CSA 441/541
Technical Computing Tools
Greg Reese, Ph.D
Adjunct Assistant Professor
Computer Science
Fall 2010
Who am I?
Greg Reese
Ph.D in Engineering
University of California, Irvine
MSEE
University of California, Irvine
B.A. in Physics and Math
Oberlin

User Input and Output
Greg Reese, Ph.D
Research Computing Support Group
Academic Technology Services
Miami University
User Input and Output
2010 Greg Reese. All rights reserved
2
User I/O
Terminology
GUI: Graphical User Interface
I/O: Input or Output
Two

LP Exercises
and Excel Solver
A formulation problem
The solver
A Simplex problem
Solve
the following problem by the
solver:
max Z = - 3 x1 + 6 x2
st:
5 x 1 + 7 x 2 35
- x1 + 2 x 2 2
x1 , x2 0
Solution by the Solver
Solver Solution
Production Planning pro

Logical Indexing
Greg Reese, Ph.D
Research Computing Support Group
Academic Technology Services
Miami University
Logical Indexing
2010 Greg Reese. All rights reserved
2
Logical indexing
One method of selecting elements in a matrix
or vector is to choose

Adapting the Simplex
algorithm to other LP Models
= and type of constraints
The Big-M Method
Negative RHSs
Minimization models
No solution case
= type of constraints
Recall that we have a basic variable (a slack variable
for a constraint of the canonical

MATLAB
File Input and Output
Greg Reese, Ph.D
Research Computing Support Group
Academic Technology Services
Miami University
MATLAB
File Input and Output
2010 Greg Reese. All rights reserved
2
Output
Convenient to store output in file
Creates record of w

The Simplex Method
Tie breaking
And different solutions
Tie Breaking and other situations
1.
2.
A tie for an entering variable
->break the tie arbitrarily.
A tie for leaving variable
degenerate solution (a basic variable having zero
value): break the tie

MATLAB
Data Analysis
Greg Reese, Ph.D
Research Computing Support Group
Academic Technology Services
Miami University
MATLAB
Data Analysis
2010 Greg Reese. All rights reserved
2
Data analysis
MATLAB has functions for the basic
statistical analysis of numb

The Simplex Method
Solving the Canonical LP
models
HW1 on Blackboard
Setting a LP model for the
Simplex
Lets reconsider an earlier model:
Max Z = 3 x1 + 5 x2
st:
These
models are
equivalent!
4
x1
2 x2
3 x 1 + 2 x2
12
18
x1 0 x2 0
Now, add a set of slack

LP Model Patterns
Exercise: Solve the LP model
Max Z = 10 x1 + 20 x2
st:
-x1 + 2 x2 10
x1 +
x2
8
5 x1 + 3 x2 30
x1 0, x2 0
Assumptions of LP:
Note the following assumptions that we are
making about the following LP sample
formulation:
Proportionality of

Introduction to
OR and LP
What is OR?
Short History of OR.
Introduction to Linear Programming
What is OR?
The
OR is concerned with solving
complex decision problems (system
design, operation management and
prediction)
Controllable
(decision) Variables
De

NAVIGATION
>
PUBLICATION
BODYBUILDER FOR BIOMECHANICS
1
BODYBUILDER FOR BIOMECHANICS
2002 Oxford Metrics Ltd
All rights reserved
Revision history
Created July 1995
Development version of VICON Editor and Modeller software (16 bit)
First update August 199