1.1
INTRODUCTION WHAT IS AN ELECTROCHEMICAL REACTION? One way to answer this question is to try to distinguish electrochemical reactions from other chemical reactions. You should recall from earlier courses that reactions can occur via the collision

MSci331: Introduction to Optimization
Assignment 2
Spring 2008
Due date: 12th June 2008 (In class); Maximum Marks: 100
Please work in groups of two (only). The names and IDs of the two partners
should be listed together, with a single hand-in for the grou

MSci331: Solutions to Practice Questions
Spring 2008
1.
a) Since both constraints have a fractional part of 1/2 in the optimal tableau, we arbitrarily choose
to use the first constraint to yield the cut:
x2 + 7s1/22 + s2/22 = 3 + 1/2 or
x2 - 3 = 1/2 - 7s1

MSci 331- Integer Programming
James H. Bookbinder
Department of Management Sciences,
University of Waterloo
Disjunctive Constraints
Applying logic to constraints e.g. either
constraints C1 or C2 should be valid
depending on an outcome.
Suppose
C1: X + Y

MSci 331- Integer Programming
James H. Bookbinder
Department of Management Sciences,
University of Waterloo
Disjunctive Constraints
Applying logic to constraints e.g. either
constraints C1 or C2 should be valid
depending on an outcome.
Suppose
C1: X + Y

MSci 331- Transportation Problem
Selvaprabu Nadarajah
Department of Management Sciences,
University of Waterloo
G.B. Dantzig
most practical planning problems could be
reformulated as a system of linear inequalities.
ground rules for selecting good plans b

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 9-Solution
Submit your assignment through Crowdmark by Friday, November 18, 1:00 PM.
Problem 1
Consider the following IP problem:
min z 2

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 1-Solution
Joyce and Marvin run a day care for preschoolers. They are trying to decide what to feed the
children for lunches. They would l

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 2
Submit your assignment through Crowdmark by Friday, September 30, 1:00 PM.
Problem 1: You are given the following data for a linear prog

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 4
Submit your assignment through Crowdmark by Friday, October 14, 1:00 PM.
Problem 1:
A cargo plane has three compartments for sorting car

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 10-Solution
Submit your assignment through Crowdmark by Friday, November 25, 1:00 PM
Problem 1
The warehouse Lumber Company will soon begi

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 3
Submit your assignment through Crowdmark by Friday, October 7, 1:00 PM.
Problem 1
Consider the following problem:
min
s.t.
z - x1 - 4 x2

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 5
Submit your assignment through Crowdmark by Friday, October 21, 1:00 PM.
Problem 1
a) Find the dual of the following LP:
max
s.t.
z 4 x1

University of Waterloo
Department of Management Sciences
MSCI 331: Introduction to Optimization
Fall 2016
Assignment 6
Submit your assignment through Crowdmark by Friday, October 28, 1:00 PM.
Problem 1:
Solution for problem 1:

MSci331: Introduction to Optimization
Assignment 1 Solutions Spring 2008
1. 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

MSci331: Introduction to Optimization
Assignment 1
Spring 2008
Due date: 29th May 2008; Maximum Marks: 100
Please work in groups of two (only). The names and IDs of the two
partners should be listed together, with a single hand-in for the group.
Note: Ass

2.1
Basic Concepts and Conventions A table of useful names, symbols and units is given below:
Current - The current I gives the rate of charge transfer across a circuit due to the flow of electrons. It has the units of coulombs/sec, or amperes (amp

Chapter 4: The Simplex Method
Chapter 4: The Simplex Method
courtesty of xkcd.com
Chapter 4: The Simplex Method
1
Chapter 4: The Simplex Method Outline
Outline
Graphical Interpretation of the Simplex Method (Section 4.1) Setting up the Simplex

Chapter 9: Integer Programming Outline
Outline
For Fun Introduction BIP Applications Modeling Tricks with Binary Variables Some Perspectives on Solving IPs Branch and Bound
Chapter 9: Integer Programming 1
Chapter 9: Integer Programming For Fun
Ou

Class Notes
Due to reasons beyond my control, the course webpage will be on Google Groups I have to add you manually, so please send your email address to [email protected] with the subject msci 331. I will post course slides and the syllabus to the g

Algebra Day!
courtesty of xkcd.com
Ostrowski ()
Lecture 3
Jan 13
1 / 19
Homework!
If you have not already, register for the course webpage (on gmail). Do this by emailing my your address with the subject msci 331. Homework is posted online (du

Example BigM and 2 Phase
1
Formulating the problem
min z = x1 + x2 + x3 s.t. x1 + x2 + x3 3 2x1 + x2 = 3 2x1 + x2 + 3x3 5 x1 , x2 0
We need to reformulate the above problem so that there is a feasible solution with x1 , x2 , and x3 equal to zer

MSci331: Introduction to Optimization
Assignment 3 Solutions
1.
a)
Spring 2008
Vogel's method yields the following bfs:
20
11
3
6
2
5
5
5
9
10
18
7
4
3
7
3
3
7
3
10
1
5
12
15
12
b) The initial BFS from Vogels method is optimal as all reduced costs
are pos

MSci331: Introduction to Optimization
Practice Questions
Spring 2008
1. Problem 1, page 549
a. Obtain a first cut constraint (only)
b. Solve by branch and bound, using graphical methods to solve any
resulting LPs
2. Problem 6, page 408
3. Problem 2, page

Topics/SectionsforMSci331Final
% is on post-midterm material.
But, if you dont know earlier stuff on Tableaux, graphical solution, formulation, youre cooked
Chapter 7: omit 7.4 (sensitivity analysis for transportation problems)
- cover all else, including

MSci 331- Integer Programming
James H. Bookbinder
Department of Management Sciences,
University of Waterloo
Disjunctive Constraints
Applying logic to constraints e.g. either
constraints C1 or C2 should be valid
depending on an outcome.
Suppose
C1: X + Y

MSci 331- Transportation Problem
Selvaprabu Nadarajah
Department of Management Sciences,
University of Waterloo
G.B. Dantzig
most practical planning problems could be
reformulated as a system of linear inequalities.
ground rules for selecting good plans b