Ch11_153-166 - 72106 CH11 GGS 2:23 PM Page 153 C H A P T E...

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153 T EACHING S UGGESTIONS Teaching Suggestion 11.1: Topics in This Chapter. The overall purpose of this chapter is to provide a framework for the topics of integer programming, branch and bound, nonlinear programming and goal programming. These are fairly advanced topics in a mathematical sense, and the chapter’s intention is solely to introduce them through a series of simple graphical problems. Some of the topics are on the cutting edge of QA. For example, in integer and nonlinear programming, no one solution procedure exists to handle all problems. Teaching Suggestion 11.2: Using the Computer to Solve Mixed-Integer Programming Problems. Note that the Excel printout in Program 11.2 allows users to spec- ify which variables are integers and which, by default, can be fractional. Teaching Suggestion 11.3: How the Branch and Bound Method Can Help. In this section we illustrate how branch and bound is used to solve small assignment and integer programming problems. But its real strength is in dealing with huge problems (for example, thousands of variables/constraints). Branch and bound allows us to divide a large problem into smaller parts, thereby eliminating one-half or two-thirds of the options and reducing the problem to a more man- ageable level. Teaching Suggestion 11.4: Multiple Goals. Ask studdents what other goals a company might have beyond maximizing profit. Socially conscious firms need to state as their mission a whole series of objectives. Encourage students to re- search an article showing a goal programming application. There is a wealth of research in journals. One interesting application is in the box later in this section that deals with budgeting for prisons. Teaching Suggestion 11.5: Deviational Variables Are the Key in Goal Programming. The concept of deviational variables requires careful explanation to the class. Students are accustomed to the decision variables of X 1 and X 2 . Now they need to concentrate on goal achievement. The minus and plus signs on deviational variables need a thought- ful classroom discussion. Teaching Suggestion 11.6: Difficulty of Graphical Goal Programming. Solving goal programming problems graphically can be a confus- ing concept relative to graphical LP. Students often have difficulty with the direction of deviational variables. Teaching Suggestion 11.7: Using the Goal Programming Simplex Method. Point out the similarities and differences between the simplex method and the modified goal programming tableau. You can show that the structure is almost the same. The big change is the addition of two rows for each new goal. Surprisingly, the compu- tation is not as difficult as it looks. A LTERNATIVE E XAMPLES Alternative Example 11.1: 0–1 Integer Programming. Indiana’s prison budget allows it to consider four new installations next year. They are X 1 1 if maximum security prison in Ft. Wayne, 0 otherwise X 2 1 if minimum security prison in Bloomington, 0 otherwise X 3 1 if halfway house in Indianapolis, 0 otherwise X 4 1 if expanded tricounty jail in South Bend, 0 otherwise
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