Assignment vs. Thesis

What is research all about?

How to do a decent research?

DefineWhat do you want to solve?Literature Review

First solutionBest solution

What will you do?Problem Identification/FormulationProblem SolutionPresentation/MarketingApplications

ExampleLinear Model

How to be famousCriterion (AIC, R2)Algorithm (EM)Methodology (Response Surface)Thinking Process & Philosophy (Bayesian) Intelligent ApplicationsNo, No, No.Case Studies/Extension(except Review Paper)

:

(Atmosphere) (Taste)Culture

Dennis Lins Lectures

04 to 08 July 2005DKL5@psu.edu

Potential TopicsWhats Statistics All AboutBIG StatisticsResponse Surface Methodology

Multiple Response OptimizationDesign of ExperimentQuality Assurance & Six SigmaStatistical Data Mining & Machine Learning

Classification & Support Vector MachineFuture Opportunities

Search Engine & RFID

Whats StatisticsAll About?

Making Sense Out of Numbers

+

=

() ()

+= )...( 1 kxxfy

I love noise ! I love noise !I love noise !

E.F. SchumacherWhen the Lord created the world and people to live in itan enterprise which, according to modern science, took a very long timeI could well imagine that He reasoned with Himself as follows:If I make everything predictable, these human beings, whom I have endowed with pretty good brains, will undoubtedly learn to predict everything, and they will thereupon have no motive to do anything at all, because they will recognize that the future is totally determined and cannot be influenced by any human action.On the other hand, if I make everything unpredictable, they will gradually discover that there is no rational basis for any decision whatsoever and, as in the first case, they will thereupon have no motive to do anything at all.Neither scheme would make sense.I must therefore create a mixture of the two. Let some things be predictable and let others be unpredictable. They will then, amongst many other things, have the very important task of finding out which is which.

Inference about Population(Assuming Population will never change)

Sample Population

Inference about Population(Assuming Population will change)

Before After

Statistics in China (1960-1990)Highly influenced by RussiaMathematics is the leading disciplineMore Probability than StatisticsMore Theoretical than Applied

Cultural Revolution (1966-1976)Wang Yuan ()

There are two ways for (pure) mathematicians to do applied work(a) Treat applied problem as an pure mathematical problem, or(b) Adapt existing methodologies from outside

BIG Statistics

Dennis LinUniversity Distinguished ProfessorThe Pennsylvania State University

atZhejiang University

04 July, 2005

Knowledge Discovery in Sciences

Deduction ()PhysicsMathematics

Induction ()BiologyChemistry

Statistics is more powerful/useful in empirical study & experience accumulation, namely induction type.

Where have all the Data gone?No need for data (Theoretical Development)Survey Sampling and Design of ExperimentComputer SimulationData from Internet

On-line auctionSearch Engine

BIG Statistics

Business StatisticsIndustrial StatisticsGovernmental/Official Statistics

, (True)

, (Practical)

BIG Statistics

Business StatisticsIndustrial StatisticsGovernmental/Official Statistics

Business Statistics

Component of Business Research

ManagementBehaviorQuantitative

Business SchoolsAccounting/(Statistics)FinanceMarketingManagement & OrganizationInsurance & Real EstateManagement Science & Information SystemsSupply Chain ManagementBusiness LogisticInternational BusinessBusiness AdministrationEconomics

Business Intelligent

What is the same?What is new?

Elements of the exchange process

A buyerA sellerBuyer and seller can find each other (with some way to authenticate the other party)

Each has something of value to offer the otherThey can voluntarily complete the exchange

What is the Same?

Whats the Same?

Do the right thing!Do the thing right!

Right or Wrong Win or Lose

What is New?

(e-business)

(Globalization)

TechnologyInformation Systeme-BusinessSupply ChainValue NetGlobalization

What is New?

Example of a Supply Chain

RAW MATERIALSRAW MATERIALS PRODUCTIONPRODUCTION

STORAGESTORAGEDISTRIBUTIONDISTRIBUTION

Information FlowsGoods Flow

What is new? e-Supply Chain

Customers

Manufacturers

Wholesale Distributors

Suppliers

Retailers

Contract Manufacturers

ConsortiaExchanges

LogisticsExchanges

Logistics Providers

Virtual Manufacturers

Virtual Distributors

Whats different about the electronic exchange process?Buyers have more control in the exchange process (To some extent, the online medium also helps sellers find buyers)Customers behave differently online The exchange process for digital products is being completely redefined The exchange process for non-digital products is being transformed It redefines the way marketing information is gathered, analyzed, and deployedThe medium alters the nature of competition

What Kind of Job?

