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an introduction to management science

Questions and Answers of An Introduction to Management Science

=Eb. After considering seasonal effects, use the last-value method to forecast water consumption next winter.
=c. Assuming that each of the forecasts for the next three seasons is correct, what would the last-value method forecast as the water consumption in each of the four seasons next year?
=Ed. After considering seasonal effects, use the averaging method to forecast water consumption next winter.
=Ee. After considering seasonal effects, use the movingaverage method based on four seasons to forecast water consumption next winter.
=f. After considering seasonal effects, use the exponential smoothing method with an initial estimate of 46 and a smoothing constant of 0.1 to forecast water consumption next winter.
=E g. Compare both the MAD and MSE values of these four forecasting methods when they are applied retrospectively to the last three years.10.31. Reconsider Problem 10.8. Ralph Billett realizes that
=Ea. Determine the seasonal factors for the four quarters.
=Eb. Apply the last-value method.
=Ec. Apply the averaging method.
=Ed. Apply the moving-average method based on the four most recent quarters of data.
=e. Apply the exponential smoothing method with an initial estimate of 25 and a smoothing constant of 0.25.
=Ef. Apply exponential smoothing with trend with smoothing constants of 0.25 and 0.25. Use initial estimates of 25 for the average value and 0 for the trend.
=E g. Compare both the MAD and MSE values for these methods. Use the one with the smallest MAD to forecast sales in Quarter 1 of next year.
=h. Use the forecast in part g and the seasonal factors to make long-range forecasts now of the sales in the remaining quarters of next year.
=E10.32. Transcontinental Airlines maintains a computerized forecasting system to forecast the number of customers in each fare class who will fly on each flight in order to allocate the available
=a. After considering seasonal effects, compare both the MAD and MSE values for the last-value method, the averaging method, the moving-average method(based on the most recent three months), and the
=b. Use the forecasting method with the smallest MAD value to forecast the average number of these passengers flying in January of the new year.
=10.33. Reconsider Problem 10.32. The economy is beginning to boom so the management of Transcontinental Airlines is predicting that the number of people flying will steadily increase this year over
=a. Repeat part a of Problem 10.32 for the two years of data.
=Eb. After considering seasonal effects, apply exponential smoothing with trend to just the new year. Use initial estimates of 80 for the average value and 2 for the trend, along with smoothing
=Ec. Repeat part b when exponential smoothing with trend is begun at the beginning of the first year and then applied to both years, just like the other forecasting methods in parta. Use the same
=d. Based on these results, which forecasting method would you recommend that Transcontinental Airlines use hereafter?
=10.34. Quality Bikes is a wholesale firm that specializes in the distribution of bicycles. In the past, the company has maintained ample inventories of bicycles to enable filling orders
=Ea. Determine the seasonal factors for the 12 months based on past sales.
=Eb. After considering seasonal effects, apply the movingaverage method based on the most recent three months to forecast monthly sales for each month of this year.
=Ec. After considering seasonal effects, apply the exponential smoothing method to forecast monthly sales this year. Use an initial estimate of 420 and a smoothing constant of 0.2.
=Ed. After considering seasonal effects, apply exponential smoothing with trend to forecast monthly sales this year. Use initial estimates of 420 for the average value and 0 for the trend, along
=e. Compare both the MAD and MSE values obtained in partsb, c, and d.
=f. Calculate the combined forecast for each month by averaging the forecasts for that month obtained in partsb, c, andd. Then calculate MAD for these combined forecasts.
=g. Based on these results, what is your recommendation for how to do the forecasts next year?
=10.35.* Long a market leader in the production of heavy machinery, the Spellman Corporation recently has been enjoying a steady increase in the sales of its new lathe. The sales over the past 10
=a. Plot these data on a two-dimensional graph with the month on the horizontal axis and sales on the vertical axis.
=b. Find the formula for the linear regression line that fits these data.
=c. Plot this line on the graph constructed in part a.
=d. Use this line to forecast sales in month 11.
=e. Use this line to forecast sales in month 20.
=f. What does the formula for the linear regression line indicate is roughly the average growth in sales per month?
=10.36. Reconsider Problems 10.15 and 10.16. Since the number of applications for admission submitted to Ivy College has been increasing at a steady rate, causal forecasting can be used to forecast
=a. Plot the data for years 1, 2, and 3 on a two-dimensional graph with the year on the horizontal axis and the number of applications on the vertical axis.
=b. Since the three points in this graph line up in a straight line, this straight line is the linear regression line. Draw this line.
=Ec. Find the formula for this linear regression line.
=d. Use this line to forecast the number of applications for each of the next five years (years 4 through 8).
=e. As these next years go on, conditions change for the worse at Ivy College. The favorable ratings in the national surveys that had propelled the growth in applications turn unfavorable.
=f. Plot the data for all seven years. Find the formula for the linear regression line based on all these data and plot this line. Use this formula to forecast the number of applications for year 8.
=E g. Apply exponential smoothing with trend to all seven years of data to forecast the number of applications in year 8. Use initial estimates of 3,900 for the average and 700 for the trend, along
=10.37. Reconsider Problem 10.27. Despite some fluctuations from year to year, note that there has been a basic trend upward in the annual demand for copper ore over the past 10 years. Therefore, by
=a. Plot the data for the past 10 years (years 1 through 10) on a two-dimensional graph with the year on the horizontal axis and the demand on the vertical axis.
=Eb. Find the formula for the linear regression line that fits these data.
=c. Plot this line on the graph constructed in part a.
=d. Use this line to forecast demand next year (year 11).
