Linear Programming
Z00_REND1011_11_SE_MOD7 PP2.QXD
2/21/11
12:39 PM
Page 1
7
MODULE
Linear Programming:
The Simplex Method
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.
CHAPTER OUTLINE
M7.1
M7.2
M7.3
M7.4
M7.5
M7.6
M7.7
Introduction
How to Set Up the Initial Simplex Solution
Simplex Solution Procedures
The Second Simplex Tableau
Developing the Third Tableau
Review of Procedures for Solving LP Maximization
Problems
Surplus and Artificial Variables
M7.8
M7.9
M7.10
M7.11
M7.12
M7.13
Solving Minimization Problems
Review of Procedures for Solving LP
Minimization Problems
Special Cases
Sensitivity Analysis with the Simplex Tableau
The Dual
Karmarkar’s Algorithm
Summary • Glossary • Key Equation • Solved Problems • Self-Test •
Discussion Questions and Problems • Bibliography
M7-1
Z00_REND1011_11_SE_MOD7 PP2.QXD
M7-2
M7.1
12:39 PM
Page 2
MODULE 7 • LINEAR PROGRAMMING: THE SIMPLEX METHOD
Introduction
Recall that the theory of LP states the optimal solution will lie at a corner point of the feasible region. In large LP problems, the feasible region cannot be graphed because it has many dimensions, but the concept is the same.
The simplex method systematically examines corner points, using algebraic steps, until an optimal solution is found. M7.2
2/21/11
In Chapter 7 we looked at examples of linear programming (LP) problems that contained two decision variables. With only two variables it is possible to use a graphical approach. We plotted
the
2/21/11
12:39 PM
Page 1
7
MODULE
Linear Programming:
The Simplex Method
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.
CHAPTER OUTLINE
M7.1
M7.2
M7.3
M7.4
M7.5
M7.6
M7.7
Introduction
How to Set Up the Initial Simplex Solution
Simplex Solution Procedures
The Second Simplex Tableau
Developing the Third Tableau
Review of Procedures for Solving LP Maximization
Problems
Surplus and Artificial Variables
M7.8
M7.9
M7.10
M7.11
M7.12
M7.13
Solving Minimization Problems
Review of Procedures for Solving LP
Minimization Problems
Special Cases
Sensitivity Analysis with the Simplex Tableau
The Dual
Karmarkar’s Algorithm
Summary • Glossary • Key Equation • Solved Problems • Self-Test •
Discussion Questions and Problems • Bibliography
M7-1
Z00_REND1011_11_SE_MOD7 PP2.QXD
M7-2
M7.1
12:39 PM
Page 2
MODULE 7 • LINEAR PROGRAMMING: THE SIMPLEX METHOD
Introduction
Recall that the theory of LP states the optimal solution will lie at a corner point of the feasible region. In large LP problems, the feasible region cannot be graphed because it has many dimensions, but the concept is the same.
The simplex method systematically examines corner points, using algebraic steps, until an optimal solution is found. M7.2
2/21/11
In Chapter 7 we looked at examples of linear programming (LP) problems that contained two decision variables. With only two variables it is possible to use a graphical approach. We plotted
the
Bibliography: at the end of Chapter 7. M7-53 1,000 Z00_REND1011_11_SE_MOD7 PP2.QXD 2/21/11 12:40 PM Page 54