# NLP - Management Science with Practical Spreadsheet...

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Management Science with Practical Spreadsheet Modeling Chapter 5 Patrick Johanns Page 1 9/15/2009 C:\Documents and Settings\pjohann\My Documents\BOOK\Second Edition\NLP.docx Chapter 5 Non-Linear Optimization Chapter Objectives Identify situations where a non-linear model is appropriate. Understand the concepts of convexity and concavity. Formulate non-linear model. Create and solve non-linear spreadsheet models. Apply modeling techniques to the following problem types: o Optimal Pricing o Portfolio Selection o Location Analysis Introduction It can be reasonably argued that linear models are just approximations of non-linear models. If linear programs are only approximations, why do we use them? Linear models are desirable for several reasons. First they are easy to understand and explain. Second, the Simplex method used to solve them runs very fast on the computer. Finally, the optimal solution can reliably found with a linear model. However, some business problems would not make sense or generate invalid results if we tried to model them in a linear fashion. Consider the following business concepts which are clearly nonlinear functions: decreasing marginal returns from advertising dollars, price elasticity, time value of money, portfolio variance, economies of scale, and revenue as a function of price. To build more realistic models incorporating these concepts and others like them, we may need to formulate an objective function or constraints that are not in a linear format. These formulas tend to be more complex and difficult to model. Finding the optimal solution becomes more challenging also as the Simplex method will not work with nonlinear models. In this chapter we will Discuss the mathematical formulation and solving of nonlinear models. Differentiate between global and local optimal solutions. Identify when Solver can find the global optimal solution to a nonlinear program. Formulate mathematical and spreadsheet models for several common applications. Formulation of a Nonlinear Program (NLP)

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Management Science with Practical Spreadsheet Modeling Chapter 5 Patrick Johanns Page 2 9/15/2009 C:\Documents and Settings\pjohann\My Documents\BOOK\Second Edition\NLP.docx The formulation of a nonlinear program can be look very similar to a linear program. In both you need to define the decision variables, compose the objective function, and formulate the constraints. The main difference is the objective function or one or more of the constraints are not linear equations. It may require the multiplying of two variables together, raising a variable to a power, taking the natural log of a variable or some other function that would cause the graph of the equation to be non-linear. These non-linear equations pose extra challenges when we build spreadsheet models which we will discuss in several examples in this chapter.
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## This note was uploaded on 10/14/2009 for the course MGMT 360 taught by Professor Yanjunli during the Spring '09 term at Purdue.

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NLP - Management Science with Practical Spreadsheet...

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