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AEM412 Computational Methods for Management and Economics Carla P. Gomes. Module 1 Introduction. Overview of this Lecture. Course Administration Course Themes, Goals, and Syllabus Background on Mathematical Programming The Impact of Information Technology on Business Practice.

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Aem412 computational methods for management and economics carla p gomes l.jpg

AEM412Computational Methods forManagement and EconomicsCarla P. Gomes

Module 1

Introduction


Overview of this lecture l.jpg
Overview of this Lecture

  • Course Administration

  • Course Themes, Goals, and Syllabus

  • Background on Mathematical Programming

  • The Impact of Information Technology on Business Practice



Slide4 l.jpg

AEM412 - Introduction to

Mathematical Programming

Lectures: Tuesday and Thursday - 11:40 - 12:55

Location: WN 245

Lecturer: Prof. Gomes

Office: 448 Warren Hall

Phone: 255 1679 or 255 9189

Email: [email protected] or [email protected]

TA: Vivian Eliza Hoffmann ([email protected])

Administrative Assistant: Dawn Vail ([email protected])

    147 Warren Hall, 254-6761

Web Site: http://courseinfo.cit.cornell.edu/courses/aem412/


Office hours l.jpg
Office Hours

  • Prof. Gomes

  • TA – Vivian Hoffmann

Monday and Wednesday: 3:00p.m – 4:00 p.m.

Tuesday (WN360) and Wednesday (WN201):

1:30 p.m – 2:30 p.m.


Grades l.jpg
Grades

Midterm (15%)

Homework                     (35%)

Participation                   (5%)

Final                               (45%)

Note: The lowest homework grade will be dropped before the

final grade is computed.


Required textbook l.jpg
Required Textbook

Introduction to Operations Research by

Frederick S. Hillier and

Gerald. J. Lieberman,

7th Edition


Overview of this lecture8 l.jpg
Overview of this Lecture

  • Course Administration

  • Course Themes, Goals, and Syllabus

  • Background on Mathematical Programming

  • The Impact of Information Technology on Business Practice



What s mathematical programming mp l.jpg
What’s 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


Optimization l.jpg
Optimization

  • Financial planning

  • Marketing

  • E-business

  • Telecommunications

  • Manufacturing

  • Operations Management

  • Production Planning

  • Transportation Planning

  • System Design

  • Health Care


Some of the themes of 412 l.jpg
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


What s mathematical programming l.jpg
What’s 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


Syllabus 412 l.jpg
Syllabus 412

  • Linear Programming

    • Introduction

    • Simplex/Revised Simplex

    • Duality and Sensitivity Analysis

    • Other LP Algorithms


Slide15 l.jpg

  • 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


Goals in 412 l.jpg
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.



Origins of operations research or l.jpg
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


Slide19 l.jpg

  • 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.


Slide20 l.jpg

Impact of applied outside the military as well.

Operations

Research


Key factors for rapid growth of or l.jpg
Key Factors for Rapid Growth of OR applied outside the military as well.

  • 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.


Timeline l.jpg

Timeline applied outside the military as well.


Operations research over the years l.jpg
Operations Research Over the Years applied outside the military as well.

  • 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


Operations research over the years24 l.jpg
Operations Research Over the Years applied outside the military as well.

  • 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.


Operations research in the 00 s l.jpg
Operations Research in the 00’s applied outside the military as well.

  • 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)


The impact of information technology on business practice l.jpg
The Impact of Information Technology on Business Practice applied outside the military as well.


Slide27 l.jpg

Advances in information technology are applied outside the military as well.

increasingly impacting on business and

business practices.

Exciting new opportunities (and some risks).

Examples of applications


Driving force l.jpg
Driving Force applied outside the military as well.

Exponential Growth

a)Compute power

b) Data storage

c) Networking

Combined with algorithmic advances

(software)


Slide29 l.jpg

Compute power: Doubling every 18 months applied outside the military as well.

100,000,000

transistors

per processor

4,000 transistors

per processor


Slide30 l.jpg

How much can be stored in one Terabyte? applied outside the military as well.

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.


Slide31 l.jpg

The Network: The Internet applied outside the military as well.

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)


Examples of business impact l.jpg
Examples of business impact applied outside the military as well.

  • Supply-chain-management

  • Electronic markets

  • Beyond traditional scheduling application


Slide33 l.jpg

Dell premier example of integration of information technology into the business 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

Direct business-to-consumer model


Slide34 l.jpg

Reporting technology into the business model.

Solution

Report Users

Supply

Chain

Planning

Legacy

Systems

Factory

Planner

Supply Chain

Planning Users

Supplier

Collaboration

Supply

Logistics

Center

Collaboration

Internet

Factory

Planner

Users

Suppliers

Supply Hubs

Real-time Access

and Transactions

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


    Electronic markets l.jpg

    Electronic Markets technology into the business model.

    Combinatorial Auctions


    Why combinatorial auctions l.jpg
    Why Combinatorial Auctions? technology into the business model.

    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 @ time slot X ) AND

    (landing right in LAX @ 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


    Slide37 l.jpg

    Procurement Transportation Services on the web technology into the business model..

    OPTIBID - software for combinatorial auctions

    Managing over 100,000 trucks a day (June 2002),

    >$8 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.


    Slide38 l.jpg

    FCC Auction #31 technology into the business model.700 MHz

    Winner Determination Problem

    $12e6+$16e6 +$8e6 =

    $36e6

    $22e6 + $8e6 =

    $30e6

    Bid

    1

    2

    3

    4

    5

    6

    7

    8

    Bid amt.

