Quantitative Analysis for Management
Chapter 9
Learning Objectives
After completing this chapter, students will be able to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables 2. Set up and solve LP problems with simplex tableaus 3. Interpret the meaning of every number in a simplex tableau 4. Recognize special cases such as infeasibility, unboundedness, and degeneracy 5. Use the simplex tables to conduct sensitivity analysis 6. Construct the dual problem from the primal problem
© 2009 Prentice-Hall, Inc. 9–2
Linear Programming: The Simplex Method
© 2008 Prentice-Hall, Inc.
Chapter Outline
9.1 Introduction 9.2 How to Set Up the Initial Simplex Solution 9.3 Simplex Solution Procedures 9.4 The Second Simplex Tableau 9.5 Developing the Third Tableau 9.6 Review of Procedures for Solving LP Maximization Problems 9.7 Surplus and Artificial Variables 9.8 9.9 9.10 9.11 9.12 9.13
Chapter Outline
Solving Minimization Problems Review of Procedures for Solving LP Minimization Problems Special Cases Sensitivity Analysis with the Simplex Tableau The Dual Karmarkar’s Algorithm
© 2009 Prentice-Hall, Inc.
9–3
© 2009 Prentice-Hall, Inc.
9–4
Introduction
With only two decision variables it is possible to
Introduction
Why should we study the simplex method? It is important to understand the ideas used to
use graphical methods to solve LP problems
But most real life LP problems are too complex for
simple graphical procedures We need a more powerful procedure called the simplex method The simplex method examines the corner points in a systematic fashion using basic algebraic concepts It does this in an iterative manner until an optimal solution is found Each iteration moves us closer to the optimal solution
© 2009 Prentice-Hall, Inc. 9–5
produce solutions
It provides the optimal solution to the decision
variables and the maximum profit (or minimum cost) It also provides important economic information To be able
Learning Objectives
After completing this chapter, students will be able to: 1. Convert LP constraints to equalities with slack, surplus, and artificial variables 2. Set up and solve LP problems with simplex tableaus 3. Interpret the meaning of every number in a simplex tableau 4. Recognize special cases such as infeasibility, unboundedness, and degeneracy 5. Use the simplex tables to conduct sensitivity analysis 6. Construct the dual problem from the primal problem
© 2009 Prentice-Hall, Inc. 9–2
Linear Programming: The Simplex Method
© 2008 Prentice-Hall, Inc.
Chapter Outline
9.1 Introduction 9.2 How to Set Up the Initial Simplex Solution 9.3 Simplex Solution Procedures 9.4 The Second Simplex Tableau 9.5 Developing the Third Tableau 9.6 Review of Procedures for Solving LP Maximization Problems 9.7 Surplus and Artificial Variables 9.8 9.9 9.10 9.11 9.12 9.13
Chapter Outline
Solving Minimization Problems Review of Procedures for Solving LP Minimization Problems Special Cases Sensitivity Analysis with the Simplex Tableau The Dual Karmarkar’s Algorithm
© 2009 Prentice-Hall, Inc.
9–3
© 2009 Prentice-Hall, Inc.
9–4
Introduction
With only two decision variables it is possible to
Introduction
Why should we study the simplex method? It is important to understand the ideas used to
use graphical methods to solve LP problems
But most real life LP problems are too complex for
simple graphical procedures We need a more powerful procedure called the simplex method The simplex method examines the corner points in a systematic fashion using basic algebraic concepts It does this in an iterative manner until an optimal solution is found Each iteration moves us closer to the optimal solution
© 2009 Prentice-Hall, Inc. 9–5
produce solutions
It provides the optimal solution to the decision
variables and the maximum profit (or minimum cost) It also provides important economic information To be able