IOE310: Introduction
to Optimization
Tuesday, December 8, 2009
Professor Amy Cohn
1
Project Announcements
Project is due on Monday the 14th; will be
accepted through Friday the 18th at 9am sharp
No late submissions accepted under any
circumstances
Typical
IOE310: Introduction
to Optimization
Thursday, December 3, 2009
Professor Amy Cohn
1
Announcements
PS 11 due next Thursday
Upcoming dates:
Next
Thursday (12/10) optional makeup exam (in
class or in evening)
Project due 12/14 but will be accepted late wi
IOE310: Introduction
to Optimization
Tuesday, December 1, 2009
Professor Amy Cohn
1
Announcements
PS 10 due this Thursday
Implementation updates due this Thursday
PS 11 due next Thursday
Upcoming dates:
Next
Thursday (12/10) optional makeup exam (in
clas
IOE310: Introduction
to Optimization
Tuesday, November 24, 2009
Professor Amy Cohn
1
Announcements
Next PS will be due Thursday instead of
Tuesday
Implementation is also due
Students who emailed me about formulation:
Please talk to me briefly after class
IOE310: Introduction
to Optimization
Tuesday, November 17, 2009
Professor Amy Cohn
1
Announcements
Exam issues:
Topics:
Time and location
Basic feasible solutions
Simplex method
Means for solving LPs
True/false
Computational
Modeling
Alternate at 7pm, roo
IOE310: Introduction
to Optimization
Thursday, November 12, 2009
Professor Amy Cohn
1
Finding an Initial BFS
We need an initial BFS to start the
algorithm where does this come from?
If we just randomly choose a basis and
solve for xB, it might turn out t
IOE310: Introduction
to Optimization
Tuesday, November 10, 2009
Professor Amy Cohn
1
Announcements
Data for projects due on Thursday 11/12
2
Simplex Method for
Solving LPs
3
Simplex Pivots
The key to the simplex method is to pivot
from one BFS to another
IOE310: Introduction
to Optimization
Thursday, November 5, 2009
Professor Amy Cohn
1
Announcements
Returning re-graded exams
Data for projects due in one week (Thursday
11/12)
Reminder about labs, AMPL, projects, and GSI
help
2
Simplex Method for
Solving
IOE310: Introduction
to Optimization
Tuesday, November 3, 2009
Professor Amy Cohn
1
Simplex Method for
Solving LPs
2
Motivation
The graphical method only works in R2 or R3
The basic feasible solution approach isnt
guaranteed to work if the feasible region
IOE310: Introduction
to Optimization
Tuesday, October 27, 2009
Professor Amy Cohn
1
Announcements
Exam re-grade requests must be put in my
mailbox by Thursday
Project formulations are due by this
Thursday at 7pm
2
Techniques for Solving LPs
3
Wrapping Up
IOE310: Introduction
to Optimization
Thursday, October 22, 2009
Professor Amy Cohn
1
Announcements
Make sure youve met with your project
advisors!
Exams to be handed back at the end of
class
Mean TK
Standard deviation TK
Re-grade policy
2
Techniques f
IOE310: Introduction
to Optimization
Thursday, October 15, 2009
Professor Amy Cohn
1
Announcements
Please fill out mid-term evaluations!
Exams will be returned next week
Make sure youve met with your project
advisors!
2
Graphical Method
3
An Example
Min
IOE310: Introduction
to Optimization
Thursday, October 8, 2009
Professor Amy Cohn
1
Quick Note
Please fill out mid-term evaluations!
We really do read these
We really do change things to try to
improve the course
2
Exam
Next Tuesday in class
Alternate
IOE310: Introduction
to Optimization
Tuesday, October 6, 2009
Professor Amy Cohn
1
Project Discussion
Re-submitting topics
Meeting with project advisor
Next steps and new deadlines
How projects will be graded
Sample project
2
Exam
Next Tuesday in clas
IOE310: Introduction
to Optimization
Thursday, October 1, 2009
Professor Amy Cohn
1
Min Cost Flow Problem
2
Problem Description
Consider a directed network which has source
nodes, sink nodes, and transshipment nodes.
We also have capacity limits (possibly
IOE310: Introduction
to Optimization
Tuesday, September 29, 2009
Professor Amy Cohn
1
Binary Programs
2
Dorm Assignment
A new dorm has been completed, consisting of
100 two-person suites. 200 students have been
assigned to that dorm, and your job is to as
IOE310: Introduction
to Optimization
Thursday, September 24, 2009
Professor Amy Cohn
1
Recap
Weve learned:
What
an optimization problem is
What it means to represent mathematically
(decision variables, constraints, objective
function)
Sample mathematic
Robust Airline Planning
Measuring and Minimizing Delay Propagation in
Airline Plans
Outline
Overview
Motivation Behind Research
Propagation Analysis
Single Layer Model/Multi-Layer Model
Building
a solution
Solving the math program
Simulation
2
Causes
IOE310: Introduction
to Optimization
Thursday, September 17, 2009
Professor Amy Cohn
1
Product Mix
Every unit of product i that I produce uses
dij units of resource j. I can sell a unit of
product i for $si. I have to buy resource j at
$bj. There is an up
IOE310: Introduction
to Optimization
Tuesday, September 15, 2009
Professor Amy Cohn
1
Resource Allocation
Problems
2
Resource Allocation Problems
Class of optimization problems
Set of resources (e.g. raw materials, personnel, money,
time)
Need to use the
IOE310: Introduction
to Optimization
Thursday, September 10, 2009
Professor Amy Cohn
1
The Diet Problem
2
Problem Statement
An example:
Minimize the cost of my diet, subject to
satisfying lower bounds on protein and
taste, and upper bounds on calories and
IOE310: Introduction
to Optimization
Tuesday, September 8, 2009
Professor Amy Cohn
1
Pop Quiz
What do the following things have in common:
Major League Baseball
American Airlines
The United States Army
Goldman Sachs
Ford Motor Company
2
Answers
They all f
BIRTH AND DEATH PROCESS
I
Assumptions:
Given N (t ) = n, the current probability of remaining time to next
birth is exponential with parameter n , for each n = 0, 1, .
Given N (t ) = n, the current probability of the remaining time to next
death is expone
QUEUEING THEORY
Saigal ()
IOE 202
1 / 18
A QUEUEING QUESTION
I
The Problem: A county hospital runs an emergency care facility.
Patients are brought to this facility via an ambulance or private auto.
At any hour, there is one doctor on duty.
The hospital i
SENSITIVITY ANALYSIS - AN EXAMPLE
I
A manufacturer produces two toys
Soldiers: sell at $27 and require $10 (raw mat), $14 (labor).
Trains: sell at $21 and require $9 (raw mat), $10 (labor).
Two types of scarce skilled labor is needed.
Finishing. Hours ava
INTRODUCTION TO LINEAR AND INTEGER
PROGRAMMING
What is linear and integer programming.
Some models of linear and integer programming. [Pages 34-50]
EXCEL Solution of linear and integer programming. [Pages 6-26]
Graphical solution of a linear programming p
IOE 202: OPERATIONS MODELING
MS Excel and Modeling
November 3, 2003
(1) How to open Excel from the CAEN Lab:
On the toolbar
at the bottom
of the screen,
click on:
Start
All Programs
General Office
Applications
Microsoft
Office XP
Microsoft
Excel
IOE