IND E 599: Intro to Optimization
Models
Lecture 11: Uncertainty & Stochastic (contd)
Yield Management
Prof. W. Art Chaovalitwongse
Yield Management (12.24)
An airline is selling tickets for flights to a particular
destination. The flight will depart in 3

IND E 599: Intro to Optimization
Models
Lecture 14: Nonlinear Optimization
Prof. W. Art Chaovalitwongse
Is everything linear?
Risk & Variance Financial Optimization.
Engineering/Design Considerations.
Tires are made by combining rubber, oil, and carbon

IND E 599: Intro to Optimization
Models
Lecture 15: Nonlinear Modeling
Prof. W. Art Chaovalitwongse
Nonlinear Programming Models
Linear models (LP, IP, and GP) have linear objec;ve
func;on and constraints
A non-
linear program is p

IND E 599: Intro to Optimization
Models
Lecture 16: Goal Programming
Prof. W. Art Chaovalitwongse
Goal Programming Models
In some situa3ons, a decision maker may face mul3ple
objec3ves, and there may be no point in an LPs feasible

IND E 599: Intro to Optimization
Models
Lecture 17: Dynamic Programming
Prof. W. Art Chaovalitwongse
Descrip)on
Dynamic programming is a technique that can be
used to solve many op)miza)on problems.
Transforms a complex op)miz

IND E 599: INTRODUCTION TO OPTIMIZATION MODELS
HOMEWORK 1 (100 points)
Due on 10/10/2012 (in class)
1) (25 points) Graphically solve the following LP, find its optimal solution and all basic
feasible solutions:
max z = 5 x1 + x2
s.t.
2 x1 + x2 6
x1 + x2 4

IND E 599: INTRODUCTION TO OPTIMIZATION MODELS
HOMEWORK 2 (100 points)
Due on 10/29/2012 (in class)
1) (25 points) Solve a traveling salesman problem with the distance matrix given below. Use
the node index constraint:
.
2) (25 points) Solve the TSP in Pr

IND E 599: INTRODUCTION TO OPTIMIZATION MODELS
HOMEWORK 3 (100 points)
Due on 11/7/2012 (in class)
You may work with one classmate and submit the homework as a group of 2.
1) (25 points) Given a knapsack problem with four items that have the weights and u

IND E 599: INTRODUCTION TO OPTIMIZATION MODELS
HOMEWORK 4 (100 points)
Due on 12/10/2012 (before 4:30pm)
You may work with one classmate and submit the homework as a group of 2.
1) (25 points) In a location problem we must determine whether to put a facil

IND E 599: Intro to Optimization
Models
Lecture 13: (Stochastic vs. Robust) Optimization
Prof. W. Art Chaovalitwongse
Optimization Against Uncertainty
Stochastic Optimization.
Optimize the expected cost given the probability
distribution on the scenario

IND E 599: Intro to Optimization
Models
Lecture 12: Review 2
Prof. W. Art Chaovalitwongse
TSP: Example
Given six locations, how should you go about visiting each location
starting to minimize travel cost?
An Allocation Problem
A small hardware manufactu

IND E 599: Intro to Optimization
Models
Lecture 10: Uncertainty & Stochastic
Prof. W. Art Chaovalitwongse
Deterministic vs. Stochastic
What we have done so far is deterministic.
How to incorporate uncertainty into optimization models
Decision making un

IND E 599: Intro to Optimization
Models
Lecture 2: Building LP Models (Ch. 3),
Interpreting and Using an LP solution (Ch. 6)
Duality
Prof. W. Art Chaovalitwongse
Defining Objectives
Common Objectives
Minimize cost
Maximize profit
Maximize utility
Maximiz

IND E 599: Intro to Optimization
Models
Lecture 3: Portfolio Optimization
Prof. W. Art Chaovalitwongse
Portfolio Theory
One of the major advances in investment over the last few
decades has been the creation of an optimum investment
portfolio.
The creat

IND E 599: Intro to Optimization
Models
Lecture 4: Game Theory,
Regression
Prof. W. Art Chaovalitwongse
Business is a game, the greatest game in the world if you know how to play it.
- IBM founder Thomas J. Watson
Game theory forces you to see a business

IND E 599: Intro to Optimization
Models
Lecture 5: Integer Programming
Prof. W. Art Chaovalitwongse
Integer Programming Deni/on
An Integer Programming problem (IP) is a Linear Programming (LP) in
which some or all the variables are

IND E 599: Intro to Optimization
Models
Lecture 6: Recap
Prof. W. Art Chaovalitwongse
x0=60
y-1=2
y0=0
rt required flight attendant hours
in t
lt number of flight attendants
resigning in t
c=5100 monthly cost of one flight
attendant
d=3600 monthly cos

IND E 599: Intro to Optimization
Models
Lecture 7: IP/MIP
Prof. W. Art Chaovalitwongse
TSP: Example
Given six locations, how should you go about visiting each location
starting to minimize travel cost?
Traveling Salesman Problem
The solution of the 15,11

IND E 599: Intro to Optimization
Models
Lecture 8: Network Models
Prof. W. Art Chaovalitwongse
Network Models
Use of network models are widespread
Transportation networks, communication networks, electrical
networks, social networks, financial networks

IND E 599: Intro to Optimization
Models
Lecture 9: Network Models (contd)
Prof. W. Art Chaovalitwongse
Shortest Path Model for Lot-Sizing Problem
Consider the following scenario
Costs
= 2000 items per year
K = $500 per order
c = $50 per item
i = 24%

IND E 599: Intro to Optimization
Models
Lecture 1: Administration, Introduction, Examples
of optimization problems
Prof. W. Art Chaovalitwongse
(Dr. Chao-va-lit-wongs, Dr. Art, Dr. C, Art, etc)
General Information
Instructor:
W. Art Chaovalitwongse (artch