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Unformatted text preview: CHAPTER 6 INTEGER, GOAL, AND NONLINEAR PROGRAMMING MODELS SOLUTIONS TO DISCUSSION QUESTIONS 6-1. (a) LP allows only one goal (for example, profit maximization) whereas GP permits multiple goals. (b) LP always optimizes; GP sometimes only satisfices. (c) In GP, we deal with deviation variables as well as real variables. 6-2. The student should provide five realistic examples of IP. One good exercise would be to require students to find five articles and use those as examples. 6-3. In a pure IP model, all variables are integers whereas in a mixed-IP model, some but not all variables are integers. Mixed IP models are more common, as firms generally have only a few variables that must be integers. 6-4. Satisficing is a term used in GP because it is often not possible to optimize a multi-goal problem. We come as close as possible to reaching goals. 6-5. Deviation variables, similar to slack variables in LP, are the difference between set goals and the current solution. In LP models, only real variables are used, representing physical quantities. 6-6. A college presidents goals might be to (1) increase enrollments by 1,000 students; (2) stay within budget; (3) keep class sizes down to an average of 25 students; (4) increase faculty salaries; (5) develop 10 new off-campus courses; (6) reduce average teaching loads to three courses per semester, and so on. There will be financial, space, tenure, and many other constraints. 6-7. Ranking goals just means more weight can be placed on one goal over another. The higher-ranked goals must be achieved completely before GP moves on to meet lower-ranked goals. 6-8. The purpose of this question is to have the student come up with additional examples of NLP models based on their own experience. Examples include the relationship between price and sales, study time and earned score, etc. 6-9. Unlike an LP model, the solution of an IP model need not be at a corner point. Since the simplex procedure evaluates only corner points, we may have to solve several LP models in order to solve a single IP model. Even though the Branch-and-Bound procedure uses efficient stopping rules during the search process, it could become computationally quite burdensome depending on the number of LP models that need to be solved during the solution of an IP model. 6-10. In the weighted GP approach, we use weights to establish the relative importance of the deviation goal variables. We then solve a single LP model that simultaneously determines the optimal values of these deviation variables. In contrast, in the ranked goal approach, we use ranks to establish a hierarchy of the goals. That is, a lower rank goal is considered only after all higher rank goals have been optimized. 6-11. When the objective function of a model contains squared terms (such as X 2 ) and the constraints are linear, it is called a quadratic programming problem. A number of useful problems in the field of portfolio selection fall into this category.selection fall into this category....
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This note was uploaded on 03/09/2011 for the course COM 315 taught by Professor Bryan during the Spring '10 term at St. Leo.
- Spring '10