the other exclusively for landings. Airplanes arrive randomly in the Centerville air space to
=11.15. Jake’s Machine Shop contains a grinder for sharpening the machine cutting tools. A decision must now be made on the speed at which to set the grinder.The grinding time required by a
=11.14.* The Seabuck and Roper Company has a large warehouse in southern California to store its inventory of goods until they are needed by the company’s many furniture stores in that area. A
=E11.13. Suppose a queueing system fitting the M/M/1 model has W 120 minutes and L 8 customers. Use these facts (and the formula for W) to find and . Then find the various other measures of
=11.11.* The 4M Company has a single turret lathe as a key work center on its factory floor. Jobs arrive randomly at this work center at a mean rate of two per day. The processing time to perform
=11.10. 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 servicetime distribution
=11.9. Explain why the utilization factor for the server in a single-server queueing system must equal 1 – P0, where P0 is the probability of having 0 customers in the system.
=11.8.* Newell and Jeff are the two barbers in a barber shop they own and operate. They provide two chairs for customers who are waiting to begin a haircut, so the number of customers in the shop
=11.7. Mom-and-Pop’s Grocery Store has a small adjacent parking lot with three parking spaces reserved for the store’s customers. During store hours, when the lot is not full, cars enter lot and
=11.2. Identify the customers and the servers in the queueing system in each of the following situations.a. The checkout stand in a grocery store.b. A fire station.c. The toll booth for a bridge.d. A
=5. What is the effect of combining separate single-server queueing systems into one multipleserver queueing system (without changing the utilization factor)?
=4. How many one-person tech rep territories need to be combined into a larger territory in order to satisfy Dupit’s proposed new service standard?
=10. What is the total additional cost of the approach suggested by Dupit’s vice president for engineering?
=9. For the M/G/1 model, what is the effect on Lq, L, W, and Wq of decreasing the standard deviation of the service-time distribution?
=7. How does the M/G/1 model differ from the M/M/1 model?
=2. What are the assumptions of the M/M/1 model?
=1. What are represented by the symbols and ? By 1/ and 1/ ? By ?
=4. How many alternative approaches have been suggested for dealing with the issue facing top management?
=3. What is the proposed new service standard?
=2. What is the issue currently facing top management?
=7. What is the formula that relates L and Lq?
=5. What is the formula that relates W and Wq?
=2. How long do these customers typically have to wait?
=1. How many customers typically are waiting in the queueing system?
=3. What are transportation service systems? Also give a new example (not included in Table 11.4)of such a system, including identifying the customers and server.
=2. What are internal service systems? Also give a new example (not included in Table 11.3) of such a system, including identifying the customers and server.
=1. What are commercial service systems? Also give a new example (not included in Table 11.2) of such a system, including identifying the customers and server.
=11. What information is provided by the three parts of the label for queueing models?
=10. What are the two most important service-time distributions?
=4. What is the shape of the exponential distribution?
=10. Apply economic analysis to determine how many servers should be provided in a queueing system.
=9. Describe some key insights that queueing models provide about how queueing systems should be designed.
=8. Describe how differences in the importance of customers can be incorporated into priority queueing models.
=7. Apply a queueing model to determine the key measures of performance for a queueing system.
=6. Determine which queueing model is most appropriate from a description of the queueing system being considered.

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