Chapter 17 - Solution of Linear Programming Problems

Abstract

While the previous chapter discussed the modeling of linear programming problems, this chapter discusses the possible solution methods. The set of feasible solutions and the optimal solution for a simple linear programming problem can be obtained in a graphical way, through the analytical method, by using the Simplex method, and through software packages. All the real linear programming problems modeled in Chapter 16 will be solved by the Solver in Excel. The special cases that may happen in a linear programming model will be graphically identified through the Simplex method and by using a computer. The sensitivity analysis, which will be studied at the end of this chapter, has as its main objective to analyze how changes in the model parameters impact the optimal solution. These possible changes will be analyzed in a graphical way and by Solver in Excel. The concepts of shadow price and reduced cost will also be discussed in the study of the sensitivity analysis. Through the Sensitivity Report found on Solver in Excel, the special cases “multiple optimal solutions” and “degenerate optimal solution” will be identified.