orf 411 25 - information - princeton university...© 2013 w.b. powell slide 11 data, information and...

Outline

What is information? The evolution of information The five classes of information

» Knowledge» Forecasting» Values» Planning» Goals

The organization of information and decisions

What is data?

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Bits and bytes

Information

What is data?

… information?

Situation:» You wake up in the morning and look at the

thermometer. It reads 42 degrees.

» From this, you estimate that the afternoon will probably be in the upper 50’s, and you do not need your heavy winter jacket.

Questions:» What decision is being made here? » What information was used to make the decision?

Information

Discussion:» What is the difference between data and information?

» What role do decisions play in defining information?

InformationTemperature

=Set of possible temperatures

Let:Sample outcome of temperature, where

Temperature given realization rounded to the nearest degree.

Set of possible outcomes of

0,1,...,100( ) Probability of outcome

e that ( ) ( )e

Information

How do we make a decision?

Our set of possible decisions is:1 Wear coat0 Do not wear coat

Our decision function is:

Information Given our decision, we can live with a simpler event space:

Temperature

Wear coat

No coat

55 1000

Data, information and knowledge

What is data?

… information?

… knowledge?

“…When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot … your knowledge is of a meager and unsatisfactory kind: it may be the beginning of knowledge, but you have scarcely in your thoughts, advanced the state of science…”

William Thompson, Lord Kelvin

Data, information and knowledge Information refers to exogenous (and endogenous) data

arriving to the system. Knowledge is what is retained after information is

absorbed and represented.» Example 1:

• Information: the latest customer demand• Knowledge is the average demand (used for forecasting the future).

» Example 2:• Information: the latest stock price• Knowledge: the latest stock price and the estimate of the slope.

» “Information” is inherently dynamic in nature, representing data arriving to the system. “Knowledge” is the state of the information you have acquired.

Data, information and knowledge Knowledge

» Knowledge comes in two forms:

• Data knowledge - Exogenously derived data which provides information about the characteristics of the state of our system.

• Functional knowledge - Relationships which allow us to use knowledge to make inferences about data elements that are not yet known to our system.

» Can we have knowledge about something that we do not know perfectly?

Example» Commodities prices

» Assume that we derive the functional relationship:

Old prices 0Current price 0Future prices 0

5 4 3 2 1 0 1UnknownKnowledge

, , , , , ,P P P P P P P

1 1 2 2 3 3 4 4 5 5t t t t t t t t t t t tP a P a P a P a P a P

Data, information and knowledge Without the “knowledge” of this functional relationship,

our “knowledge” of the future price would be captured by:

With the knowledge of the functional relationship:

Forecasting wind to make energy commitments» How do we classify current wind, the forecast of wind,

and the forecast model?

Information

Forecast

Forecast distribution

Forecasting wind to make energy commitments» Perhaps our policy is to make a commitment at the 30th

percentile.

CommitmentUnder (incur penalty)

Over (storage/lost energy)

Information

Forecasting wind to make energy commitments» Using a better model

Information

Dilbert on knowledge

Outline

The evolution of information

Systems evolve through a cycle of exogenous and endogenous information

1W 2W 3W 4W 5W 6W

1x 2x 3x 4x 5x 6x

The information that arrives can depend on the decisions you make!

Given the state which includes a forecast , we decide on a plan using a policy :

After we implement the decision new information arrives and we update

our state

Repeat endlessly.

Mt t t tS S S x W

Both kinds of information evolve over time:

, 1 , ', ,..., ,... "A forecast"t tt t t t tf f f f

, 1 , ', ,..., ,... "A plan"t tt t t t tx x x x

A plan is a forecast of a decision.

Outline

Air Mobility Command

AirMobility

Command

Cargo HandlingRamp Space

Maintenance

Cargo Holding

Outputs of optimizing simulator

Goals G

Expert knowledge

The five information classes

Forecasts of impacts on others tV

tForecasts of exogenous events

Knowledge tK

Knowledge

Myopic policies using “knowledge”:

» Cost-based• Choose the decision that produces the least cost, highest

utility/reward

» Rule-based• Decision comes from a lookup table – if in this state, take this

action.• Earlier, we referred to this as a policy function approximation

Knowledge

Rule-based decisions» This is currently what is used in the model for the air

mobility command:• Choose first available requirement to be served

– Choose the first available aircraft» If the assignment is feasible, execute it.» If not, find next available aircraft » …

• Next requirement

» Notes• Ignores the location of aircraft or requirement• Ignores the type of aircraft and the particular needs of the

requirement.• Ignores any impact of a decision now on the future.

