Geometry & Preparation
Algebra & Tableau Form
Special Cases
Post-optimality Analysis
IEE 376 - Chapter 4
Michael Clough, Muhong Zhang, Ahmet Keha
Arizona State University
Michael Clough, Muhong Zhang, Ahmet Keha
IEE 376 - Chapter 4
Geometry & Preparation

IEE 376 - Chapter 3
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Chapter 3
Linear Programming (LP)
What is a linear program?
An optimization problem where all of the equations are linear
Not to be confused with computer programming
Exa

IEE 376 - Network Optimization
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Network Optimization
Network basics
A network (or graph) is made up of a set of points and a set
of lines connecting certain points
Points are called nodes (or

IEE 376 - Dynamic Programming
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Dynamic Programming
Dynamic programming
Mathematical technique for making sequential decisions
Tasked with finding the best (optimal) combination of
decisions
D

IEE 376
Spring 2016
Exam 1
2/18/2016
Time Limit: 75 Minutes
Name (Print):
Major:
ASU Affiliate ID:
This exam contains 6 pages (including this cover page) and 5 problems. Check to see if any pages
are missing. Enter all requested information on the top of

IEE 376 - Chapter 2
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Chapter 2
Modeling for OR
1
Define the problem of interest and gather relevant data
2
Formulate a mathematical model to represent the problem
Develop a solution methodolo

IEE 376 - Dual Simplex
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Dual Simplex
Primal-dual relationships
Weak duality : If x is a feasible solution for the primal problem
(P) and y is a feasible solution for the dual problem (D), the

IEE 376 - Worked Problems - Chapter 7
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Worked Problems - Chapter 7
First some duality - Problem 6.1-5
Consider the following problem.
Maximize Z =
S.t.
2x1
x1
+6x2
+9x3
+x3
x2
+2x3
x1 , x2 ,

IEE 376
Spring 2016
Exam 2 - Solutions
3/29/2016
Time Limit: 75 Minutes
Name (Print):
Major:
ASU Affiliate ID:
This exam contains 7 pages (including this cover page) and 4 problems. Check to see if any pages
are missing. Enter all requested information on

IEE 376 - Chapter 1
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Chapter 1
What do IEs do?
Other engineering disciplines are known for tangible products
they design
Industrial engineers are known for the systems they design
IEs integra

IEE 376 - Chapter 2
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Chapter 2
Modeling for OR
1
Define the problem of interest and gather relevant data
2
Formulate a mathematical model to represent the problem
Develop a solution methodolo

Introductions
Syllabus Information
IEE 376 - Operations Research Deterministic
Techniques
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Operations Research Deterministic Techniques
Introductions
Syllabus Information
Your Instructor
Some

IEE 376 - Chapter 6
Michael Clough
Arizona State University
Michael Clough
IEE 376 - Chapter 6
Primal and dual formulation
LPs have two formulations that solve the same problem
The original problem is called the Primal Problem
The alternative formulation

IEE 376 - Network Optimization Models
Muhong Zhang, Ahmet Keha, Rene Villalobos and Gary Hogg
DEPARTMENT OF INDUSTRIAL ENGINEERING
Nov. 14, 2012
Network Analysis
A network (graph) consists of a set of points and a set of lines connecting
certain points. T

IEE 376 - Simplex Method in Tableau FORM
Muhong Zhang, Ahmet Keha, J. Ren Villalobos and Gary L. Hogg,
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 08, 2012
Simplex Method in Tableau Format
The tableau format allows us to represent the problem compactly and

IEE 376 - Minimum Cost Network Flow
Muhong Zhang and Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Dec. 03, 2012
Minimum Cost Flow Problem
The network is a directed and connected network.
At least one of the nodes is a supply node
At least one of the ot

IEE 376 - Shortest Path Problem
Muhong Zhang and Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Nov. 19, 2012
Shortest Path Problem
The shortest-path problem is concerned with finding the shortest path in a
network from one node (or set of nodes) to anot

IEE 376 - Maximum Flow Problem
Muhong Zhang and Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Nov. 28, 2012
Maximum Flow Problem
Many situations can be modeled by a network in which the arcs may be thought
of as having a capacity that limits the quantit

IEE 376 - Introduction to Operations Research
Muhong Zhang, Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Aug. 27, 2012
History of Operations Research
Operations Research started from the World War II.
How to allocate scarce resources in an efficient ma

IEE 376 - Duality
Muhong Zhang, Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Nov. 14, 2012
The Windsor Glass Co. Problem
The Windsor Glass Company is planning to launch two new products: Product
1: An 8-foot glass door with aluminum framing; Product 2:

IEE 376 - Review of Linear Algebra
Muhong Zhang
DEPARTMENT OF INDUSTRIAL ENGINEERING
Aug. 27, 2012
Matrices and Vectors
Matrices
Definition
A matrix is a rectangular array of numbers.
Example:
1 2
4 8 26
2
,
,
,
3 4
23 4 9
1
1 2
Definition
The order o

IEE 376 - Setting up the Simplex Method
Muhong Zhang, Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 03, 2012
Setting Up The Simplex Method
Simplex method is based on solving system of equations
The first step is converting inequality constraints to

IEE 376 - Graphical Solution of LP
Muhong Zhang, Ahmet Keha, Rene Villalobos and Gary Hogg
DEPARTMENT OF INDUSTRIAL ENGINEERING
Sep. 05, 2012
Outline
1
Modeling LP in steps
2
Graphically solve the LP
3
Assumptions of Linear Programming
Zhang
IEE 376 Graph

IEE 376 - Adopting to Other Model Forms in Simplex
Method
Muhong Zhang, Ahmet Keha, J. Ren Villalobos and Gary L. Hogg,
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 17, 2012
Inspector Assignment Problem
A company has two grades of inspectors, 1 and 2, who ar

IEE 376 - Geometry of Simplex Method
Muhong Zhang, Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 03, 2012
Corner-point solutions
The points of the intersection of constraints are called corner-point
solutions of the problem.
Corner-point solutions

IEE 376 - Advanced Topics in Simplex Method
Muhong Zhang, Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 24, 2012
LP in matrix form
LP in canonical form:
n
P
max
i=1
n
P
s.t.
ci xi
aij xi bj , j = 1, ., m
i=1
xi 0, i = 1, ., n
LP in augmented (stand

IEE 376 - Special Cases in Simplex Method
Muhong Zhang, Ahmet Keha, J. Ren Villalobos and Gary L. Hogg,
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 10, 2012
Degenerate Solution
When two or more variables tie for being the leaving variable, this
causes one o

IEE 376 - The Algebra of Simplex Method
Muhong Zhang, Ahmet Keha
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 08, 2012
Simplex Algorithm
Simplex method starts from an initial CPF solution. It then moves to an
adjacent CPF solution that is better. If no such

IEE 376 - Sensitivity Analysis
Muhong Zhang, Ahmet Keha, J. Ren Villalobos and Gary L. Hogg,
DEPARTMENT OF INDUSTRIAL ENGINEERING
Oct. 22, 2012
Sensitivity Analysis
Post-optimal analysis uses the information provided by the final simplex
tableau.
It serve