AgricultureIndustryServiceWhats next?High-tech and high-touch

Business StatisticsisTime Series ???

Time Series AnalysisTime Series Analysis (Univariate)

Linear, ARIMANon-linear

Time Series Analysis (Multi-variate)ARCH Model

AutoRegressive Conditional HeteroscedasticityGARCH, GARCH-M, Expo-GARCH etc

Long-Memory, high-frequency dataItos Lemma and Black-Scholes Differential EquationFinancial Time SeriesValue at Risk

The Newsboy ProblemAn international newsstand must decide how many copies, Q, of the Toronto Star to stock.

The owner can purchase papers wholesale at $0.80 each, and sell them for $1.20.Leftover paper are sold to a recycling at $0.05 each.

Profit for the day=Min (Q,X) * $1.20

+ Max (0, Q-X) * $0.05Q* $0.80where X is the Demand for the day.

The Newsboy ProblemSolve for Q which maximize the Profit

Suppose a historical demands are availableOptimization problem:

X is known (or use x-bar)

Statistical Problem: X follows Normal distribution (say), orDensity Estimation for X

Eventually most OR problems can be (more or less) converted into Stat problems

Newsboy Problem

The newsboy needs to determine how many newspapers to order for the next day.

The optimal number of newspapers to order is given by:

+

= cost overage cost underage

cost underageLevelOrder Optimal 1F

Implosion & the Inverse NewsboySuppose that the supply of c1 is given by x.

How many units of product A should we commit to sell?

Assume that:Orders must be satisfied in a FCFSEach order is for one unit of product A

Let SA(x) be the quantity of A that can be satisfied from a supply of x units of c1.

c1

A( ) )(~:max1

xHxYnxS An

iinA

= =

Sales & Operations Planning Manufacturing

sales marketing accounting finance manufacturing

Suppliers

Sales targets explode

implodeCommitment to Sales

Configure-To-Order (FTO) System

Unfortunately, Life is Not SimpleMultiple configurable productsComponent commonalityMulti-period rolling planning horizonMulti-level Bill-of-Materials

A B C

Stochastic BOM Layer

Deterministic BOM Layer

Problem StatementGiven:

A set of m products and n componentsA set of sales targets over T weeksA set of component supply commitments over T weeks

Determine:A set of commitments to sales over T weeks

Subject to:Supply constraints

Objective:To maximum expected profit over T weeks while minimizing the penalty for deviating from the sales targets

a 2

a 3

s

a 1R e c e iv ere q u e s t

V e r ifyc re d i tc a rd

A s k fo rr e su b m is s io n

o f r e q u e s t

a 5F in d n om a tc h

a 4T im e

o u t

a 6

C o n ta c th o te l 1

a 7

C o n ta c th o te l 2

a 8C o n ta c th o te l 3

a 1 5

E v a lu a ter e p l ie s

a 9

a 1 1R e c e iv e r e p ly 2

a 1 3a 1 4

a 1 0

a 1 2T im e o u t h o te l 2

T im e o u t h o te l 1

R e c e iv e r e p ly 3

T im e o u t h o te l 3

R e c e iv e r e p ly 1

a 1 6a 1 7

C h a rg ec re d i t c a rd

a 1 8

N o tifyc u s to m e r

F in d ah o te l e

a 1 9

B o o k h o te l

c 1

c 2

c 3

c 4

c 5

c 7

c 1 1c 1 0

c 9c 8

c 6

c 1 6c 1 4 c 1 5

c 1 3c 1 2

How do you know your Flow-Chart is correct?

