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Title: AEM412 Computational Methods for Management and Economics Carla P. Gomes


1
AEM412Computational Methods forManagement and
EconomicsCarla P. Gomes
  • Module 1
  • Introduction

2
Overview of this Lecture
  • Course Administration
  • Course Themes, Goals, and Syllabus
  • Background on Mathematical Programming
  • The Impact of Information Technology on Business
    Practice

3
Course Administration
4
AEM412 - Introduction to Mathematical Programming
Lectures Tuesday and Thursday - 1140 -
1255 Location WN 245 Lecturer Prof.
Gomes Office 448 Warren Hall Phone 255 1679
or 255 9189 Email cpg5_at_cornell.edu or
gomes_at_cs.cornell.edu TA Vivian Eliza Hoffmann
(veh4_at_cornell.edu) Administrative Assistant
Dawn Vail (dmv9_at_cornell.edu)     147 Warren Hall,
254-6761 Web Site http//courseinfo.cit.cornell.
edu/courses/aem412/
5
Office Hours
  • Prof. Gomes
  • TA Vivian Hoffmann

Monday and Wednesday 300p.m 400 p.m.
Tuesday (WN360) and Wednesday (WN201) 130 p.m
230 p.m.
6
Grades
Midterm (15) Homework                     (35
) Participation                   (5) Final     
                          (45)
Note The lowest homework grade will be dropped
before the final grade is computed.
7
Required Textbook

Introduction to Operations Research by
Frederick S. Hillier and Gerald. J. Lieberman,
7th Edition
8
Overview of this Lecture
  • Course Administration
  • Course Themes, Goals, and Syllabus
  • Background on Mathematical Programming
  • The Impact of Information Technology on Business
    Practice

9
Course Themes, Goals, and Syllabus
10
Whats Mathematical Programming (MP)?
Main focus Optimization Optimization is
pervasive in business and economics and almost
all aspects of human endeavor, including science
and engineering. Optimization is everywhere
part of our language and the way we think!
  • Firms want to maximize value to shareholders
  • People want to make the best choices
  • We want the highest quality at the lowest price
  • In games, we want the best strategy
  • We want to optimize the use of our time,
  • etc

11
Optimization
  • Financial planning
  • Marketing
  • E-business
  • Telecommunications
  • Manufacturing
  • Operations Management
  • Production Planning
  • Transportation Planning
  • System Design
  • Health Care

12
Some of the themes of 412
  • Optimization!!!
  • Models, Models, Models
  • (insights not numbers)
  • Applications in business and economics
  • Algorithms, Algorithms, Algorithms
  • Efficient Algorithms --- whenever possible
  • Importance of factoring in computational issues
    in business and economic applications
    computational limits and intractability

13
Whats Mathematical Programming?
  • Very broad discipline covering a variety of
    Optimization
  • topics such as
  • Linear Programming
  • Advanced Linear Programming Models
  • Network Models
  • Integer Programming
  • Dynamic Programming
  • Heuristic techniques
  • Simulated Annealing
  • Genetic Algorithms
  • Tabu Search
  • Neural Networks
  • Non-linear Programming
  • Decision Making under Uncertainty
  • Decision Making with Multiple Objectives
  • Game Theory
  • etc

14
Syllabus 412
  • Linear Programming
  • Introduction
  • Simplex/Revised Simplex
  • Duality and Sensitivity Analysis
  • Other LP Algorithms

15
  • Network Models
  • Transportation Problems
  • Assignment Problems
  • Network Optimization Models
  • Special Topics()
  • Integer Programming
  • Dynamic Programming
  • Heuristic techniques
  • Simulated Annealing
  • Genetic Algorithms
  • Tabu Search
  • Neural Networks
  • Computational complexity()

()time permitting
16
Goals in 412
  • Present a variety of models, algorithms, and
    tools for optimization
  • Illustrate applications in business and
    economics, and other fields.
  • Prepare students to recognize opportunities for
    mathematical optimization as they arise
  • Prepare students to be aware of computational
    complexity issues importance of using efficient
    algorithms whenever possible and the limits of
    computation that can affect the validity of
    business and economic models.

