Another LP Example (cont.)
Classes of LPs
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 6:
Another LP Example (cont.)
& Classes of LPs (I)
1/7
Another LP Example (cont.)
Classes of LPs
Outline
1
Another LP Examp
Before we start
Course Theme
Optimization WarmUp
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 1:
WarmUp
1 / 12
Before we start
Course Theme
Optimization WarmUp
Outline
1
Before we start
2
Course Theme
3
Opti
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Fall 2013
ISE 240
HW02 Solution
ISE 240
HW02 Solution
ISE 240
HW02 Solution
ISE 240
HW02 Solution
ISE 240
Modelling and AMPL question:
The optimal solution is:
XT = 23.5714, XC = 25.7143, XL = 15
The optimal profit is 28071.42.
The model file is:
The data file is:
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
IE220 Introduction to Operations Research
Spring 2011 Quiz #2
March 29, 2011
First name
Last name
Lehigh email
You have 75 minutes. There are three problems. This quiz accounts for
17.5% of the nal grade. There are 40 points available. Please write clear
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
IE220 Introduction to Operations Research
Spring 2013 Final
May 3, 2013
First name
Last name
Lehigh email
You have 180 minutes. There are 5 problems. This test accounts for 25%
of the nal grade. There are 110 points available, everything above 100
points
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
IE220 Introduction to Operations Research
Spring 2011 Quiz #2 Solutions
April 5, 2011
1 Modeling, Relaxation, Duality (14 pts.)
You are working on a project from Department of Transportation of Nebraska. They
want to decide which road construction/maintan
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
IE220 Introduction to Operations Research
Spring 2013 Quiz #2
April 25, 2013
1
Sensitivity analysis (16 pts.)
Consider the following LP:
max
3x1 +3x2 +6x3
3x1
+x2 +3x3
2x1 +2x2 +3x3
x1 ,
x2 ,
x3
30
40
0
1. Formulate the dual and solve it either by guess
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
IE220 Introduction to Operations Research
Spring 2013 Quiz #2
March 25, 2013
First name
Last name
Lehigh email
You have 75 minutes. There are three problems. This quiz accounts for
17.5% of the nal grade. There are 40 points available. There are 3 bonus
p
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
(b) Length of the shortest path: 17
IE240 HW4 Solutions
Spring 2014
9.35
9.35.
The shortestpath problem is a minimum cost flow problem with a unit supply at the
origin and a unit demand at the destination. Label the origin as node and the destination
a
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
11.13.
(a)
if the decision is to invest in project ,
otherwise
for
.
maximize
NPV
subject to
IE240 HW5 Solutions
binary
(b)  (c)
Spring 2014
11.14.
11.14
if the decision is to invest in opportunity ,
otherwise
(a)
for
.
Let
denote the estimated profit
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
minimize
subject to
(b) The dual problem has no feasible solution.
IE240 HW3 Solutions
6.13.
(a) Apply the simplex method to the dual of the problem, since the dual has fewer
Spring 2014
constraints (not including nonnegativity constraints). We expect th
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
IE220 Homework1 Solution
IE240 HW1 Solutions
Spring 2014
February 2, 2013
Question 1
(1)
Let xi be the portion of time that the student spend on subject i. This problem can be formulated as the
following linear programming model:
max
5
X
xi g i
i
Introduction to Deterministic Optimization Models in Operations Research
ISE 240

Spring 2014
B
C
D
E
F
The point C is optimal.
Feasible
Feasible
Feasible
Infeasible
Feasible
IE240 HW2 Solutions
(c) The starting point F is not optimal, since B and D have better objective values. The
Spring 2014
objective value increases faster along the edge FB (
Optimization Jargon
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 2:
Optimization Jargon,
1 / 10
Optimization Jargon
Outline
1
Optimization Jargon
2 / 10
Optimization Jargon
Toy Optimization Problem
Example (A t
Classes of LPs
Largescale LP
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 7:
Classes of LPs (II) & A Largescale LP
1/9
Classes of LPs
Largescale LP
Outline
1
Classes of LPs
2
Largescale LP
A Dedication Port
Why Optimization is complex
Science of the Better
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 3:
Optimization Complexity, Science of the Better
1 / 12
Why Optimization is complex
Science of the Better
Outline
Production Planning
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 10:
Another largescale LP
1/4
Production Planning
Outline
1
Production Planning
2/4
Production Planning
Production Planning Problem
A company wa
LP & Graphical Solution Example
Simplex Tableau
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 11:
Intro to Simplex Method: The Simplex Tableau
1/6
LP & Graphical Solution Example
Simplex Tableau
Outline
1
LP & G
Linear Programming (LP) Problem
Simple LP example
Graphical LP Solution
Introduction to Deterministic Optimization Models
in Operations Research
(IE 240)
Lecture 4:
Linear Programming Problem, Graphical Solution
Method (Part I)
1 / 14
Linear Programming (