A business process example is used to show how to use process graphs to represent and analyze process modelsAn online name-your-price hotel reservation process modelIdentify blocks that are to be modeled as subprocesses

Two blocks are identified in this model

a 2

a 3

s

a 1R e c e iv ere q u e s t

V e r ifyc re d i tc a rd

A s k fo rr e su b m is s io n

o f r e q u e s t

a 5F in d n om a tc h

a 4T im e

o u t

a 6

C o n ta c th o te l 1

a 7

C o n ta c th o te l 2

a 8C o n ta c th o te l 3

a 1 5

E v a lu a ter e p l ie s

a 9

a 1 1R e c e iv e r e p ly 2

a 1 3a 1 4

a 1 0

a 1 2T im e o u t h o te l 2

T im e o u t h o te l 1

R e c e iv e r e p ly 3

T im e o u t h o te l 3

R e c e iv e r e p ly 1

a 1 6a 1 7

C h a rg ec re d i t c a rd

a 1 8

N o tifyc u s to m e r

F in d ah o te l e

a 1 9

B o o k h o te l

c 1

c 2

c 3

c 4

c 5

c 7

c 1 1c 1 0

c 9c 8

c 6

c 1 6c 1 4 c 1 5

c 1 3c 1 2

Search hotels

Find a match

What is Supply Chain Scheduling?

Classical Scheduling Problem

M1

M2

J1

J1

J2 J3

J2 J3

Supply Chain Scheduling Problem

M1

M2

J1

J1

J2 J3

J2 J3

MachinesM1 and M2are operatedby the samedecision maker.

MachinesM1 and M2are operatedby differentdecision makers.

Supplier

Manufacturer

Manufacturer

Distributor

What is Supply Chain Scheduling?

Classical Scheduling Problem

M1

M2

J1

J1

J2 J3

J2 J3

Supply Chain Scheduling Problem

J1

J1

J2 J3

J2 J3

Supplier

Manufacturer

Inventory: Lead Time

Lead time of order 1

Effective lead time of order 1

Lead time of order 2

Effective lead time of order 2

Order 1 is placed

Order 1 is received

Order 2 is placed

Order 2 is received

Time t

SCHEME

Demand Rate Deterministic

Demand Rate Stochastic

Lead Time Deterministic

Model 0 Model 1

Lead Time Stochastic

Model 2 Model 3

Common Assumption: Exponential Distribution

What is Research: ExampleTravel Salesman Problem (TSP)Chinese Postman Problem (CPP)Lawn Mowing Problem (LMP)

Vehicle Routing Problem (VRP)m-TSP

Travel Salesman Problem (TSP)Given a set of points and all distances between them, find the tour that visits all points and cover minimum distances.

Travel Salesman Problem (TSP)

Given a set of points and all distances between them, find the tour that visits all points and cover minimum distances.Problem Formulation

Minimize

Subject To

Chinese Postman Problem (CPP)Lawn Mowing Problem (LMP)

Vehicle Routing Problem (VRP)What if there are m salesmen? What if there are m salesmen with logistical realism?

m vehicles with some capacities (possibly different capacities by vehicle type, time windows etc.

{ }1,0

xxQxopt

st

Basic Idea

{ }1,0

,...1

==x

mibxaj

ijij

=j

jj xcxfopt )(

Linear to Non-linear!!!

Link Analysis

What are the issues here?How do you quantify (measure) your observations (people or dog)?How do you characterize your observations?How do you classify (match) them?Others?

SVM:Support Vector Machine

Dimension ReductionDimension Expansion

Plane Bisect Closest Points

dc

Dual of Closest Points Method is Support Plane Method

( )

2 2

,1

1 1

1 12 2

. . 1 1 . . 1

0 1,..,

|| || || ||min mini i iw bi

i i i ii i

y x w

s t s t y x w b

i

=

= =

=

l

l

Solution only depends on support vectors: 0i>

1

1 1:

1 1i i i ii

i Classw y x y

i Class

=

= = l

Linearly Inseparable Case:Supporting Plane Method

( )1

1 22, ,

min || ||

1.

1,..,0

w b z

i i

ii

i

i

w C z

zy x w bs t

iz

=

+

+

=+

l

l

Just add non-negative errorvector z.