17
Background on Mathematical Programming
18
Origins of Operations Research (OR)
  • The roots of OR can be traced back many decades
    and even centuries (Newton, Euler, Bernoulli,
    Bayes, Lagrange, etc).
  • Beginning of the activity called Operations
    Research --- attributed to the military services
    early in the World War II (1937).
  • Need to allocate scarce resources to the various
    military operations in an effective manner.
  • The British first and then the U.S military
    management called upon a large number of
    scientists to apply a scientific approach to
    dealing with several military problems

19
  • End of war scientists understood that OR could
    be applied outside the military as well.
  • The industrial boom following the war led to an
    increasing complexity and specialization of
    organizations ? scientific management techniques
    became more and more crucial.
  • By the early 1950s, OR techniques were being
    applied to a variety of organizations in
    business, industry, and government.
  •  

20
Impact of Operations Research
21
Key Factors for Rapid Growth of OR
  • Substantial progress was made early in improving
    the techniques in OR
  • Simplex, Dynamic Programming, Integer
    Programming, Inventory Theory, Queing Theory, etc
  • Computer revolution - 1980s the PC further
    boosted this trend.

22
Timeline
23
Operations Research Over the Years
  • 1947
  • Project Scoop (Scientific Computation of Optimum
    Programs) with George Dantzig and others.
    Developed the simplex method for linear programs.
  • 1950's
  • Lots of excitement, mathematical developments,
    queuing theory, mathematical programming. cf.
    A.I. in the 1960's
  • 1960's
  • More excitement, more development and grand
    plans. cf. A.I. in the 1980's.

Source J. Orlin (MIT) 2003
24
Operations Research Over the Years
  • 1970's
  • Disappointment, and a settling down.
    NP-completeness. More realistic expectations.
  • 1980's
  • Widespread availability of personal computers.
    Increasingly easy access to data. Widespread
    willingness of managers to use models.
  • 1990's
  • Improved use of O.R. systems.Further inroads of
    O.R. technology, e.g., optimization and
    simulation add-ins to spreadsheets, modeling
    languages, large scale optimization. More
    intermixing of A.I. and O.R.

25
Operations Research in the 00s
  • LOTS of opportunities for OR as a field
  • Data, data, data
  • E-business data (click stream, purchases, other
    transactional data, E-mail and more)
  • The human genome project and its outgrowth
  • Need for more automated decision making
  • Need for increased coordination for efficient use
    of resources (Supply chain management)

26
The Impact of Information Technology on
Business Practice

27
  • Advances in information technology are
  • increasingly impacting on business and
  • business practices.
  • Exciting new opportunities (and some risks).
  • Examples of applications

28
Driving Force
  • Exponential Growth
  • a) Compute power
  • b) Data storage
  • c) Networking
  • Combined with algorithmic advances
  • (software)

29
Compute power Doubling every 18 months
100,000,000 transistors per processor
4,000 transistors per processor
30
How much can be stored in one Terabyte?
Yr 06, 1 Terabyte for 200.
Storage for 200
Wal-Mart customer data 200 terabyte --- daily
data mining for customer trends Microsoft
already working on a PC where nothing is ever
deleted. You will have a personal Google on your
PC.
31
The Network The Internet
1981 --- 200 computers 1990 --- 300,000 1995 ---
6.5M 1997 --- 25M 2002 --- 300M
This new level of connectivity allows for much
faster, and more substantive interactions
between companies/suppliers/customers (e.g.
electronic markets)

32
Examples of business impact
  • Supply-chain-management
  • Electronic markets
  • Beyond traditional scheduling application

33
Dell premier example of integration of
information technology into the business model.
Direct business-to-consumer model
  • 1984 -- Michael Dell founds Dell
  • 1996 Dell starts selling computers via Internet
    at www.dell.com
  • 1999 "E-Support Direct from Dell" online
    technical support
  • 2001 Company sales via Internet exceed 40 M
    per day
  • Dell ranks No 1 in global market share
  • 2003 Revenue 32.1 Billion

