Lesson 1. Introduction
SA305 Spring 2015
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What is operations research?
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What is operations research?
“The most influential academic discipline field you’ve never
heard of”
Boston Globe, 2004
Operations Research (OR) is the discipline of applying
advanced mathematical methods to help make better
decisions
“The Science of Better”
INFORMS slogan
“A liberal education in a technological world”
Thomas Magnanti, former Dean of Engineering at MIT
2
What is operations research?
Numerous applications, e.g.
logistics
manufacturing
workforce scheduling
finance
marketing
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OR and the military
The military uses OR to improve decision making in a variety
of ways, e.g.
force composition
weapon selection
search and detection
flight operations scheduling
training and personnel assignment
Assessment Division (OPNAV N81) at the Pentagon
The Naval Postgraduate School has one of the oldest and
highest ranking OR departments in the US
Naval Research Logistics is a prominent academic journal
featuring research in OR
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The traveling nationalatlas.gov
salesperson problem
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The National Atlas of the United States of AmericaO
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states_capitals2.pdf INTERIOR-GEOLOGICAL SURVEY, RESTON, VIRGINIA-2003
A salesperson located in Annapolis wants to visit clients in
each of the 48 state capitals of the continental US and
Washington DC
What is shortest way of visiting all the capitals and then
returning to Annapolis?
5
The traveling salesperson problem
Entire books have been written on the TSP
6
The traveling salesperson problem
1962: contest by Proctor and Gamble - best TSP tour
through 33 US cities
http://www.tsp.gatech.edu
7
The traveling salesperson problem
1998: The Florida Sun-Sentinel’s Science page ponders Santa
Claus’s traveling problem
http://www.tsp.gatech.edu
8
The traveling salesperson problem
One of the most popular problems in operations research
Numerous applications in expected and unexpected places
Circuit board manufacturing
Genome sequencing
9
The traveling salesperson problem
Your turn! Try to find the shortest way of visiting all the
capitals and then returning to Annapolis
10
The traveling salesperson problem
STATES AND CAPITALS
TM
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Salem
Helena
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n City
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FO R
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Cheyenne
City
UTAH
ILLINO IS
Springfield
COLO RADO
Topeka
KANSAS
100 mi
Santa Fe
Oklahoma City
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CUBA
The National Atlas of the United States of AmericaO
R
states_capitals2.pdf INTERIOR-GEOLOGICAL SURVEY, RESTON, VIRGINIA-2003
11
The traveling salesperson problem
What about 13,509 cities in the US?
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The traveling salesperson problem
What about 13,509 cities in the US?
Sophisticated mathematical techniques are our best bet
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The OR approach
Interpreting
Problem statement and data
Solution
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Indianapolis
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a
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OREG
AT
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AN
STATES AND CAPITALS
C A N A D
A
Olympia WASH
Salem
O C E
A N
What is the shortest
way of visiting all
the capitals and
then returning
to Annapolis?
TM
A T
L A
N T
I C
nationalatlas.gov
Where We Are
AN
U.S. Departmentof the Interior
U.S. Geological Survey
0
OF
AL A
J uneau
SK
A
200 mi
200 km
E
X
IC
GU
O
XI C
F ME
LF O
0
0
100
100
200
200
O
FLORIDA
T
300 mi
300 km
H
E
B
A
H
A
M
AS
CUBA
The National Atlas of the United States of AmericaO
R
states_capitals2.pdf INTERIOR-GEOLOGICAL SURVEY, RESTON, VIRGINIA-2003
Modeling
Optimization (this course),
Stochastic processes
P
min
{i,j}∈E c{i,j} x{i,j}
P
s.t.
{i,k}∈E x{i,k} = 2 ∀i ∈ N
P
{i,j}∈δ(S) x{i,j} ≥ 2 ∀S ⊆ N
x{i,j} ∈ {0, 1}
Solving
∀{i, j} ∈ E
Mathematical model
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Goals for this course
Modeling
Recognize opportunities for mathematical optimization
Formulate optimization models – linear programs – that
capture the essence of the problem
Illustrate applications of real-world problems
Solving
Algorithms to solve these mathematical models
Detailed topic list and schedule is on the syllabus
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Optimization is everywhere
“Minimize” time it takes to get from class to class
“Maximize” the company’s profits
(Moneyball) “Best” lineup for the Oakland A’s
We are always trying to make decisions in a way that meets
some objective subject to some constraints
Some success stories of optimization helping solve complex
real-world decision-making problems ...
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Package delivery
UPS has an air network consisting of 7 hubs,
nearly 100 additional airports in the US, 160
aircraft of nine different types
Decision:
Objective:
Constraints:
UPS credits optimization-based planning tools with
identifying operational changes that have saved
over $87 million to date, reduced planning times,
peak and non-peak costs, fleet requirements
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Sports scheduling
ACC Basketball earns over $30 million in revenue
annually, almost all from TV and radio
TV networks need a steady stream of “high quality”
games, NCAA rules, school preferences and traditions
Decision:
Objective:
Constraints:
Optimization approaches yields reasonable schedules very
quickly
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Radiation therapy
High doses of radiation can kill cancer
cells and/or prevent them from growing
and dividing
Can also kill healthy cells!
Radiation can be delivered at different
angles and intensities
Decision:
Objective:
Constraints:
Many successes reported using different
types of optimization models
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Next time...
Introduction to optimization models
Homework is on the syllabus!
Read the course policy statement and be aware of the
course website:
http://www.usna.edu/www/dphillip/sa305.s13/
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