Faculty of Engineering
Lecture Outline
Linear Programming
Model Formulation
Linear Programming Model
Graphical Solution Method
Solving Linear Programming Problems
Sensitivity Analysis
Dr. Ahmed Mohib
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
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Chapter 4: The
LinearProgramming:SensitivityAnalysis
andInterpretationofSolution
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s
s
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IntroductiontoSensitivityAnalysis
GraphicalSensitivityAnalysis
SensitivityAnalysis:ComputerSolution
SimultaneousChanges
Slide
ILP Application
Faculty of Engineering
Assignment Problem
Network Models
ILP Applications
& Networking
Shortest-Route Problem
Minimal Spanning Tree Problem
Maximal Flow Problem
Transportation
Trans
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).
Th
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. Ahme
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:
Line
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,IndustrialEn