Dual of Closest Points Method is Support Plane Method

( )

2 2

,1 1

1 1

1 12 2

. . 1 1 . . 0

0 0 1,..,

|| || || ||min mini i i iw bi i

i i i i ii i

i i

y x w C z

s t s t y x w b z

D z i

= =

+

= = +

=

l l

l

Solution only depends on support vectors: 0i >

1i i i

iw y x

=

=l

Marron

Marron

Marron

What is Hot in B-Stat?Supply Chain ManagementFinancial Statisticse-Business (real time business)Marketing analysisData MiningValue NetSecurityAuction (On-Line)Supply Chain Event Management (Sense & Response)More Examples? (RFID/Search Engine)

A Specific Example: RFID

Statistics (Fundamental)Population vs Sample

Distribution AssumptionParameter EstimationStatistical Inference

Observations of Entire PopulationEmpirical Distribution FunctionDensity EstimationPopulation DescriptionForecasting

Low-Storage Single-Pass Density Estimation

UnivariateCertain (say, 20) representative quantiles(Cubic Smoothing) Spline fitting to these quantilesStatistical inference

MultivariateConvex Hulls PeelingCertain (say, 20) representative convex hullsThin Plate Splines fitting to these quantilesStatistical inference

Convex Hull Peeling Depth Contour

Astronomy Dataset: Near infra-red vs. blue-green(subset of 11355 for illustration/comparison)

Astronomy Dataset: Depth Contour

Astronomy Dataset: Thin Plate Splines

Secure Communication (PAIN)Privacy

message is secret

Authenticationmessage originates/reaches from a particular sender/receiver

Integritymessage is not altered

Non-repudiationsender can not deny having sent the message

Industrial Statistics

Industrial Statistics (Lin)

Process Capacity Index (PCI)Chao and Lin (2005)

Control ChartYeh and Lin (2002, 2005)

ReliabilityHighly reliable products

Design of ExperimentLins recent work

Quality Assurance & Six-Sigma Development Data Management & Value NetOthers

Whats Next?

Quality inService Industry(Service Science)

Process Capacity IndexCpCpkCpmCpmkCp(u,v)Cpwetc.

Process capability

Over time, a typical process will shift and drift by approximately 1.5

As a bio-statistician, you must knowp-valueAs an industrial-statistician, you must knowCp value

Common values:t, Z, 2, F etc.

Basic Idea:Process yield = 2(3*Cy)-1

Thus, we (Chao and Lin, 2005) have

Shewhart Control Charts

0Subgroup 5 10 15 20 2573.985

73.995

74.005

74.015

Sam

ple

Mea

n

X=74.00

3.0SL=74.01

-3.0SL=73.99

0.00

0.01

0.02

Sam

ple

StD

ev

S=0.009240

3.0SL=0.01930

-3.0SL=0.00E+0

Xbar and S Chart for Piston Ring Example

Yeh and Lin (2003)

Design of Experiment

How to collect useful information?

AgriculturalExperiments

IndustrialExperiments

Number of factors Small LargeNumber of Runs Large SmallReproducibility Large SmallTime taken Long ShortBlocking Nature Not obviousMissing values Often SeldomRandomization Important OKOther

Designing industrial experiments is very different From designing agricultural experiments

What is a

good design???

Design of Experiment (Lin)Multiple Response Problems

Optimization: Kim and Lin (JRSS-C, 2000)Design: Chang, Lo, Lin & Young (JSPI, 2001)

Computer ExperimentBeattie and Lin (1998)

Dispersion EffectMcGrath and Lin (Technometrics, 2002)

Foldover PlanLi and Lin (Technometrics, 2003)

Supersaturated DesignsLin (Technometrics, 1993, 1995, 2001) and others

Uniform DesignsFang, Lin, Winker & Yang (Technometrics, 1999)

Supersaturated Designs

Lin (UTK Technical Report, 1991)Lin (Technometrics, 1993, 1995, 2001) and many others

Supersaturated Design

# of experimental runs is less than # of experimental variables

# X1 X2 . X24 Resp1 2 . . . 14

y1 y2 . . . y14

Half Fraction of William's (1968) DataFactor

Run 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 y1 + + + - - - + + + + + - + - - + + - - + - - - + 1332 + - - - - - + + + - - - + + + + - + - - + + - - 623 + + - + + - - - - + - + + + + + + - - - - + + - 454 + + - + - + - - - + + - + - + + - + + + - - - - 525 - - + + + + - + + - - - + - + + + - - + - + + + 566 - - + + + + + - + + + - - + + - + + + + + + - - 477 - - - - + - - + - + - + + + - + + + + + + - - + 888 - + + - - + - + - + - - - - - - - - + - + + + - 1939 - - - - - + + - - - + + - - + - + + - - - - + + 32

