ABSTRACT
The purpose of this book is to cover the basic modelling techniques of optimization problem solving, discuss the widely used theoretical optimization models and some practical optimization problems, and demonstrate the use of available software packages for optimization problem solving. Although the interpretation of solutions and sensitivity analysis are also provided with sufficient detail, an understanding of the basic optimization techniques would help to gain more insight about the problem solution space and the decision to be made. In addition, it will provide greater confidence of the quality of solutions to be obtained and decision to be made. With these views in mind, we present a few basic techniques briefly in this chapter as follows:
. Graphical solution method for linear programming (LP)
. Simplex method for LP
. Branch-and-bound technique for integer programming
The graphical method is used to solve optimization models involving two variables and a few constraints, and the method helps to gain insights about the feasible solution space, optimality, and the interaction between different model parameters. The educational software Win QSB, discussed in Chapter 9, is capable of producing graphical solutions. In this section, we solve a small LP problem using Win QSB and then discuss how the method works. To demonstrate the method, let us consider an example.
