(a) You are given the following differential equation where () is the input and
() is the output:
Question 1
4( ) + 7 ( ) + 2 ( ) ( ) = 3()
.
Put this system in canonical state space form and specify the matrices A, B, C, and
D.
(b) How would your answer

Chapter 6Integer Programming Methods
Discussion and Review Questions
1. When solving a linear programming problem, it is acceptable to obtain fractional values
because the variables are continuous. Often, if integer values are needed, simple rounding
will

Chapter 7Nonlinear Programming
Discussion and Review Questions
1. When a function has a local max or min, the first derivative is necessarily equal to zero at
this point. This condition must be satisfied to find a functions local min or max. After
this ha

Chapter 3Linear Programming: Sensitivity Analysis and Computer Solution
Interpretation
Discussion and Review Questions
1. Changing the availability of a resource can affect the optimal solution because it changes
the RHS of a constraint. This can mean tha

Chapter 1Introduction to Management Science
Discussion and Review Questions
1. Management Science is a discipline that uses quantitative models to aid in the solution to
managerial-type problems. It is a logical approach that uses the problem as a focal p

Part One: Introduction to Management Science
Chapter1
Introduction to
Management Science
ByBillMcConkey
UniversityofTorontoatScarborough
Learning Objectives
After completing this chapter, you should be able to:
1. Describe the importance of management
sci

Decision Tree for Methods Taught in SYSC-5004
general LP all fcns linear min cost network flow Ford/Fulkerson for max flow/min cut Dijkstra's algorithm for shortest route min spanning tree simplex method
network all vars continuous
gradient methods uncons

To appear in INFORMS TRANSACTIONS ON EDUCATION
Formulating Integer Linear Programs:
A Rogues Gallery
Gerald G. Brown and Robert F. Dell
Operations Research Department, Naval Postgraduate School
Monterey, California 93943
April 2006
Convincing yourself is

SYSC 3200 Fall 2013
Laboratory 3
Two-phase Simplex and Sensitivity
Analysis
1
General Steps for Solving LPs
Step 1: Formulate the problem.
Step 2: Convert for tableau:
2.1: Objective: if min, multiply by -1 to convert to max.
2.2: Constraints: add slack/s

Chapter 6: Sensitivity Analysis
Suppose that you have just completed a linear programming solution which will have a
major impact on your company, such as determining how much to increase the overall
production capacity, and are about to present the resul

Fall 2013
SYSC 3200
Lab 9
Markov chains, Queuing theory
Markov Chains
Four Properties of a Markov:
Finite number of states
Memoryless Markovian property
Transition probability depends only on the current state
Transition probabilities are stationary
Th

Q1. A small software development company has proposed the schedule given below for a client
project.
[Recall that we are using the activity-on-arc formalism. Use the information in the table to construct
an activity-on-arc PERT network diagram before answ

Practice Problem Set 2
Q1
A charity has 9 volunteers to staff 5 locations where they are soliciting donations. Each location
must have at least one volunteer, but not more than 4. The charity knows from experience that
the amount of money collected at eac

Chapter 5Distribution and Network Flow Models
Discussion and Review Questions
1. In a balanced transportation problem, the quantity supplied equals the quantity
demanded. In an unbalanced transportation problem, the quantity supplied does not equal
the qu

Chapter 2Linear Programming: Basic Concepts, Graphical Solution, and Computer
Solution
Discussion and Review Questions
1. Linear programming eases decision making involving restricted situations. Next, it allows
for several techniques that come towards th

Chapter 11Markov Analysis
Discussion and Review Questions
1. Markov systems are systems that will operate for a number of periods, and can assume
one of a number of specific states during each period. The states are both mutually
exclusive and collectivel

Carleton University
Systems and Computer Engineering
SYSC-3200: Industrial Engineering
Assignment 1 - Fall Term 2013
Due by 7:25 p.m. on Tuesday September 24 in the class. Assignments submitted after this
deadline, but before marked assignments are return

Linear Programming Formulation and Simplex Method - Worked examples
FORMULATE the following linear programming problem
1.
A machine tool company conducts a job-training program for machinists.
Trained machinists are used as teachers in the program at a ra

