ISE 2404
Topic #4: Advanced LP Modeling
Reading: Chapter 6 of AIMMS Optimization Modeling
In Topic #3, we formulated a number of typical LP models. One of those examples (a
blending problem) involved linearizing a quotient constraint. We now discuss some
ISE 2404 Deterministic Operations Research 1
Exam 2-B
3-7-2014
Cherbaka
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1:25
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calculators,
ISE 2404
Midterm
Summer I 2013
Name:_
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Points on Midterm Problems
Problem 1
20 points
_
Problem 2
20 points
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ISE 2404 Deterministic Operations Research 1
Exam 4-A
4-30-2014
Natalie Cherbaka
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cal
ISE 2404 Deterministic Operations Research
Spring 2014, Cherbaka
Exam 1
Name: _
Section:
11:15
1:25
Directions:
You may use only the two pages of notes that you uniquely generated for your
reference no calculators, electronic devices, classmates, etc.
Wri
Problem 6rp_12
Farmer Leary grows wheat and corn on his 45-acre farm. He can sell at most 140 bushels of wheat and
120 bushels of corn. Each planted acre yields either 5 bushels of wheat or 4 bushels of corn. Wheat
sells for $30 per bushel, and corn sells
ISE 2404
Topic #8: The Simplex Algorithm
Reading: Winston & Venkataramanan Sections 4.5 - 4.8, 4.11
In this topic, we talk about implementing the simplex algorithm in tableau form. First, we
motivate the process by a graphical example.
g 1.1!. I'
As we di
ISE 2404
Topic #19: Max Flow Problems
Reading: Winston & Venkataramanan Section 8.3
We continue our discussion of network problems in Chapter 8 by addressing max ow
problems. In these problems, we are trying to see how much material we can force through
a
ISE 24-04-
Topic #16: Assignment Problems
Reading: Winston & Venkataramanan Section 7.5
We now discuss assignment problems, which often deal with pairing up a particular
individual with a particular task. Assignment problems can be thought of as transport
ISE 2404
Topic #10.5: More on Matrix Representation of Tableaus
I just wanted to clarify some concepts from Topic #10 before moving on to duality. In a
couple of weeks, we will discuss sensitivity analysis, which is an important concept in
optimization, p
ISE 24-04
Topic #11: Duality
Reading: Winston & Venkataramanan Sections 6.5, 6.7, 6.10
In this topic, we begin discussing the concept of duality. Duality is one of the most
important topics in optimization. It leads to important economic interpretations,
ISE 2404
Topic #13: Dual Simplex Method
Reading: Winston & Venkataramanan Section 6.11
We now discuss an alternative implementation of the simplex algorithm, known as the dual
simplex method. In this method, we essentially solve the dual problem using the
ISE 2404
Topic #3: Basic LP Modeling
Reading: Winston & Venkataramanan Sections 3.4 - 3.12
In Topic #1, we formulated two introductory LP models, a product mix problem and a
model for media selection. These models introduced us to the basic steps of LP mo
ISE 24-04-
Topic #10: Matrix Representation of Tableaus
Reading: Winston & Venkataramanan Section 6.2
In this topic, we discuss how the entire simplex tableau can be constructed given only a
listing of which variables are basic. We will also discuss how t
ISE 2404-
Topic #3: Basic LP Modeling
Reading: Winston & Venkataramanan Sections 3.4 3.12
In Topic #1, we formulated two introductory LP models, a product mix problem and a
model for media selection. These models introduced us to the basic steps of LP mod
ISE 2404
Topic #7: Prelude to the Simplex Algorithm
Reading: Winston & Venkataramanan Sections 4.1 4.4
In the next topic, we will be introducing the simplex algorithm, which is the main algorithm
for solving LP problems. Before we begin that discussion, w
ISE 2404
Midterm Exam #1
Wednesday, March 4, 2015
Instructions:
1. This exam contains a total of 8 problems on 8 pages, for a total of 100 points. There
is also a 5 point bonus question on page 8. Please make sure that you have all the
questions.
2. Quest
Wednesday, May 3, 2017 (8 AM)
ISE 24-04: Quiz #12 % Y
Name: $73359) Balm/en lD#- 61055" 207%
Lr my lasmmehuirm
= mm, m)
X46=6 J
a. Perform Que iteration of the Floyd-Fulkerson algorithm,
Recall that nodes can be labeled in two cases.