Modeling information: Knowledge

Information arrives over time

KnowledgetK

Knowledge

Rule-based: one aircraft and one requirement

California

Germany

New Jersey

Colorado

Taiwan

England

New Jersey

Aircraft Requirements

The rule limits consideration to one aircraft and one requirement at a time to keep the complexity manageable.

Knowledge

Rule-based decisions» Limitations:

• First available aircraft and first available requirement may be very far apart.

• Hard to design rules that juggle among competing resources.• Hard to make tradeoffs between other factors:

– This is a large load – ideally we would like a larger aircraft.

– We might prefer to reposition an aircraft farther if it is set up for carrying passengers. But only up to a limit. Too far, and we would rather reconfigure another aircraft to carry passengers.

– A particular aircraft might require maintenance skills that are not available at the destination that the requirement will take the aircraft to.

Knowledge

Cost based: one requirement and multiple aircraft

California

Germany

New Jersey

Colorado

Taiwan

England

New Jersey

Knowledge

Costs allow you to make tradeoffs:

California

Germany

Issue “cost”/“bonus”Repositioning cost -$17,000Appropriate a/c type +5000Utilization +8000Requires modifications -3000Special maintenance at airbase -1000Total “cost” -8000

We have to capture the importance of each issue by choosing a cost/penalty of an appropriate size.

Knowledge

Cost based: multiple requirements and aircraft

California

Germany

New Jersey

Colorado

Taiwan

England

New Jersey

If we have costs, finding the best combination of assigning aircraft to requirements is easily solved as a linear program.

Knowledge tK

Forecasts of exogenous information

California

Germany

New Jersey

Colorado

Taiwan

England

New Jersey

( ) involves solving a linear program/network model.X I

Resources that are known now…

Forecastt

Modeling information: Forecasts

Information arrives over time

KnowledgetK

California

Germany

New Jersey

Colorado

Taiwan

England

New Jersey

( ) involves solving a linear program/network model.X I

CaliforniaGermany

New Jersey

Colorado

TaiwanEngland

New Jersey

Resources that are known now…

Aircraft Requirements California

Germany

New Jersey

Colorado

TaiwanEngland

New Jersey

… and are forecasted for the future.

CaliforniaGermany

New Jersey

Colorado

Taiwan

England

New Jersey

Knowledge tK

Approximate dynamic programming

Decisions now may need to know the impact on future decisions:» What is the cost of assigning this type of aircraft to

move a requirement?» What is the value of having a certain number of aircraft

in a region?» Should this requirement be satisfied now? Later?

Never?

For these questions, it is important that we optimize over time.

Two examples:» A single entity illustration

• The “nomadic trucker” – a single (complex) entity moving around the country over time.

» A multiple resource illustration• Long-term planning of energy resources

Start with a trucker in Texas

Nomadic trucker illustration

1 ( )=( )

Location TXS

Time avail t

Learns new information: four loads out of Texas

ˆ( , )t t

Need to estimate the value of being at each destination

0 ( ) 0V CO

0 ( ) 0V MN

$4500 ( ) 0V CA

0 ( ) 0V NY

ˆ( , )t t

We choose to go to NY

0 ( ) 0V CO

0 ( ) 0V CA

0 ( ) 0V NY

0 ( ) 0V MN

Update the value of being in Texas.

1( ) 450V TX

0 ( ) 0V CO

0 ( ) 0V CA

0 ( ) 0V NY

0 ( ) 0V MN

Repeat the process in NY – choose to go to CA

0 ( ) 0V CO

0 ( ) 0V CA

0 ( ) 0V NY

1( ) 450V TX

1 1ˆ( , )

0 ( ) 0V MN

Update value of being in NY

0 ( ) 600V NY

0 ( ) 0V CO

0 ( ) 0V CA

1( ) 450V TX

1 ( )2

0 ( ) 0V MN

Repeat the process in CA – choose to go to TX

0 ( ) 0V CA

0 ( ) 0V CO

1( ) 450V TX

0 ( ) 600V NY

2 2ˆ( , )

