AEM412 Computational Methods for Management and Economics Carla P. Gomes Module 1 Introduction.

AEM412Computational Methods forManagement 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

Course Administration

Lectures: Tuesday and Thursday - 11:40 - 12:55Location: WN 245

Lecturer: Prof. GomesOffice: 448 Warren HallPhone: 255 1679 or 255 9189Email: [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/

AEM412 - Introduction to Mathematical Programming

mailto:[email protected]




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

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

Midterm (15%)

Homework (35%)

Participation (5%)

Final (45%)

Note: The lowest homework grade will be dropped before the final grade is computed.

Required Textbook

Introduction to Operations Research by Frederick S. Hillier and Gerald. J. Lieberman, 7th Edition

Overview of this Lecture

• Course Administration

• Course Themes, Goals, and Syllabus

• Background on Mathematical Programming

• The Impact of Information Technology on Business Practice

Course Themes, Goals, and Syllabus

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

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?

– 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

•Very broad discipline covering a variety of Optimizationtopics such as:

Syllabus 412

• Linear Programming

– Introduction

– Simplex/Revised Simplex

– Duality and Sensitivity Analysis

– Other LP Algorithms

• Network Models– Transportation Problems– Assignment Problems– Network Optimization Models

• Special Topics(*)– Integer Programming– Dynamic Programming– Heuristic techniques


– Computational complexity(*)

(*)time permitting

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.

Background on Mathematical Programming

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

• 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.

Impact of Operations Research

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.

Timeline

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

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.

Operations Research in the 00’s• 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

The Impact of Information Technology on Business Practice

Advances in information technology are

increasingly impacting on business and

business practices.

Exciting new opportunities (and some risks).

Examples of applications

Driving ForceExponential Growth

a) Compute power

b) Data storage

c) Networking

Combined with algorithmic advances

(software)

Compute power: Doubling every 18 months

4,000 transistors per processor

100,000,000transistors

per processor

How much can be stored in one Terabyte?

video 1 Gigabyte/hour

1000 hours

scanned color images

1 Megabyte each

1 million images

text pages 3300 bytes/page

300 million pages (Library of Congress)

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.

Storage for

$200

Yr ’06, 1 Terabyte for $200.

1981 --- 200 computers 1990 --- 300,0001995 --- 6.5M1997 --- 25M 2002 --- 300M

The Network: The Internet

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

1) Supply-chain-management

2) Electronic markets

3) Beyond traditional scheduling application

• 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

Dell premier example of integration of information technology into the business model.

Direct business-to-consumer model

LegacySystems

SupplyLogistics

CenterCollaboration

FactoryPlanner

ReportingSolution

SupplyChain

Planning

SupplierCollaboration

Suppliers Supply Hubs

Internet

Real-time Accessand Transactions

Report Users

Supply ChainPlanning Users

FactoryPlannerUsers

Supply Chain Strategy and Processes

Efficient supply chain:

Innovative product design,

An Internet order-taking process,

An innovative assembly system,

Close cooperation with suppliers.

Power of Virtual Integration

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).

Direct business-to-consumer model

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 toolsOptimization is everywhere

Electronic MarketsCombinatorial Auctions

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 @ 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

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

>$8 billion worth of transportation services.

OPTIBID - software for combinatorial auctions

Procurement Transportation Services on the web.

• 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.

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

Bid

Bid amt.

2

$12e6

3

$30e6$22e6

1 4

$16e6

5

$8e6

Package B ABCABD AD C

6

$11e6

BC

7

$10e6

A

8

$7e6

D

(source: Hoffman)

Hard Computational

Problem

bidsallforxb 1,0

x3 + x5 + x6

+ x3x1 + x4 + x7

x1 + x4 + x8

B

C

A

D

<= 1

<= 1

<= 1

<= 1

+ x2 + x3x1 + x6

8

1bbb

xxBidAmtMax

Example: 4 licenses, 8 bids

$30e6$22e6 + $8e6 =

$36e6

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

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)

Beyond Traditional Scheduling Applications

Enforcing Safety Constraints

Beyond Traditional Scheduling Applications

Enforcing Safety Constraints

Nuclear Power Plant Outage Management

Given: •activities for refueling and maintenance•resources•technological constraints

Find a schedule that minimizes the duration of the outage while safelyperforming all the activities (up to 45,000 activities).

Cost of shutdown - $1M per day.

ACTIVITY

Activity NameESTLSTDurationPredecessors

Name: D21-1 Affects: ACPLOSS DIV1PredecessorsEST: 65 LST: 65 DURATION: 15 START: 65 FINISH: 80 PECO

ROME LABORATORY OUTAGE MANAGER (ROMAN)

Parameters Load Run Gantt Charts Utilities Exit

0 10 20 30 40 50 60 70 80 90 100 110 120D23-3

RHRB-1D23-2D21BUS-1DIV4DC-1

RHRA-1D21-1

Parameters Load Run Gantt Charts Utilities Exit



Parameters Load Run Gantt Charts Utilities ExitParameters Load Run Gantt Charts Utilities Exit

D23-3

RHRB-1

D23-2

D21BUS-1

DIV4DC-1

RHRA-1

D21-1

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

31 - 45: ACPOWER? 0 NUM-UNAV-RESS 1UNAV-RES-MAP (DIV2 D24BUS-3 D24-2 D24-1) (ACPLOSS D24BUS-3 D24-2 D24-1)LIST-AV-RESS (DIV1 DIV3 DIV4 SU10 SU20)



AC-POWER StatusAC PowerDIV1DIV2DIV3DIV4SU10SU20

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

impacts

impactsimpacts

STATE-Of-PLANT

SCHEDULE

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.

[ Gomes et al, 1996, 1997, 1998 ]

Main risk The residual heat produced by the

nuclear materials can melt the fuel and breach the reactor nvessel

Examples of Monitored Safety Systems

•ac power control system

•primary containment system

•shutdown cooling system

Nuclear Power Plant Outage Management

Activity withAC Power loss

Potential?

Example of decision tree for a safety function for AC-Power

Offsite sourcesavailable

Operable emergencySafeguard

bus

>3210

no

yes2

Operable emergencySafeguard

bus

1 >321

(…)




D23-3

RHRB-1

D23-2

D21BUS-1

DIV4DC-1

RHRA-1

D21-1

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

31 - 45: ACPOWER? 0 NUM-UNAV-RESS 1UNAV-RES-MAP (DIV2 D24BUS-3 D24-2 D24-1) (ACPLOSS D24BUS-3 D24-2 D24-1)LIST-AV-RESS (DIV1 DIV3 DIV4 SU10 SU20)



AC-POWER StatusAC PowerDIV1DIV2DIV3DIV4SU10SU20

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

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

Safety threshold

Time

Syllabus 412

• Linear Programming

– Introduction

– Simplex/Revised Simplex

– Duality and Sensitivity Analysis

– Other LP Algorithms

• Network Models– Transportation Problems– Assignment Problems– Network Optimization Models

• Special Topics(*)– Integer Programming– Dynamic Programming– Heuristic techniques


– Computational complexity(*)

(*)time permitting

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.

AEM412 Computational Methods for Management and Economics Carla P. Gomes Module 1 Introduction.

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