PPT: Linear Programming | Industrial Engineering - Mechanical Engineering PDF Download

 Page 1


1
Linear and Integer 
Programming Models
Chapter 2
Page 2


1
Linear and Integer 
Programming Models
Chapter 2
2
• A Linear Programming model seeks to maximize or 
minimize a linear function, subject to a set of linear 
constraints.
• The linear model consists of the following
components:
– A set of decision variables.
– An objective function.
– A set of constraints.
2.1   Introduction to Linear Programming
Page 3


1
Linear and Integer 
Programming Models
Chapter 2
2
• A Linear Programming model seeks to maximize or 
minimize a linear function, subject to a set of linear 
constraints.
• The linear model consists of the following
components:
– A set of decision variables.
– An objective function.
– A set of constraints.
2.1   Introduction to Linear Programming
3
Introduction to Linear Programming
• The Importance of Linear Programming
– Many real world problems lend themselves to linear  
programming modeling. 
– Many real world problems can be approximated by linear models.
– There are well-known successful applications in:
• Manufacturing
• Marketing
• Finance (investment)
• Advertising
• Agriculture
Page 4


1
Linear and Integer 
Programming Models
Chapter 2
2
• A Linear Programming model seeks to maximize or 
minimize a linear function, subject to a set of linear 
constraints.
• The linear model consists of the following
components:
– A set of decision variables.
– An objective function.
– A set of constraints.
2.1   Introduction to Linear Programming
3
Introduction to Linear Programming
• The Importance of Linear Programming
– Many real world problems lend themselves to linear  
programming modeling. 
– Many real world problems can be approximated by linear models.
– There are well-known successful applications in:
• Manufacturing
• Marketing
• Finance (investment)
• Advertising
• Agriculture
4
• The Importance of Linear Programming
– There are efficient solution techniques that solve linear 
programming models.
– The output generated from linear programming packages 
provides useful “what if” analysis.
Introduction to Linear Programming
Page 5


1
Linear and Integer 
Programming Models
Chapter 2
2
• A Linear Programming model seeks to maximize or 
minimize a linear function, subject to a set of linear 
constraints.
• The linear model consists of the following
components:
– A set of decision variables.
– An objective function.
– A set of constraints.
2.1   Introduction to Linear Programming
3
Introduction to Linear Programming
• The Importance of Linear Programming
– Many real world problems lend themselves to linear  
programming modeling. 
– Many real world problems can be approximated by linear models.
– There are well-known successful applications in:
• Manufacturing
• Marketing
• Finance (investment)
• Advertising
• Agriculture
4
• The Importance of Linear Programming
– There are efficient solution techniques that solve linear 
programming models.
– The output generated from linear programming packages 
provides useful “what if” analysis.
Introduction to Linear Programming
5
Introduction to Linear Programming
• Assumptions of the linear programming model
– The parameter values are known with certainty.
– The objective function and constraints exhibit 
constant returns to scale.
– There are no interactions between the decision 
variables (the additivity assumption).
– The Continuity assumption: Variables can take on 
any value within a given feasible range.