System Optimization Models

Optimization plays an important role in the system engineering design process. This chapter provides a basic review of the most commonly used optimization models for systems engineers to understand the nature of optimization problems. First, we introduced the concepts of unconstrained optimization models. These models are based on basic differentiation theory. In the second part of the chapter, we describe constrained optimization models using mathematical programming. The fundamental form of mathematical programming is Linear Programming (LP). With LP models, both the objective functions and constraint functions are linear. LP models are formally defined and we use some examples to illustrate how to formulate an LP model. If an LP model has only two or three decision variables, we can solve it by using graphical methods. If more than three variables are involved, we need to apply a more general algorithm called the Simplex method. A tabular format of the Simplex algorithm is described in detail, and at the end of the chapter, we briefly discuss how to use spreadsheet software to implement the Simplex method.