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business
an introduction to management science
Questions and Answers of
An Introduction to Management Science
=a. Ash decides to allocate $4 million to fund the exhibit. Given the pieces available and the specific requirements from Ash and Celeste, formulate and solve a binary integer programming problem to
=b. Now suppose that ACC is considering saving money by closing some of its production facilities and/or warehouses. Suppose there is a fixed cost to operate each plant and each warehouse as
=a. Formulate and solve a linear programming model in a spreadsheet to determine the plan for weekly production and distribution of the WebSurfer from the various plants, through the warehouses, to
=E*7.18. Aberdeen Computer Corp. (ACC) is located in Aberdeen, Washington. The company has developed the WebSurfer, a low-cost e-mail and Web-surfing appliance. This product is manufactured at four
=E*7.17. Noble Amazon sells books online. Management is trying to determine the best sites for the company’s warehouses. Five potential sites are under consideration. Most of the sales come from
=E*c. Now suppose that Macwin has not submitted its final bid yet, so the per computer cost is not known with certainty. Generate a Solver Table to show the optimal order quantities and total cost of
=7.16. The school board for the Bellevue School District has made the decision to purchase 1,350 additional Macintosh computers for computer laboratories in all its schools. Based on past
=7.15. An electrical utility needs to generate 6,500 megawatts of electricity today. It has five generators. If any electricity is generated by a given generator, that generator must be started up
=7.14. Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section 7.5. Briefly describe how mixed BIP was applied in
=7.13. Yakima Construction Corporation (YCC) is considering a number of different development projects. The cash outflows that would be required to complete each project are indicated in the table
=7.12. Reconsider the Southwestern Airways crew scheduling problem presented in Section 7.4. Because of a blizzard in the Chicago area, all the flights into and out of Chicago(including flights 4,
=E*b. Display and solve this model on a spreadsheet.
=a. Formulate the algebraic form of a pure BIP model with five binary variables for this problem.
=7.11. Reconsider Problem 7.10. The management of Sunny Skies Unlimited now has decided that the decision regarding the locations of the paramedic stations should be based mainly on costs.The cost of
=E*7.10. An increasing number of Americans are moving to a warmer climate when they retire. To take advantage of this trend, Sunny Skies Unlimited is undertaking a major real-estate development
=b. Describe how the problem addressed in part a is analogous to the crew scheduling problem described in Section 7.4.
=E*a. Using the data in the table, demonstrate how Dispatcher can formulate and solve this BIP model on a spreadsheet.
=7.8. Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section 7.4. Briefly describe how BIP and related techniques
=7.9. Speedy Delivery provides two-day delivery service of large parcels across the United States. Each morning at each collection center, the parcels that have arrived overnight are loaded onto
=E*7.7. Consider the following special type of shortest path problem (discussed in Section 6.4) where the nodes are in columns and the only paths considered always move forward one column at a time.3
=E*7.6. The Fly-Right Airplane Company builds small jet airplanes to sell to corporations for use by their executives. To meet the needs of these executives, the company’s customers sometimes
=b. Perform sensitivity analysis on the amount of capital made available for the investment opportunities by using the Solver Table to solve the model with the following amounts of capital (in
=a. Formulate and solve a BIP model on a spreadsheet for this problem.
=E*7.5. The board of directors of General Wheels Co. is considering seven large capital investments. Each investment can be made only once. These investments differ in the estimated long-run profit
=E*c. Perform sensitivity analysis on the amount of investment capital made available for the development projects by using the Solver Table to solve the model with the following amounts of
=7.4. A real-estate development firm, Peterson and Johnson, is considering five possible development projects. Using units of millions of dollars, the following table shows the estimated longrun
=E*b. Formulate and solve this model on a spreadsheet.
=a. Formulate a BIP model in algebraic form for this problem.
=7.2. Reconsider the California Manufacturing Co. case study presented in Section 7.1. The mayor of San Diego now has contacted the company’s president, Armando Ortega, to try to persuade him to
=7.1. Read the referenced article that fully describes the management science study summarized in the application vignette presented in Section 7.1. Briefly describe how mixed BIP was applied in
=4. What caused the optimal solution for the revised Wyndor problem to differ from that for the original Wyndor problem?
=3. How can a binary variable be defined in terms of whether a setup is performed to initiate the production of a certain product?
=2. Why is a linear programming formulation no longer valid for a product-mix problem when there are setup costs for initiating production?
=1. How does a mixed BIP problem differ from a pure BIP problem?
=3. For the Southwestern Airways problem, there is a constraint for each flight to ensure that this flight is covered by a crew. Describe the mathematical form of this constraint. Then explain in
=2. What are the yes-or-no decisions that need to be made when addressing a crew scheduling problem?
=1. What is the crew scheduling problem that is encountered by companies in the travel industry?
=4. What is a set covering constraint and what is a set covering problem?
=3. What was the objective for the Caliente City problem?
=2. What are some types of emergency services facilities for which sites may need to be selected?
=1. How are binary variables used to represent managerial decisions regarding which site or sites should be selected for new facilities?
=3. What is the objective for this problem?
=2. What types of projects are under consideration in the Tazer Corp. problem?
=1. How are binary variables used to represent managerial decisions on which projects from a group of proposed projects should be selected for approval?