    $22e6

    $12e6

    $30e6

    $16e6

    $8e6

    $11e6

    $10e6

    $7e6

    Package

    ABD

    ABC

    AD

    C

    BC

    A

    D

    B

    x1

    x1

    + x3

    + x4

    + x4

    + x7

    + x8

    <=

    1

    A

    x1

    + x2

    + x3

    + x6

    <=

    1

    B

    <=

    1

    C

    <=

    1

    D

    Hard Computational

    Problem

    x3

    + x5

    + x6

    • 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)


    Combinatorial auctions cont l.jpg
    Combinatorial Auctions cont. technology into the business model.

    • 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)


    Beyond traditional scheduling applications enforcing safety constraints l.jpg

    Beyond Traditional Scheduling Applications technology into the business model.Enforcing Safety Constraints


    Slide41 l.jpg

    Main risk technology into the business model.

    The residual heat produced by the

    nuclear materials can melt the

    fuel and breach the reactor nvessel

    ACTIVITY

    SCHEDULE

    impacts

    ROME LABORATORY OUTAGE MANAGER (ROMAN)

    Activity Name

    EST

    LST

    Duration

    Predecessors

    Parameters Load Run Gantt Charts Utilities Exit

    Parameters Load Run Gantt Charts Utilities Exit

    Name: D21-1 Affects: ACPLOSS DIV1

    Predecessors

    EST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO

    ROME LABORATORY OUTAGE MANAGER (ROMAN)

    Parameters Load Run Gantt Charts Utilities Exit

    Parameters Load Run Gantt Charts Utilities Exit

    Name: D21-1 Affects: ACPLOSS DIV1

    Predecessors

    EST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO

    0 10 20 30 40 50 60 70 80 90 100 110

    0 10 20 30 40 50 60 70 80 90 100 110 120

    D23-3

    RHRB-1

    D23-2

    D21BUS-1

    DIV4DC-1

    RHRA-1

    D21-1

    D23-3

    RHRB-1

    D23-2

    D21BUS-1

    DIV4DC-1

    RHRA-1

    D21-1

    • Examples of Monitored Safety Systems

    • ac power control system

    • primary containment system

    • shutdown cooling system

    impacts

    impacts

    ROME LABORATORY OUTAGE MANAGER (ROMAN)

    STATE-Of-PLANT

    Parameters Load Run Gantt Charts Utilities Exit

    Parameters Load Run Gantt Charts Utilities Exit

    31 - 45: ACPOWER? 0 NUM-UNAV-RESS 1

    UNAV-RES-MAP (DIV2 D24BUS-3 D24-2 D24-1) (ACPLOSS D24BUS-3 D24-2 D24-1)

    LIST-AV-RESS (DIV1 DIV3 DIV4 SU10 SU20)

    0 10 20 30 40 50 60 70 80 90 100 110

    AC-POWER Status

    AC Power

    DIV1

    DIV2

    DIV3

    DIV4

    SU10

    SU20

    Limitations of Traditional Approaches

    Rely heavily on manual procedures;

    Current procedures – PERT/CPM

    Outage Risk Assessment Methodology,

    simulation performed to assess

    the risks inherent to a schedule.

    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.


    Slide42 l.jpg

    ROME LABORATORY OUTAGE MANAGER (ROMAN) technology into the business model.

    Parameters Load Run Gantt Charts Utilities Exit

    Parameters Load Run Gantt Charts Utilities Exit

    Name: D21-1 Affects: ACPLOSS DIV1

    Predecessors

    EST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO

    0 10 20 30 40 50 60 70 80 90 100 110

    D23-3

    RHRB-1

    D23-2

    D21BUS-1

    DIV4DC-1

    RHRA-1

    D21-1

    ROME LABORATORY OUTAGE MANAGER (ROMAN)

    Parameters Load Run Gantt Charts Utilities Exit

    Parameters Load Run Gantt Charts Utilities Exit

    31 - 45: ACPOWER? 0 NUM-UNAV-RESS 1

    UNAV-RES-MAP (DIV2 D24BUS-3 D24-2 D24-1) (ACPLOSS D24BUS-3 D24-2 D24-1)

    LIST-AV-RESS (DIV1 DIV3 DIV4 SU10 SU20)

    0 10 20 30 40 50 60 70 80 90 100 110

    AC-POWER Status

    AC Power

    DIV1

    DIV2

    DIV3

    DIV4

    SU10

    SU20

    Roman extends the functionality of

    traditional project management tools

    • It incorporates the technological constraints,

    • automatically enforcing safety constraints

    • Robust schedules guaranteeing feasibility

    • over time-windows

    • Fast schedules

    • Solutions better than manual solutions

    Nuclear Power Plant Outage Management

    Example of decision tree for a

    safety function for AC-Power

    >3

    2

    1

    0

    Safety threshold

    Operable

    emergency

    Safeguard

    bus

    2

    Offsite

    sources

    available

    yes

    Activity with

    AC Power loss

    Potential?

    1

    >3

    2

    1

    Operable

    emergency

    Safeguard

    bus

    Time

    no

    (…)


    Syllabus 41243 l.jpg
    Syllabus 412 technology into the business model.

    • Linear Programming

      • Introduction

      • Simplex/Revised Simplex

      • Duality and Sensitivity Analysis

      • Other LP Algorithms


    Slide44 l.jpg

    • Network Models technology into the business model.

      • 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


    Goals in 41245 l.jpg
    Goals in 412 technology into the business model.

    • 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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