34
Direct business-to-consumer model
Power of Virtual Integration
Supply Chain Strategy and Processes

DELL manages relationships with over 80 of
suppliers through the Internet. Over half of
Dell customers use Web-enabled support (over
40,000 Premier Pages-10,000 in Europe).
Product configuration tools Online design of
made-to-order system. Constraint-based reasoning
tools (knowledge about allowable system
configurations) Customer-to-Knowledge Customers
search Dell databases Knowledge content
for typical responses Personalization tools
Efficient supply chain Innovative product
design, An Internet order-taking process, An
innovative assembly system, Close cooperation
with suppliers.
Optimization is everywhere
35
Electronic Markets
  • Combinatorial Auctions

36
Why Combinatorial Auctions?
  • More expressive power to bidders
  • In combinatorial auctions bidders have
    preferences not just for particular
  • items but for sets or bundles of Items due
    because of complementarities
  • or substitution effects.
  • Example Bids
  • Airport time slots
  • (take-off right in NYC _at_ time slot X ) AND
  • (landing right in LAX _at_ time slot y) for
    9,750.00
  • Delivery routes (lanes)
  • (NYC - Miami ) AND
  • ((Miami Philadelphia) AND (Philadelphia
    NYC)) OR
  • ((Miami Washington) AND (Washington
    NYC)) for 700.00

37
Procurement Transportation Services on the web.
  • OPTIBID - software for combinatorial auctions
  • Managing over 100,000 trucks a day (June 2002),
  • gt8 billion worth of transportation services.
  • FCC auctions spectrum licenses
  • ( geographic regions and various frequency
    bands).
  • Raised billions of dollars
  • Currently licenses are sold in separate auctions
  • USA Congress mandated that the next spectrum
  • auction be made combinatorial.

38
FCC Auction 31 700 MHz Winner Determination
Problem
  • Choose among a set of bids such that
  • Revenue to the FCC is maximized
  • Each license is awarded no more than once

?
Example 4 licenses, 8 bids
(source Hoffman)
39
Combinatorial Auctions cont.
  • There exists a combinatorial auction mechanism
    (Generalized Vickrey Auction), which guarantees
    that the best each bidder can do is bid its true
    valuation for each bundle of items. (Truth
    revealing).
  • However, finding the optimal allocation to the
    bids is a hard computational problem. No
    guarantees that an optimal solution can be found
    in reasonable time.
  • What about a near-optimal solution? Does this
    matter?
  • Yes! Problem if the auctioneer cannot compute
    the optimal allocation, no guarantee for truthful
    bidding.
  • So, computational issues have direct consequences
    for the feasibility and design of new electronic
    market mechanisms.
  • A very active area in discrete optimization.
    (Bejar, Gomes 01)

40
Beyond Traditional Scheduling ApplicationsEnfor
cing Safety Constraints
41
Nuclear Power Plant Outage Management
Gomes et al, 1996, 1997, 1998
  • Given
  • activities for refueling and maintenance
  • resources
  • technological constraints
  • Find a schedule that minimizes the
  • duration of the outage while safely
  • performing all the activities
  • (up to 45,000 activities).
  • Cost of shutdown - 1M per day.

42
Nuclear Power Plant Outage Management
Example of decision tree for a safety function
for AC-Power
gt3 2 1 0
Safety threshold
Operable emergency Safeguard bus
2
Offsite sources available
yes
Activity with AC Power loss Potential?
1
gt3 2 1
Operable emergency Safeguard bus
Time
no
()
43
Syllabus 412
  • Linear Programming
  • Introduction
  • Simplex/Revised Simplex
  • Duality and Sensitivity Analysis
  • Other LP Algorithms

44
  • Network Models
  • Transportation Problems
  • Assignment Problems
  • Network Optimization Models
  • Special Topics()
  • Integer Programming
  • Dynamic Programming
  • Heuristic techniques
  • Simulated Annealing
  • Genetic Algorithms
  • Tabu Search
  • Neural Networks
  • Computational complexity()

()time permitting
45
Goals in 412
  • Present a variety of models, algorithms, and
    tools for optimization
  • Illustrate applications in business and
    economics, and other fields.
  • Prepare students to recognize opportunities for
    mathematical optimization as they arise
  • Prepare students to be aware of computational
    complexity issues importance of using efficient
    algorithms whenever possible and the limits of
    computation that can affect the validity of
    business and economic models.
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