CARLETON UNIVERSITY
Department of Systems and Computer Engineering
Systems and Simulation
SYSC 3600A&B
Fall 2013
Assignment #1
Due Date: Friday, September 27, 2013.
Note: The Assignment Drop Box is located in the 4400 Block of Mackenzie in the
hall beside

Carleton University
SYSC 3200
Department of Systems and Computer Engineering
Industrial Engineering
Course Outline
Fall 2015
Course Description and Objectives
0B
Description: This course introduces the major topics of operations research and their
applica

SYSC 3200 Fall 2015
Laboratory 3
Two-phase Simplex and Sensitivity Analysis
Standard LP model
Example:
Non-Standard LP model
Example:
The other variables may have negative values
General Steps for Solving LPs
Step 4: Put tableau in proper form: all basic

SYSC 3200
Fall 2015
Lab 5
Max Flow / Min Cut
Network Flow Programming
Maximum Flow Problem
Example:
(a) What is the maximum flow from source to sink?
(b) What flow pattern gives this?
Arc labels represent flow capacities in a given direction:
For arc AB,

SYSC 3200 Fall 2015
Laboratory 4:
Shortest Path, Minimum Spanning Tree
1
Part I:
Shortest Path
2
Problem Statement
Imagine you are planning a road trip to attend a music festival in
another city. Supplied with a map of the region, your task is to
find the

SYSC 3200 Fall 2015
Laboratory 1
Formulating Linear Programs
TAs
Faraj Lagum
Office hours and location: TBA
Email: faraj.lagum@sce.carleton.ca
Mohammed Alzenad
Office hours and location: TBA
Email: MohamedAlzenad@cmail.carleton.ca
Jianshuang Yang
Office h

Chapter 8Project Scheduling: PERT/CPM
Discussion and Review Questions
1. Both methods provide answers to a number of questions about how to plan a complex
project with many activities, such as the starting and the finishing time of activities, the
critica

Chapter 4Applications of Linear Programming
Discussion and Review Questions
1. Six ways to apply linear programming are through marketing, finance, production,
portfolio analysis, in the work force, and for statistics. For example, marketing and
productio

Chapter 9Multicriteria Decision-Making Models
Discussion and Review Questions
1. Goal programming differs from linear programming in terms of its constraints and model
objectives. Goal constraints are not absolute, but are soft and can be approximated. Th

Chapter 12Waiting-Line Models
Discussion and Review Questions
1. The basic elements of a queuing system are:
a. Calling population
b. Customer Arrivals
c. Waiting Line
d. Processing Order
e. Service
f. Exit
2. The basic measures of system performance are:

Chapter 10Decision Analysis
Discussion and Review Questions
1. States of nature refer to possible future conditions beyond the control of the decision
maker. The decision maker can choose decision alternatives based on different states of
nature.
2. Prior

SYSC 3200 Fall 2014
Laboratory 3
Two-phase Simplex and Sensitivity
Analysis
1
General Steps for Solving LPs
Step 1: Formulate problem.
Step 2: Convert for tableau:
2.1: Objective: if min, multiply by -1 to convert to max.
2.2: Constraints: add slack/surpl

SYSC 3200 Fall 2014
Laboratory 2:
Solving Standard Form LPs via Simplex
Lab 2. SYSC-3200 Carleton University 2014
1
Formulation vs. Solution
Formulation: write out these things:
Variables (with units)
Objective Function (with units)
Constraints (with

SYSC 3200 Fall 2014
Laboratory 8:
Dynamic Programming
1
Dynamic Programming Overview
It's a general framework
For problems that require a sequence of
interrelated decisions
often related to time, e.g. optimal control
It's recursive
2
General Description
1

SYSC 3200
Fall 2014
Lab 5
Max Flow / Min Cut
Network Flow Programming
Maximum Flow Problem
(a) What is the maximum flow from source to sink?
(b) What flow pattern gives this?
Arc labels represent flow capacities in a given direction:
For arc AB, flow capa

SYSC 3200
Industrial Engineering
Fall 2014
LAB 7
B&B, BIPs, MIPs, Genetic Algorithms
Branch & Bound
Enumeration has a tree structure
Avoid growing the whole tree: too big!
Grow tree in stages (usually selecting the
most promising node for expansion)
Prune