Optimization in Excel
5. INTRODUCTION TO LINEAR PROGRAMMING (LP)
Learning Objectives
1.
Obtain an overview of the kinds of problems linear programming has been used to solve.
2.
Learn how to develop linear programming models for simple problems.
3.
Be able to identify the special features of a model that make it a linear programming model.
4.
Learn how to solve two variable linear programming models by the graphical solution procedure.
5.
Understand the importance of extreme points in obtaining the optimal solution.
6.
Know the use and interpretation of slack and surplus variables.
7.
Be able to interpret the computer solution of a linear programming problem.
8.
Understand how alternative optimal solutions, infeasibility and unboundedness can occur in linear programming problems.
9.
Understand the following terms: problem formulation constraint function objective function solution optimal solution nonnegativity constraints mathematical model linear program linear functions feasible solution
feasible region slack variable standard form redundant constraint extreme point surplus variable alternative optimal solutions infeasibility unbounded
5.1. Linear Programming (LP) Problem
Linear programming - involves choosing a course of action when the mathematical model of the problem contains only linear functions
All linear progamming problems have
1. An objective
2. constraints
Feasible solution
Optimal solution
.
Graphical solution method
If both the objective function and the constraints are linear, the problem is referred to as a linear programming problem.
Linear functions
Linear constraints
5.2. Problem Formulation
Problem formulation or modeling
General Guidelines for LP Model Formulation
1. Understand the problem thoroughly.
2. Describe the objective.
3. Describe each constraint.
4. Define the decision variables.
5. Write the objective in terms of the decision variables.
Learning Objectives
1.
Obtain an overview of the kinds of problems linear programming has been used to solve.
2.
Learn how to develop linear programming models for simple problems.
3.
Be able to identify the special features of a model that make it a linear programming model.
4.
Learn how to solve two variable linear programming models by the graphical solution procedure.
5.
Understand the importance of extreme points in obtaining the optimal solution.
6.
Know the use and interpretation of slack and surplus variables.
7.
Be able to interpret the computer solution of a linear programming problem.
8.
Understand how alternative optimal solutions, infeasibility and unboundedness can occur in linear programming problems.
9.
Understand the following terms: problem formulation constraint function objective function solution optimal solution nonnegativity constraints mathematical model linear program linear functions feasible solution
feasible region slack variable standard form redundant constraint extreme point surplus variable alternative optimal solutions infeasibility unbounded
5.1. Linear Programming (LP) Problem
Linear programming - involves choosing a course of action when the mathematical model of the problem contains only linear functions
All linear progamming problems have
1. An objective
2. constraints
Feasible solution
Optimal solution
.
Graphical solution method
If both the objective function and the constraints are linear, the problem is referred to as a linear programming problem.
Linear functions
Linear constraints
5.2. Problem Formulation
Problem formulation or modeling
General Guidelines for LP Model Formulation
1. Understand the problem thoroughly.
2. Describe the objective.
3. Describe each constraint.
4. Define the decision variables.
5. Write the objective in terms of the decision variables.