ISE 2404
Midterm
Summer I 2013
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Problem 2
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ISE 2404 Deterministic Operations Research 1
Exam 4-A
4-30-2014
Natalie Cherbaka
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11:15
1:25
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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
ISE 2404
Topic #12: Shadow Prices
Reading: Winston & Venkataramanan Sections 6.6, 6.8
We have learned that every primal problem has a partner problem, called its dual, which is
automatically solved whenever the primal problem is solved. We know that the p
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extreme point for every feasible region. As a result, this approach will not always work.
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max '7 ')v _ v
ISE 24-04
Topic #21: Minimum Spanning Trees
Reading: Winston & Venkataramanan Section 8.6
We now discuss another popular optimization problem for networks, known as the
minimum spanning tree (MST) problem. In Topic #15, we defined the concept of a tree.
R
ISE 2404
Topic #20: Project Scheduling Networks
Reading: Winston & Venkataramanan Section 8.4
In Topic #18, we discussed shortest and longest path problems. We now discuss a popular
application area for longest path problems: project management. These pro
Part 2 Summary
Slide Contributions: James Orlin and H. Sarper
ISE 2404, Cherbaka 2014
Data for the GTC Problem
Want to determine the number of wrenches and pliers
to produce given the available raw materials, machine
hours and demand.
ISE 2404, Cherbaka 2
VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY
GRADO DEPARTMENT OF INDUSTRIAL AND SYSTEMS ENGINEERING
DETERMINISTIC OPERATIONS RESEARCH
ISE 2404 SPRING 2014
MWF 11:15-12:05 Surge 107
MWF 1:25-2:15
Surge 107
CRN 14260
CRN 14261
Final Exam 11M May 09,
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
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
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
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 24-04
Topic #14: Sensitivity Analysis
Reading: Winston & Venkataramanan Sections 6.1, 6.3, 6.11
As we have mentioned before, when solving optimization problems, the optimal values of
the variables and objective value are not the only important results
ISE 24-04
Topic #17: Transshipment Problems
Reading: Winston & Venkataramanan Section 7.6
We conclude our discussion of Chapter 7 by addressing a type of problem known as a
transshipment problem. This problem is not a transportation problem, since the gra
ISE 24-04
Topic #22: Min Cost Network Flow Problems
Reading: Winston & Venkataramanan Section 8.5, 8. 7
For the last several topics, we have considered a number of problems that can be
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Investment Problem:
You have $2,200 to invest, and you want to maximize your total cash on hand at five years from now.
At the beginning of each year you can invest your money in a one- or two-year CD. The bank
pays 8% interest on one-year time deposits a
Cargo Balancing
A Cargo Plane has 3 cargo areas, each with weight and volume limits.
Areas Weight (tons)
Volume (f3)
1
12
7000
2
18
8000
3
10
4000
For performance reasons, the weight of cargo in the 3 areas must be in the same proportion as the weight lim
Kathryn Cotter DOR Spring 2014
Homework 7 Shortest Path and Maximum Flow (Sections 8.2,8.3,8.5)
Due Friday, April 25, 9pm
1.
Shortest Path: 125
Length=14
2.
Minz=208x12+258x13+355x14+537x15+841x16+228x23+278x24+375x25+557x26+248x34+298x35+395x36+288x45+
3
1. Decision variables
x= the number of 1-minute comedy ads purchased
y= the number of 1-minute football ads purchased
Model
min z=50x+100y
Subject to
7x + 2y > 28
(commercials must reach at least 28 HIW)
2x + 12y > 24
x, y > 0
a)
(commercials must reach a
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 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