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

9 Linear Optimization

9.1 INTRODUCTION

In Chapter 8, we introduced optimization with Solver, and we focused on nonlinear programming. The nonlinear solver is the default algorithm in Solver, and it can be applied to a variety of optimization problems. Linear programming is a special case for which certain mathematical conditions must hold, but it is much more widely used in practice than nonlinear programming. Because of the mathematical structure of a linear program, it is possible to harness a more powerful algorithm (called the simplex method) for linear problems than for nonlinear problems, and we can accommodate larger numbers of variables and constraints. In this chapter, we cover the use of the linear solver, and we examine several examples that illustrate the wide applicability of linear programming models. In the fifty years or so that computers have been available for this kind of decision support, linear programming has proven to be a valuable tool for understanding business decisions.

As in the previous chapter, our optimization models contain a set of decision variables, an objective function, and a set of constraints. (In fact, we strongly recommend reading our general introduction to Solver in Sections 8.1 through 8.4 before proceeding.) In the case of linear models, we can impose additional design guidelines on our worksheets that lead to a more standardized approach than we were able to adopt with nonlinear models. These additional guidelines help us develop models ...