Post on 25-Dec-2015
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: cpg5@cornell.edu or gomes@cs.cornell.edu
TA: Vivian Eliza Hoffmann (veh4@cornell.edu)
Administrative Assistant: Dawn Vail (dmv9@cornell.edu) 147 Warren Hall, 254-6761
Web Site: http://courseinfo.cit.cornell.edu/courses/aem412/
AEM412 - Introduction to Mathematical Programming
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
• Simulated Annealing• Genetic Algorithms• Tabu Search• Neural Networks
– 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
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 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)
ROME LABORATORY OUTAGE MANAGER (ROMAN)
Parameters Load Run Gantt Charts Utilities ExitParameters Load Run Gantt Charts Utilities Exit
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
(…)
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 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)
ROME LABORATORY OUTAGE MANAGER (ROMAN)
Parameters Load Run Gantt Charts Utilities ExitParameters Load Run Gantt Charts Utilities Exit
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
• Simulated Annealing• Genetic Algorithms• Tabu Search• Neural Networks
– 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.