=e. Use this line to forecast demand in year 15.
=f. What does the formula for the linear regression line indicate is roughly the average growth in demand per year?
=g. Use the forecasting module in your Interactive Management Science Modules to generate a graph of the data and the linear regression line. Then experiment with the data to see how the linear
=10.38. Luxury Cruise Lines has a fleet of ships that travel to Alaska repeatedly every summer (and elsewhere during other times of the year). A considerable amount of advertising is done each winter
=a. To use causal forecasting to forecast sales for a given amount of advertising, which need to be the dependent variable and the independent variable?
=b. Plot the data on a graph.
=Ec. Find the formula for the linear regression line that fits these data. Then plot this line on the graph constructed in part b.
=d. Forecast the sales that would be attained by expending $300,000 on advertising.
=e. Estimate the amount of advertising that would need to be done to attain a booking of 22,000 passengers.
=f. According to the linear regression line, about how much increase in sales can be attained on the average per $1,000 increase in the amount of advertising?
=10.39. Reconsider Problem 10.38. Use the forecasting module in your Interactive Management Science Modules to generate the linear regression line. On the resulting graph that shows this line and
=a. Change the sales from 16 to 19 when the amount of advertising is 225.
=b. Change the sales from 23 to 26 when the amount of advertising is 450.
=c. Change the sales from 20 to 23 when the amount of advertising is 350.
=10.40. To support its large fleet, North American Airlines maintains an extensive inventory of spare parts, including wing flaps. The number of wing flaps needed in inventory to replace damaged wing
=Va. Identify the dependent variable and the independent variable for doing causal forecasting of the number of wing flaps needed for a given number of flying hours.
=b. Plot the data on a graph.
=Ec. Find the formula for the linear regression line.
=d. Plot this line on the graph constructed in part b.
=f. Repeat part e for 200,000 flying hours.
=g. Use the forecasting module in your Interactive Management Science Modules to generate a graph of the data and the linear regression line. Then experiment with the data to see how the linear
=E10.41. Joe Barnes is the owner of Standing Tall, one of the major roofing companies in town. Much of the company’s business comes from building roofs on new houses. Joe has learned that general
=a. Mark first asks you to forecast daily demand for the next week using the data from the past 13 weeks. You should make the forecasts for all the days of the next week now (at the end of week 5),
=1. From working at the records and benefits administration center, you know that demand follows “seasonal” patterns within the week. For example, more employees call at the beginning of the week
=2. Using the seasonally adjusted call volume, forecast the daily demand for the next week using the last-value forecasting method.
=V3. Using the seasonally adjusted call volume, forecast the daily demand for the next week using the averaging forecasting method.
=4. Using the seasonally adjusted call volume, forecast the daily demand for the next week using the moving-average forecasting method. You decide to use the five most recent days in this analysis.
=5. Using the seasonally adjusted call volume, forecast the daily demand for the next week using the exponential smoothing forecasting method. You decide to use a smoothing constant of 0.1 because
=b. After one week, the period you have forecasted passes. You realize that you are able to determine the accuracy of your forecasts because you now have the actual call volumes from the week you had
=You realize that the forecasting methods that you have investigated do not provide a great degree of accuracy, and you decide to use a creative approach to forecasting that combines the
=c. At the end of the hour, Mark arrives at your desk with two data sets: weekly case volumes for the decentralized center and weekly case volumes for the centralized center. You ask Mark if he has
=1. Find a mathematical relationship between the decentralized case volume data and the centralized case volume data.
=2. Now that you have a relationship between the weekly decentralized case volume and the weekly centralized case volume, you are able to forecast the weekly case volume for the new center.
=3. Using the actual call volumes given in partb, calculate the mean absolute deviation and evaluate the effectiveness of this forecasting method.
=d. Which forecasting method would you recommend Mark use and why? As the call center continues its operation, how would you recommend improving the forecasting procedure?
=1. Describe how a nonlinear programming model differs from a linear programming model.
=2. Recognize when a nonlinear programming model is needed to represent a problem.
=3. Formulate a nonlinear programming model from a description of the problem.
=4. Construct nonlinear formulas needed for nonlinear programming models.
=5. Distinguish between nonlinear programming problems that should be easy to solve and those that may be difficult (if not impossible) to solve.
=6. Use the Excel Nonlinear Solver to solve simple types of nonlinear programming problems.
=7. Combine the Excel Nonlinear Solver with the Solver Table to attempt to solve some more difficult nonlinear programming problems.
=8. Use Evolutionary Solver to attempt to solve some difficult nonlinear programming problems.
=9. Recognize when the separable programming technique is applicable to enable using linear programming with a nonlinear objective function.
=10. Apply the separable programming technique when applicable.
=9. When it is given a starting solution, how does the Excel Nonlinear Solver then proceed to attempt to solve a maximization problem with multiple local maxima?
=10. What can be done to give the Excel Nonlinear Solver a better chance of obtaining an optimal solution (or at least a very good solution) for a maximization problem with multiple local maxima?
=1. What are the three characteristics of a simple type of nonlinear programming problem that can be readily solved by the Excel Nonlinear Solver?
=3. What additional characteristic must this type of nonlinear programming problem have in order to be a quadratic programming problem?
=3. For problems where the activities have profit graphs with shapes similar to the one shown in Figure 8.17, what are some advantages of using the kind of approximation displayed in this figure to

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