10 + + + + - + + + - - - + - + + - + - + - + - - + 5311 - + - + + - - + + - + - - + - - - + + - - - + + 27612 + - - - + + + - + + + + + - - + - - + - + + + + 14513 + + + + + - + - + - - + - - - - - + - + + - + - 13014 - - + - - - - - - - + + - + - - - - - + - + - - 127

Lin (1993, Technometrics)

Supersaturated Design Example

How can we study k parameterswith n(

Run FactorsNo. I 1 2 3 4 5 6 7 8 9 10 (11)1 + + + - + + + - - - + -2 + + - + + + - - - + - +3 + - + + + - - - + - + +4 + + + + - - - + - + + -5 + + + - - - + - + + - +6 + + - - - + - + + - + +7 + - - - + - + + - + + +8 + - - + - + + - + + + -9 + - + - + + - + + + - -

10 + + - + + - + + + - - -11 + - + + - + + + - - - +12 + - - - - - - - - - - -

Supersaturated Design From Hadamard Matrix of Order 12(Using 11 as the branching column)

X = H RH

orthogonal orthogonal

not orthogonalThus Permute rows of RHto minimize , say.E s( )2

UD OD SSD

Fang, Lin & Ma (2000)

SSD: Looking AheadSupersaturated Design

SSD is much more mature than ever.

Micro-Array Design and Analysis

Computer Experiment: Model Building (using SSD)

Higher Level SSD

Spotlight Interaction Effects (Lin, 1998, QE)

Combination Designs: Rotated FFD & SSD

Computer Experiment

Beattie and Lin (1998)

Statistics vs. Engineering Models

Statistical Model

y=0+ixi+ijxixj+

+= ),(xfy

Statistical Simulation Research

Random Number GeneratorsDeng and Lin (1997, 2001)

Robustness of transformation(Sensitivity Analysis)

From Uniform random numbers to other distributions

A Typical Engineering Model (page 1 of 3, in Liao and Wang, 1995)

Irrelevant Issues

ReplicatesBlockingRandomization

Question: How can a computer experiment be run in an efficient manner?

Rotated Factorial Designs

Computer experiments are gaining in popularity

main research area of the next 10 years

Rotated factorial designsgood factorial design properties(orthogonality and structure)good Latin hypercube properties(unique and equally-spaced projections)easy to constructcomparable by Bayesian criteriavery suitable for computer experiments

Reliability

More on Highly reliable Products

Quality Assurance & Six-Sigma: The Past & The Future

Later

Define

Improve Analyze

MeasureControl

Six Sigma Project Process

Rigorous, data-driven and customer-focusedmethodology

Governmental Statistics

(Official Statistics)

Statistics

Information about the state

Official Statistics

-- (390 B.C.)

Index ManagementSampling

Index ManagementWhat to measure?How to measure?

(population): Age, geographical, etc and distribution (Wealth):

Economics IndexSocial Index

What to Measure: IndexAccidental Rate Example

Number of Car AccidentsDivided by

???* Population -- China* Total Number of cars -- Japan* Total mileages driven -- USA

6.68

3.06

3.934.30

3.384.77

1.2

5.86

5.424.57

6.16.42

7.17

3.98 4.22

-2.18

-4

-2

0

2

4

6

8

82 83 84 85 86 87 88 89 90 91Q1 91Q2 91Q3 91Q4 92Q1 92Q2 92Q3 92Q4

% 90-2.18

Government/Official StatisticsIndex ManagementFrom Census to SamplingSampling in modern technology(Web, Palm)

Error in VariablesMissing valuesData Mining

Send $500 toDennis Lin483 Business BuildingSupply Chain &Information SystemsPenn State University

+1 814 865-0377 (phone)+1 814 863-7076 (fax)DKL5@psu.edu

(Customer Satisfaction or your money back!)

Potential TopicsWhats Statistics All AboutBIG StatisticsResponse Surface Methodology

Multiple Response OptimizationDesign of ExperimentQuality Assurance & Six SigmaStatistical Data Mining & Machine Learning

Classification & Support Vector MachineFuture Opportunities

Search Engine & RFID

Assignment #1Suppose thaty1=0+1x+11x2+1 and y2=0+1x+11x2+2Find x=x* such that both Yis are maximized.

Suppose thaty1=f1(x,1)+1 and y2=f2(x,2)+2Find x=x* such that both Yis are maximized.What will you do?