=6. What is the tentative managerial decision on which sensitivity analysis needs to be performed?
=5. What are the contingent decisions in this problem? For each one, what is the form of the resulting constraint in the BIP model?
=4. What are the mutually exclusive alternatives in this problem? What is the form of the resulting constraint in the BIP model?
=3. What is the objective specified by management for this problem?
=2. Why are binary decision variables appropriate to represent these decisions?
=1. What are the four interrelated decisions that need to be made by the management of the California Manufacturing Co.?
=7. Use mixed binary integer programming to deal with setup costs for initiating the production of a product.
=6. Formulate other basic binary integer programming models from a description of the problems.
=5. Formulate a binary integer programming model for crew scheduling in the travel industry.
=4. Formulate a binary integer programming model for the selection of sites for facilities.
=3. Formulate a binary integer programming model for the selection of projects.
=2. Use binary decision variables to formulate constraints for mutually exclusive alternatives and contingent decisions.
=1. Describe how binary decision variables are used to represent yes-or-no decisions.
=1. Explain what is meant by what-if analysis.
=2. Summarize the benefits of what-if analysis.
=3. Enumerate the different kinds of changes in the model that can be considered by what-if analysis.
=4. Describe how the spreadsheet formulation of the problem can be used to perform any of these kinds of what-if analysis.
=5. Use the Solver Table to systematically investigate the effect of changing either one or two data cells to various other trial values.
=6. Find how much any single coefficient in the objective function can change without changing the optimal solution.
=7. Evaluate simultaneous changes in objective function coefficients to determine whether the changes are small enough that the original optimal solution must still be optimal.
=8. Predict how the value in the target cell would change if a small change were to be made in the right-hand side of one or more of the functional constraints.
=9. Find how much the right-hand side of a single functional constraint can change before this prediction becomes no longer valid.
=10. Evaluate simultaneous changes in right-hand sides to determine whether the changes are small enough that this prediction must still be valid.
=1. What are the parameters of a linear programming model?
=2. How can inaccuracies arise in the parameters of a model?
=7. What is meant by sensitivity analysis?
=2. Which numbers in this model represent tentative managerial decisions that management might want to change after receiving the Management Science Group’s analysis?
=Question 1: What happens if the estimate of the unit profit of one of Wyndor’s new products is inaccurate?
=3. In Excel’s sensitivity report, what is the interpretation of the Objective Coefficient column? The Allowable Increase column? The Allowable Decrease column?
=1. Why might it be of interest to investigate the effect of making changes in a functional constraint?
=3. What is meant by a shadow price?
=4. How can a shadow price be found by using the spreadsheet? By using the Solver Table? By using Solver’s sensitivity report?
=5. Why are shadow prices of interest to managers?
=7. What does a shadow price of 0 tell a manager?
=8. Which columns of the Solver’s sensitivity report are used to find the allowable range for the right-hand side of a functional constraint?
=9. Why are these allowable ranges of interest to managers?
=3. What are the capabilities of the Solver Table for investigating simultaneous changes in the functional constraints?
=a. For each of the three products in turn, use graphical analysis to determine how much the total advertising cost would change if the required minimum increase in the sales of that product were to
=b. Use the spreadsheet shown in Figure 2.14 (available on the CD-ROM) to obtain the information requested in part a.
=c. For each of the three products in turn, use the Solver Table(available on the CD-ROM) to determine how the optimal solution for the model and the resulting total advertising cost would change if
=d. Use the Solver to generate the sensitivity report and indicate how the report is able to provide the information requested in parta. Also use the report to obtain the allowable range for the
=e. Suppose that all the original numbers in MinimumIncrease(G8:G10) were to be increased simultaneously by the same amount. How large can this amount be before the shadow prices provided by the
=f. Below is the beginning of a memorandum from the management science team to Profit & Gambit management that is intended to provide management with the information it needs to perform its
=a. Identify verbally the components of a linear programming model for this problem.
=b. Display the model on a spreadsheet.
=c. Obtain an optimal solution and generate the sensitivity report.
=d. Identify the parameters of the linear programming model that should be classified as sensitive parameters. Make a resulting recommendation about which parameters should be estimated more
=e. Analyze the effect of an inaccuracy in estimating each cost parameter given in the third table. If the true value were 10 percent less than the estimated value, would this change the optimal
=f. For each pollutant, specify the rate at which the total cost of an optimal solution would change with any small change in the required reduction in the annual emission rate of the pollutant.Also
=g. For each unit change in the policy standard for particulates given in the first table, determine the change in the opposite direction for sulfur oxides that would keep the total cost of an
=h. Letting denote the percentage increase in all the policy standards given in the first table, use the Solver Table to systematically find an optimal solution and the total cost for the revised
=i. For the value of chosen in part h, generate the sensitivity report and repeat parts f and g so that the decision makers can make a final decision on the relative values of the policy standards
=a. Identify verbally the components of a linear programming model for this problem.
=b. Display the model on a spreadsheet.
=c. Obtain an optimal solution and generate the sensitivity report. What does the model predict regarding the family’s monetary worth at the end of the coming year?
=d. Find the allowable range for the net value per acre planted for each of the three crops.
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