# CO 370 Deterministic OR Models - Lecture 1 - PowerPoint

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```					    CO 370/CM 443
Deterministic Operations
Research Models
Chaitanya Swamy
cswamy@math.uwaterloo.ca
Office: MC 4033
Today’s lecture
• What is Operations Research (OR)?
– Examples and success stories

• What you will learn in this course
– Course outline

• A little LP review + LP formulations
What is Operations Research?
•   Enterprises typically consist of various units whose
operations need to be coordinated
– A typical problem: how to distribute resources across units
so as to maximize efficiency
•   OR is the discipline of applying analytical tools based on
mathematical models to help take better decisions in
managing these operations (the “science of better”)
•   Typical decision-making process in OR entails:
1.   Gathering available data                   Feedback: may
2.   Building an abstract mathematical model    need to enhance
3.   Solving the mathematical problem           data or model
4.   Supplying the results to management
A Brief History of OR
World War II led to the birth of OR
• Scientists and engineers used mathematical tools single
Perhaps the to
deploy, manage, and analyze military operations, e.g.,
most important
– deployment of the radar             catalyst in the
– management of convoy and submarine operations

• Many important developments took place in this period.
Most notably George Dantzig invented the simplex
method for solving linear programs (LPs) in 1947
– One of the first applications was the diet problem:
given foods with varying nutrient amounts, plan a diet
that satisfies the desired nutrient requirements + the
food-amount constraints, and minimizes cost
Brief History (contd.)
After the War:
•   Industrial boom led to rapid increase in size of
corporations – growing need for systematic decision-
making tools
•   Managers began to realize both, the modeling power of
LPs and OR tools, and their potency in improving
efficiency even under existing technology; applications
increased manifold
computational technology, which allowed one to solve
problems of ever-increasing size via OR tools
Where is OR Today?
•   Immense computing power available readily and fairly
cheaply, e.g., PCs
•   A half-century of research in OR has led to:
– very good theoretical understanding
– various software packages, e.g., CPLEX, LINDO,
XPRESS-MP, being available that can be used “off-the
shelf”
•   OR is everywhere – from booking an airline ticket, to
•   By the end of this course, you will be able to solve real-
world problems on your PC using these OR tools!
OR in action:
Optimizing Harbor Operations
Picture of container
terminal Altenwerder in
Hamburg
One of the most modern
terminals: handles ~ 2.4
million containers yearly
All internal traffic and
storage cranes are
automated.
Harbor Operations (contd.)
•    Overall objective: minimize vessel waiting time
•    Containers are transported between vessels and storage area
via automated guided vehicles (AGVs)

Moehring et al. 2004
give a fast algorithm
based on shortest-path
computations that
works much better than

Subproblem: compute AGV routes that are free of conflicts
and jams while maximizing container throughput.
Also routes have to be computed in real-time.
Some other success stories
•   Continental Airlines saves ~ \$40 million by using OR tools
to near-optimally reassign crews after disruptions
•   Texas Children’s Hospital used nonlinear optimization to
monitor healthcare contract negotiations
•   Athens Olympic Organizing Committee used logistics,
optimization tools to manage its resources and plan the
2004 Olympics; estimated savings: \$70 million
•   Philips Semiconductors saves ~ \$5 million by using
stochastic multiperiod inventory theory to handle demand
uncertainty
•   Many more applications on “The Science of Better”
website on Syllabus page
Yet, it is always surprising (to me) that there are many
applications out there that are tailor-made for the use
of OR tools that are still tackled by adhoc methods.
Article in ScienceDaily titled
“Techniques for making Barbie Dolls can Improve
Health Care”
to improve health care delivery
Researchers working on optimizing Air New Zealand’s
crew scheduling reported that “many airlines still use
heuristic or manual methods”
What you will learn
• Mathematical Modeling
– learn a variety of ways of modeling real-world
problems as structured mathematical
problems
• Solution Methods
– learn to use powerful optimization tools to
solve the problems arising in your
mathematical models
Course Outline
• Linear Optimization Models
– Formulations, Sensitivity analysis
• Stochastic and Robust Optimization
– Decision-making under uncertainty
• Integer Optimization
– Formulations, Solution methods
• Network models and algorithms
– Max-flow, min-cut, shortest paths
• Dynamic Programming
– Formulations
•   Course webpage:
www.student.math.uwaterloo.ca/~co370
– Check here for announcements, assignments,
lecture notes, important dates, …
– Some material will be password protected
– Email: co370@student.math.uwaterloo.ca
•   Reading material: CO 370 course notes; highly
recommended
•   Software: AMPL; trial version from course
homepage; full version in MC 3006, MC 3009
–   Prerequisite-quiz: 5%
–   Assignments: 10%        5 assignments
–   Projects: 10%           2 projects
–   Midterm: 30%,           Final: 45%
•   Prerequisite-quiz will test knowledge of a few
topics from linear programming
– will be easy – goal: recall relevant CO350 material.
– will be held in second-week of classes – on Thursday,
Sep. 22
– Syllabus: simplex method and duality (without Farkas
lemma)
• Cheating policy
– students caught cheating will be reported to assoc.
dean, get no credit for that assignment/project and
any penalty prescribed by assoc. dean
– you may discuss the assignment with others, but must

are always most welcome.
– Come see me at MC 4033
– Office hours: Mondays, Wednesdays 4:30-5:30pm
– Office hours of TAs: see course website
LP review: Definitions
Linear programming problem:
– problem of maximizing or minimizing a linear function of a
finite number of variables
– subject to a finite number of linear constraints:
£, ³ or = constraints

max/min       f(x) = c1x1 + c2x2 + … + cnxn
£
subject to ai1x1 + ai2x2 + … + ainxn ³ bi "i=1,…,m
=
Feasible point: xÎRn s.t. x satisfies all constraints
Feasible region: set of all feasible points
P = {xÎRn: x satisfies all constraints}
LP review: more definitions
Decision variables:
should completely
Objective function
describe all decisions
max/min      f(x) = c1x1 + c2x2 + … + cnxn
subject to   a11x1 + a12x2 + … + a1nxn £ b1
a21x1 + a22x2 + … + a2nxn ³ b2
Constraints
a31x1 + a32x2 + … + a3nxn = b3

Optimal solution: feasible solution with best (max/min)
objective-function value
Optimal value: objective-f’n. value at an optimal solution

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 views: 18 posted: 9/20/2011 language: English pages: 17