CO 370 - Homework assignment 5
Winter 14
Page 1
CO 370 - Winter 14
Homework assignment #5: (Due on Wednesday, Mar 19th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed source

CO 370 - Homework assignment 5
Fall14
Page 1
CO 370 - Fall14
Homework assignment #5: (Due on Thursday, Nov 27th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of he

CO 370 - Homework assignment 1
Winter 14
Page 1
CO 370 - Winter 14
Homework assignment #1: (Due on Friday, Jan 17th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources o

CO 370 - Homework assignment 2
Winter15
Page 1
CO 370 - Winter15
Homework assignment #2: (Due on Thursday, Feb 12th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources o

CO 370 - Homework assignment 6
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #6: (Due on Wednesday, Nov 13th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: CO370 course notes notes

UNIVERSITY OF WATERLOO
CO370/CM443 Deterministic Operations Research Models
Midterm Examination
FALL TERM 2006
October 17, 2006, 7:00-9:00PM
CLOSED BOOK
Surname:
First Name:
Name:(Signature)
ID.#:
Lecture Section:
Section 1: Jochen Knemann
o
Section 2: Ro

CO 370 - Homework assignment 4
Winter 14
Page 1
CO 370 - Winter 14
Homework assignment #4: (Due on Friday, Mar 7th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of

C&O 370 Deterministic OR Models Winter 2011
Assignment 1 Due date: Friday Jan. 21, 2011
Assignments are due at the start of class on the due date. Write your name
and ID# clearly, and underline your last name.
Contents
1 Problem 1: LP Review/Duality/AMPL

CO 370 - Homework assignment 7
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #7: (Due on Never)
Instructions:
These are just a few practice questions for the nal.
Question 1 (0 points)
Consider the following two stage stochastic programming problem

CO 370 - Homework assignment 7
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #7: (Due on Never)
Instructions:
These are just a few practice questions for the nal.
Question 1 (0 points)
Consider the following two stage stochastic programming problem

CO 370 - Homework assignment 3
Winter 14
Page 1
CO 370 - Winter 14
Homework assignment #3: (Due on Monday, Feb 10th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources o

CO 370 - Homework assignment 3
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #3: (Due on Monday, Oct 14th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of he

CO 370 - Homework assignment 5
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #5: (Due on Wednesday, Nov 6th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: CO370 course notes notes

CO 370 - Homework assignment 4
Winter 14
Page 1
CO 370 - Winter 14
Homework assignment #4: (Due on Friday, Mar 7th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of

CO 370 - Homework assignment 6
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #6: (Due on Wednesday, Nov 13th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: CO370 course notes notes

CO 370 - Homework assignment 2
Winter 14
Page 1
CO 370 - Winter 14
Homework assignment #2: (Due on Monday, Jan 27th, at the beginning of the class)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources o

CO 370 - Homework assignment 5
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #5: (Due on Wednesday, Nov 6th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: CO370 course notes notes

CO 370 - Homework assignment 6
Fall 13
Page 1
CO 370 - Fall 13
Homework assignment #6: (Due on Wednesday, Nov 13th)
Instructions:
You will be graded not only on correctness, but in clarity of exposition.
Allowed sources of help: CO370 course notes notes

CO 370 A SSIGNMENT 5 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

1
UNIVERSITY OF WATERLOO
MIDTERM EXAMINATION
Fall TERM 2016
Solutions
Surname:
First Name:
Signature:
Id.#:
Course Number
Course Title
Instructors
Date of Exam
Time Period
Duration
Paper type
Number of pages (including cover)
CO370
Deterministic OR Models

C&O 370 Deterministic OR Models
Practice Questions for the Final
Problem 1: Stochastic Optimization
(15 marks)
CarCo is an automobile company that manufactures cars and trucks. Each of these requires steel, hours
on an assembly machine, and hours on a fin

CO 370 A SSIGNMENT 5 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

CO 370 A SSIGNMENT 8 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

CO 370 A SSIGNMENT 7 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

CO 370 A SSIGNMENT 4 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

CO 370 A SSIGNMENT 3 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

CO370: Deterministic Operations Research Models
c
Department
of Combinatorics and Optimization
University of Waterloo
September, 2013
2
Contents
1 Introduction
1.1 What is Operations Research?
1.1.1 Roots of OR . . . . . .
1.1.2 OR Today . . . . . . . .
1

CO 370 Deterministic OR Models
Basis and Simplex Algorithm
CO 370 Deterministic OR Models
Let A be an m n matrix where the rows of A are linearly independent.
A subset of column indices B forms a basis if the matrix AB is a square
non-singular matrix.
Exa

Solving Integer Programs
Solving Integer Programs
max
s.t.
3x1 + 4x2
2x1 + 2x2 3
x 0 integer
Solving Integer Programs
max
s.t.
3x1 + 4x2
2x1 + 2x2 3
x 0 integer
For most IPs, the LP relaxation has an optimal solution that is not integer.
Solving Integer

C&O 370 Deterministic OR Models
Practice Questions for the Final
Problem 1: Stochastic Optimization
(15 marks)
CarCo is an automobile company that manufactures cars and trucks. Each of these requires steel, hours
on an assembly machine, and hours on a fin

CO 370 A SSIGNMENT 9 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

CO 370 A SSIGNMENT 10 - SOLUTIONS
Material copyrighted, B. Guenin, University of Waterloo. This document is for personal use only. Uploading
to any non UW website (such as course hero) assignments, solutions, or any related material is an academic
offence

Consider the following maximum st-flow problem with lower bounds,
max
fx (s)
such that
(v 2 V, v 6= s, t)
fx (v) = 0
`xu
(P1 )
(a) Give an example with ` integer and u fractional where the optimal solution to (P) is fractional.
(b) Give an example with `

Consider a rational system of inequalities Ax b and define the following optimization problems,
max
c> x
(P )
such that
Ax b, x integer
and
max
c> x
(Q)
such that
x 2 convcfw_x : Ax b, x integer
(a) Show that (P) is infeasible if and only if (Q) is infeas