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 the Honor Code at all times. In addition, I understand my
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. Dotted line is z = 4x1 + x2 = 4. Feasible
region is bounded
3. x1 = Number of hours of Process 1 and x2 = Number of hours of Process 2. Then the appropriate
LP is
min z = 4x1 + x2
s.t. 3x1 + x210 (A constraint)
x1 + x25 (B constraint)
x1 3 (C constraint)
x1 x20
AB is 3x1 + x2 = 10. CD is x1 + x2 = 5. EF is x1 = 3.
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 to Houston.
x22 = Oil sent each year from Chicago to NY.
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 Health System, Health Systems Institute, Emory / Georgia
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 and then frosted. The
baker can bake 50 cupcakes per da
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 the Honor Code at all times. In addition, I understand my
ISyE6669 Homework 2
On-Campus Deadline: September 21, 2016
DL Deadline: September 26, 2016
1
Convex sets and convex functions
1. Given a function f (x, y) = x2 + y 2 , answer the following questions:
(a) Draw the epigraph of f (x, y).
(b) Write down the a
ISyE6669 Homework 3
On-Campus Deadline: Oct 5, 2016
DL Deadline: October 10, 2016
1
(25 points) Simplex method
This exercise is about using the simplex method to completely solve a linear program. Consider the
following linear program:
min 2x1
s.t.
x1
3x1
Sensitivity Analysis and Duality HW sols
Ch 6 review problems
5a.
The dual is
. min w = 6y1 + 4y2 + 3y3
s.t. 3y1 + 2y2 + y34
y1 + y2 + y31
y10 y20, y3 urs
Primal
Dual
Since x1=3, then e1=0.
Since e1=3, y1=0;
Since e2=3, then y2=0;
Now I dont know the valu
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 solution to (LP), then there is a
basic feasible solution to
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/
Cheese
1.84
McLean Deluxe w/ Cheese
2.19
Big Mac
1.84
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 : The amount of high-fat milk(lb) used as pure milk in pr
Deterministic Optimization
Lecture 3: The Simplex
Algorithm
3.2 The Simplex Mathematics
(P) = max cfw_z=cTx: Ax = b, x 0. A has m linearly
independent rows, n columns, m < n
Select a mxm nonsingular matrix B from A. Let
the associated variables be xB, t
Deterministic Optimization
Lecture 2
Example
Sunco Oil has three different processes that can be used to
manufacture various types of gasoline. Each process involves blending
oils in the companys catalytic cracker. Running process 1 for an hour
costs $5 a
Deterministic Optimization
Lecture 4: Computational
History of LP
Computational History of LP
1939 L.V. Kantorovich (USSR), Mathematical methods
of organization and planning of production,
Translated in Management Science, 6, 1960, 366422.
Quote by Dant
Deterministic Optimization ISyE 6669
Spring 2016
Instructor: Dr. Eva Lee
Email: eva.lee@gatech.edu
Office Hours: Dr. Lee ISyE Groseclose 425: Thursday 6 - 7pm
Class meetings: Sustainable Education 110, Tues/Thurs 4:35pm - 5:55pm
Teaching Assistant:
Email:
This article was downloaded by: [130.207.93.160] On: 05 November 2015, At: 13:32
Publisher: Institute for Operations Research and the Management Sciences (INFORMS)
INFORMS is located in Maryland, USA
INFORMS Transactions on Education
Publication details,
Integer Program for Shipping Cost to Fulfill Weekly Demand to each Distributor
Decision Variables:
cfw_
Pi= 1if Pool Point i open ( i=17 )
0 Otherwise
1if parcels shipped jthru
Pool Point i (i=18, j=143 )
Eij = cfw_ 0 Otherwise
T i =Number of trucks sent
ISyE6669 Advanced Optimization
Homework 1
On-Campus Deadline: September 7, 2016
DL Deadline: September 14, 2016
1
Is it a polyhedron?
Recall that a polyhedron is the intersection of a finite number of half spaces, and a half space
describes the feasible r
ISyE6669
Review on Linear Algebra and Basic Concepts of Convexity
Fall 2016
Andy Sun
In this lecture, we give a review of some basic concepts in linear algebra. We also introduce the
concept of convexity, including convex combination, convex hull, and con
Xpress-Mosel
User guide
Release 2.0
Last update 5 January, 2007
Published by Dash Optimization Ltd
c
Copyright
Dash Associates 2007. All rights reserved.
All trademarks referenced in this manual that are not the property of Dash Associates are acknowledge
ISYE 6669 A,Q
Homework #2 Solutions
Due Friday, August 31
1.
The data from the diet problem we saw in class is available at
http:/www-fp.mcs.anl.gov/otc/Guide/CaseStudies/diet/table.html
In this diet problem, our objective was to minimize the total cost o
Deterministic Optimization ISyE 6669 - Prerequisite Quiz
Name:
Major:
Year:
To know you better:
1. When did you take your first optimization course, what are the topics?
2. Why are you taking this course besides fulfilling a course requirement? What do yo
ISyE6669
Lecture Notes 5: Large Scale Optimization Techniques I:
Column Generation and Constraint Generation
Andy Sun
Oct 5 - Oct 10, 2016
In practice, we often encounter large scale optimization problems with many decision variables.
In this lecture, we
ISyE 6669
Notes 4: Lagrangian Duality and Linear Optimization
Andy Sun
Sep. 28 - Oct. 5, 2016
Duality theory is at the heart of optimization. In this lecture, we will dive deep into the
inner workings of linear programming duality. In particular, we will
ISyE 6669
Notes 3: The Simplex Method
Andy Sun
Sep. 19 - 21, 2016
In this lecture, we study one of the most celebrated algorithms in optimization, the simplex
method for solving linear optimization problems.The emphasis is to really understand the inner
w
ISyE 6669
Notes 4: Lagrangian Duality and Linear Optimization
Andy Sun
Sep. 28 - Oct. 5, 2016
Duality theory is at the heart of optimization. In this lecture, we will dive deep into the
inner workings of linear programming duality. In particular, we will