Management Science: The Art of Modeling with Spreadsheets, 4th Edition

8 Nonlinear Optimization

8.1 INTRODUCTION

Optimization is the process of finding the best set of decisions for a particular measure of performance. For example, in the Advertising Budget example of Chapter 3, we measure performance in terms of annual profit, and optimization allows us to set advertising expenditures in the four quarters so that we achieve the maximum annual profit.

In Chapter 4, we introduced a framework for spreadsheet analysis in which optimization represents one of the higher-order levels of analysis, generally coming after a base case has been established, some what-if questions have been explored, and perhaps some back-solving calculations have been made. In this chapter, we'll assume that the steps in that framework have already been carried out. However, the entire framework does not necessarily apply to every spreadsheet model. There are spreadsheets that do not lend themselves to optimization. In some models, for example, the purpose is to explore past relationships or to forecast future outcomes. But managers and analysts generally use models to improve future operations. We refer to the levers they use to bring about improved performance as decision variables. If there are decision variables in a model, it is natural to ask what the best values of those variables are. The measure of performance that defines our notion of “best” is called the objective function, or simply the objective. Once we have specified the objective in a model, it is also natural ...