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Ch08_97-108

# Ch08_97-108 - 72106 CH08 GGS 2:16 PM Page 97 C H A P T E R...

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97 T EACHING S UGGESTIONS Teaching Suggestion 8.1: Importance of Formulating Large LP Problems. Since computers are used to solve virtually all business LP prob- lems, the most important thing a student can do is to get experi- ence in formulating a wide variety of problems. This chapter pro- vides such a variety. Teaching Suggestion 8.2: Note on Production Scheduling Problems. The Greenberg Motor example in this chapter is the largest prob- lem in the book in terms of constraints, so it provides a good prac- tice environment. An interesting feature to point out is that LP constraints are capable of tying one production period to the next. Teaching Suggestion 8.3: Solving Assignment Problems by LP. The example of the law firm of Ivan and Ivan in this chapter can clearly be solved more quickly using QM for Windows’ assign- ment program than by the LP program. Students should be asked why anyone would choose to use the LP approach. There are two answers: (1) many commercial LP programs do not contain as- signment algorithms (which are more popular in academic soft- ware such as QM for Windows); and (2) the LP program can pro- vide more sensitivity analysis and economic interpretation than is available in the assignment module. The assignment problem is treated in Chapter 10. Teaching Suggestion 8.4: Labor Planning Problem—Arlington Bank. This example is a good practice tool and lead-in for the Chase Manhattan Bank case at the end of the chapter. Without this exam- ple, the case would probably overpower most students. Teaching Suggestion 8.5: Ingredient Blending Applications. Three points can be made about the two blending examples in this chapter. First, both the diet and fuel blending problems presented here are tiny compared to huge real-world blending problems. But they do provide some sense of the issues to be faced. Second, diet problems that are missing the constraints that force variety into the diet can be terribly embarrassing. It has been said that a hospital in New Orleans ended up with an LP solution to feed each patient only castor oil for dinner because analysts ne- glected to add constraints forcing a well-rounded diet. A LTERNATIVE E XAMPLES Alternative Example 8.1: Natural Furniture Company manu- factures three outdoor products, chairs, benches, and tables. Each product must pass through the following departments before it is shipped: sawing, sanding, assembly, and painting. The time re- quirements (in hours) are summarized in the tables below. The production time available in each department each week and the minimum weekly production requirement to fulfill con- tracts are as follows: The production manager has the responsibility of specifying pro- duction levels for each product for the coming week. Let X 1 Number of chairs produced X 2 Number of benches produced X 3 Number of tables produced The objective function is Maximize profit 15 X 1 10 X 2 20 X 3 Constraints 1.5 X 1 1.5 X 2 2.0 X 3 450 hours of sawing available 1.0 X 1 1.5 X 2 2.0 X 3 400 hours of sanding available 2.0 X 1 2.0 X 2 2.5 X 3 625 hours of assembly available 1.5 X

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