ISyE 6669
Homework 1 Solutions
3.3.1
AB is x1 + x2 = 4. CD is x1 - x2 = 5. From the graph, we see that there is no feasible
solution (Case 3).
1
3.3.2
AB is 8x1 + 2x2 = 16. CD is 5x1 + 2x2 = 12. Dotte
ISyE6669 Homework 3
On-Campus Deadline: Oct 5, 2016
DL Deadline: October 10, 2016
1
Simplex method
This exercise is about using the simplex method to completely solve a linear program. Consider the
fo
NAME_
Exam 1
ISYE 3133
Summer 2015
Having read the Georgia Institute of Technology Academic Honor code,
I understand and accept my responsibility as a member of the Georgia Tech
community to uphold th
ISyE 6669 Deterministic Optimization
Fall 2016
Syllabus
Instructor
Professor Andy Sun
Office: Groseclose Room 444
Office hour: Monday 10:30AM - 11:30AM
Tel: 404-385-7571 (I prefer that you email me f
Deterministic Optimization ISyE 6669
Spring 2016
Instructor: Dr. Eva Lee
Email: [email protected]
Office Hours: Dr. Lee ISyE Groseclose 425: Thursday 6 - 7pm
Class meetings: Sustainable Education 110
NAME_
Exam 2
ISYE 3133
Summer 2015
Having read the Georgia Institute of Technology Academic Honor code,
I understand and accept my responsibility as a member of the Georgia Tech
community to uphold th
ISYE 6669
Name_
Exam 1
Fall 2015
UNI_
No materials other than a pen/pencil and a one-sided notes sheet are allowed.
1. (10 points) A pastry shop sells cupcakes and cookies. Each product must be baked
ISYE 6669
Deterministic Optimization
Fall 2015
Instructor: Dawn Strickland, [email protected], 203F Groseclose
Office hours: Tuesday, 2-3pm or by appointment
Teaching Assistant: Yufeng Cao, c
ISyE6669 Deterministic Optimization
Homework 5
Due November 28, 2017 (Tuesday)
1
IP modeling
1. Let three binary variables x1 , x2 , x3 represent event i is chosen if xi = 1, and event i is not
chosen
ISyE 6669 Notes 7: Two-Stage Stochastic Linear Program and
Benders Decomposition
Andy Sun
Oct. 17 - 19, 2016
1
Deterministic Planning Problem
An electric generation company (GENCO) faces a planning pr
ISyE 6669
Notes 4: Lagrangian Duality Theory for Linear Optimization
Andy Sun
Sep. 26 - Oct. 5, 2017
Duality theory is at the heart of optimization. In this lecture, we will dive deep into the inner
w
ISyE6669 Deterministic Optimization
Homework 3
Due October 12, 2017
1
Form the dual and form the dual of the dual
Consider the following linear program:
(P )
min x1 x2 + x3
s.t. x1 + 2x2 x3 + 3x4 0
3x
ISyE6669 Homework 2
On-Campus Deadline: September 28, 2017
1
Convex functions and convexification
1. Give an example of a function of one real variable that is both convex and concave.
2. The level se
ISyE6669
Lecture Notes 10: Integer Hull, Cutting Plane Algorithm, and
Branch-and-Bound Algorithm
Andy Sun
Nov 21 - 28, 2017
In this lecture, we study the feasible region of an integer program, its rel
ISyE6669
Lecture Notes 9: Integer Programming Formulation II
Andy Sun
Nov 16, 2017
In this lecture, we will show some interesting modeling examples using integer variables.
1
Combinatorial optimizatio
ISyE6669 Deterministic Optimization
Homework 4
Posted on October 27, 2017
Due on November 9, 2017
Question 1: Cutting Stock Problem 1
In this problem, we want to walk you through one iteration of the
ISyE 6669
Notes 3: The Simplex Method
Andy Sun
Sep. 14 - 21, 2017
In this lecture, we study one of the most celebrated algorithms in optimization, the simplex
method for solving linear optimization pr
LP Modeling HW Sol
11. All variables are in millions of barrels of oil.
Let x11 = Oil sent each year from LA to Houston.
x12 = Oil sent each year from LA to NY.
x21 = Oil sent each year from Chicago t
ISyE 6669
Notes 2: The Geometry of Linear Optimization
Andy Sun
Aug. 31, 2016
In this lecture, we discuss the geometry of linear optimization. The goal is to develop a geometric
intuition of the struc
ISyE 6669
Lecture Notes 6: Dantzig-Wolfe Decomposition
Andy Sun
Oct 12, 2016
In the last few lectures, we introduced the general framework of column generation and constraint
generation for solving la
ISyE6669 Advanced Optimization
Homework 1
On-Campus Deadline: September 7, 2016
DL Deadline: September 14, 2016
1
(15 pt) Is it a polyhedron?
Recall that a polyhedron is the intersection of a finite n
Deterministic Optimization
Eva Lee
Director, Center for Operations Research in Medicine and HealthCare
Co-Director, NSF I/UCRC Center for Health Organization Transformation
Distinguished Scholar in He
4.2 Fundamental Theorems of LP
Theorem 4.1 For any linear program, there is a
1-1 correspondence between the extreme points
and the basic feasible solutions.
Theorem 4.2
If there is a feasible soluti
Deterministic
Optimization
Lecture 5: Modeling
Language and Solvers
Modeling and Solution
for LPs
MODELING (DIET
PROBLEM)
AMPL
CPLEX
Modeling Example
The diet problem
Food Item
Cost
Quarter Pounder w/
ISyE 6669
Deterministic Optimization
Spring 2016
Problem Solving Sessions
Xin Wei
1.
Decision variables:
cre : The amount of high-fat milk(lb) used as pure milk in producing cream cheese.
xm
cot
xm :
ISyE 6669
Notes 3: The Simplex Method
Andy Sun
Sep. 14 - 21, 2017
In this lecture, we study one of the most celebrated algorithms in optimization, the simplex
method for solving linear optimization pr
ISyE 6669
Notes 4: Lagrangian Duality Theory for Linear Optimization
Andy Sun
Sep. 26 - Oct. 5, 2017
Duality theory is at the heart of optimization. In this lecture, we will dive deep into the inner
w
ISyE6669
Notes 1: Linear Optimization Models
Andy Sun
Fall 2017
1
What is Linear Optimization?
A linear optimization problem has a linear objective function and linear equality and/or linear
inequalit
ISyE6669
Review on Linear Algebra and Basic Concepts of Convexity
Fall 2017
Andy Sun
In this lecture, we give a review of some basic concepts in linear algebra. We also introduce the
concept of convex
ISyE 6669 Deterministic Optimization
Fall 2017
Syllabus
Instructor
Professor Andy Sun
Office: Groseclose Room 444
Office hour: Tuesday 11AM - 12PM
Tel: 404-385-7571 (I prefer that you email me first.