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
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
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 structure of a linear program, as well as an understanding o
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.
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 4
On-campus due on October 21 (Friday), 2016
Distance learning due on October 26 (Wednesday), 2016
1
(40 pts) Column generation for solving cutting stock problem
In this problem, you will go through an iteration of the column generation
ISyE6669 Deterministic Optimization
Homework 5
Due On-Campus November 16, 2016 (Wednesday)
DL November 21, 2016 (Monday)
1
(60 pts) IP modeling
1. (5 pts) Let three binary variables x1 , x2 , x3 represent event i is chosen if xi = 1, and event
i is not ch
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
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 large scale linear optimization problems. We applied thes
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 number of half spaces, and a half space
describes the fe
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
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.
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