Faculty of Engineering
Lecture Outline
Linear Programming
Model Formulation
Linear Programming Model
Graphical Solution Method
Solving Linear Programming Problems
Sensitivity Analysis
Dr. Ahmed Mohib
Dr. Ahmed Mohib
History of Linear Programming
History o
Chapters 1& 2
Chapter 4: The Simplex Method
Adapting to Other Legitimate Forms
Equality constraints
Negative RHS
Functional constraints
Minimization
Variables allowed to be negative
44
Chapter 4: The Simplex Method
Adapting to Other Legitimate Forms
1. E
LinearProgramming:SensitivityAnalysis
andInterpretationofSolution
s
s
s
s
IntroductiontoSensitivityAnalysis
GraphicalSensitivityAnalysis
SensitivityAnalysis:ComputerSolution
SimultaneousChanges
Slide
1/53
StandardComputerOutput
SoftwarepackagessuchasTORA,
ILP Application
Faculty of Engineering
Assignment Problem
Network Models
ILP Applications
& Networking
Shortest-Route Problem
Minimal Spanning Tree Problem
Maximal Flow Problem
Transportation
Transshipment
Upper-bounded network flow problems
Maximum
Faculty of Engineering
Integer Linear
Programming
Types of Integer Programming Models
An LP in which all the variables are restricted to be
integers is called an all-integer linear program (ILP).
The LP that results from dropping the integer
requirement
Faculty of Engineering
Different Types of LP & Application
Linear Programming
Applications
Dr. Ahmed Mohib
2
Dr. Ahmed Mohib
Different Types of LP (cont.)
Different Types of LP & Application
Dr. Ahmed Mohib
3
4
Dr. Ahmed Mohib
Single-Period Production Mo
Faculty of Engineering
Sensitivity Analysis
Sensitivity analysis (or post-optimality analysis)
is used to determine how the optimal solution is
affected by changes, within specified ranges, in:
Linear Programming
the objective function coefficients
th
Topic 3: The Simplex Method
This topic details the Simplex method for solving
the general LP problem.
The topic is covered in the textbook under
Sections 3.1 to 3.5.
DrMuhammadAlSalamah,IndustrialEngineering,KFUPM
LP MODEL IN EQUATION FROM
The Simplex