QaseA 9353.3
ISE 2404
Midterm Exam #1
Wednesday, March 2, 2016
Instructions:
1. This exam contains a total of 8 problems on 8 pages, for a total of 100 points. There
is also a 5 point bonus question on page 8. Please make sure that you have all the
questions.
2. Quest
ISE 2404
Topic #9: Artificial Variables
Reading: Winston & Venkataramanan Sections 4.12 4.13
Topic #8 covered all that can happen in a simplex tableau, assuming that we began the
algorithm with a starting basic feasible solution (BFS). We now develop an a
ISE 2404
Topic #10: Matrix Representation of Tableaus
Reading: Winston & Venkataramanan Section 6.2
In this topic, we discuss how the entire simplex tableau can be constructed given only a
listing of which variables are basic. We will also discuss how to
ISE 2404
Topic #8: The Simplex Algorithm
Reading: Winston & Venkataramanan Sections 4.5 4.8, 4.11
In this topic, we talk about implementing the simplex algorithm in tableau form. First, we
motivate the process by a graphical example.
Graphical Motivation
ISE 2404
Topic #11: Duality
Reading: Winston & Venkataramanan Sections 6.5, 6.7, 6.10
In this topic, we begin discussing the concept of duality. Duality is one of the most
important topics in optimization. It leads to important economic interpretations, a
ISE 2404
Topic #6: Graphical Solution Technique for LPs
Reading: Winston & Venkataramanan Sections 3.2 3.3
We are now entering the portion of the course where we learn how to solve linear
programming models. In this topic, we will address how to solve LPs
ISE 2404
Topic #5: Modeling with Integer Variables
Reading: Winston & Venkataramanan Section 9.2
Thus far, we have focused on modeling linear programming problems. As discussed in
Topic #1, all linear programs have the assumption of divisibility, meaning
Audience Size Per Ad
Cost Per Ad
Maximum # of Ads
TV
50,000
$500
20
Radio
25,000
$200
15
Mail
20,000
$250
10
>=
<=
<=
<=
<=
RHS
1,500,000
20
15
10
15
# of Ads Purchased
Cost
LHS
Reach at least 1.5 million
TV Limit
Radio Limit
Mail Limit
Newspaper Limit
Ne
ISE 24-04
Topic #18: Shortest Path Problems
Reading: Winston & Venkataramanan Section 8.2
We are nearing the end of this course! For the remaining lectures, we will study Chapter 8
of our textbook. We will discuss a series of problems that can be formulat
ISE 2404: Quiz #4
Friday, February 17, 2017 (8 AM)
Name: _
ID#: _
1. A production facility faces the following demand over the next five months.
Month
Month 1
# Service Hours Required
5000
Month 2
5500
Month 3
6500
Month 4 Month 5
7500
8000
At the beginni
ISE 2404: Quiz #5
Friday, February 24, 2017 (8 AM)
Name: _
ID#: _
1. Consider the following problem.
maximize
subject to
=
21
21
1
1
+
+
1
,
2
2
2
2
2
8
5
3
0
a. Solve this problem graphically, and summarize the optimal solution below.
x2
x1
Summary of Op
ISE 2404: Quiz #2
Friday, February 3, 2017 (8 AM)
Name: _
ID#: _
1. At time 0, we have $5000 on hand. Investments A and B are available, with cashflows as
shown. (For example, every $1 invested in A at time 0 returns $0.2 at time 1 and $1.5 at
time 2.)
Ti
ISE 2404: Quiz #3
Friday, February 10, 2017 (8 AM)
Name: _
ID#: _
1. An experiment has produced the following results, where is the input and is the output.
-2 -1 3 4
12 5 50 101
You hypothesize that the relationship between and is of the following form
Vehicle Routing Problem
General Problem Definition
Slide references: JE Beasley; James Orlin and MIT opencourseware;
Handbooks in ORMS: Network Routing, edited by Ball, Magnant,
Monma, & Nemhouser
ISE 3434, Cherbaka
The Vehicle Routing Problem (VRP)
Route