0 ( ) 0V MN

Update the value of being in CA

0 ( ) 800V CA

0 ( ) 0V CO

1( ) 450V TX

0 ( ) 600V NY

3 ( )3

0 ( ) 0V MN

Energy resource modeling

oiltR ˆ oil

tD ˆ oiltˆ oil

tRNew information 2009

1oiltR 1

oiltx 1

ˆ oiltD 1ˆ oil

t 1ˆ oil

New information

windtxwind

tR ˆ windtD ˆ wind

tˆ windtR 1

windtR 1

windtx 1

ˆ windtD 1ˆ wind

t 1ˆ wind

coaltxcoal

tR ˆ coaltD ˆ coal

tˆ coaltR 1

coaltR 1

coaltx 1

ˆ coaltD 1ˆ coal

t 1ˆ coal

corntxcorn

tR ˆ corntD ˆ corn

tˆ corntR 1

corntx 1

corntR 1

ˆ corntD 1ˆ corn

t ˆ corn

We have to allocate resources before we know the demands for different types of energy in the future:

We use value function approximations of the future to make decisions now:

,,1x ntR

,,2x ntR

,,3x ntR

,,4x ntR

,,5x ntR

This determines how much capacity to provide:

,1ˆ ( )ntv

,2ˆ ( )ntv

,3ˆ ( )ntv

,4ˆ ( )ntv

,5ˆ ( )ntv

Marginal value:

,,1x ntR

,,2x ntR

,,3x ntR

,,4x ntR

,,5x ntR

1, 1,( )xt j t jV R

x nt jR

Using the marginal values, we iteratively estimate piecewise linear functions.

( ),ˆ n

t jv( )

,ˆ nt jv

Right derivativeLeft derivative

1, 1,( )xt j t jV R

,( )1,

x nt jR

( 1),ˆ n

t jv ( 1)

,ˆ nt jv

1, 1,( )xt j t jV R

,( 1)1,

x nt jR

Linear, separable value function approximations:

, , , ,

Linear (in the resource state): ( )t j t j t j t jV R v R

Two-stage stochastic programming

Piecewise linear, separable value function approximations:

, , , , , ,

Piecewise linear, concave:

t j t j t j l t j ll

t j t j ll

V R v r

Two-stage stochastic programming

Simulating a myopic policy

Using value functions to anticipate the future

“Here and now” Downstream impacts

Expert knowledge

Knowledge tK

Expert knowledge

Old modeling approach: Engineering costs

0, :Subject tominarg*

xbAxcxx

Objectives

“Physics”

“Behavior”

Flows from history

Flows from the model

Expert knowledge

Bottom up/top down modeling:

Specify the behaviorsyou want at a general

level.

Patterns

Specify costs,engine availability,work rules, routing

preferences, train avail.

Engineering

Expert knowledge

Knowledge of “what to do” comes in three flavors:» Plans

• Typically aggregate projections of decisions– We should move 10 locomotives from A to B this week– We should have 10 percent of our portfolio in higher risk

stocks.» Patterns

• We normally send locomotives owned by Canadian National back to Chicago

• We normally invest money with certain fund managers.» Policies

• “We must send CN locomotives back to Chicago”• “We must limit our exposure to high risk stocks below 10

percent.

Expert knowledge

Expressing “forecasts of decisions” in English

Expert knowledge

We can add patterns to a cost-based model:

* arg min ( , )x cx H x

Cost function

“Behavior”

The “happiness” function –measures the degree to which model behavior agrees with a knowledgeable expert.

( , ) || ( ) || where ( ) is an aggregation functionH x G x G x

Expert knowledge

Patterns and aggregation:» What we do:

• We define patterns based on an aggregation of the attributes of a single resource.

• Patterns indicate the desirability of a single decision.

» Patterns can be expressed at different levels of aggregation, simultaneously.

• Don’t send C-5’s into Saudi Arabia• Don’t send C-5’s needing maintenance into Saudi Arabia• Don’t send C-5’s needing maintenance loaded with freight to

southeast Asia into Saudi Arabia.

» Patterns are not hard rules – they express desirable or undesirable patterns of behavior.

Flows from history

Expert knowledge

Patterns can come from history:

Expert knowledge… or an expert:

Goals G

Expert knowledge

Knowledge tK

We often add in bonuses and penalties to achieve specific goals:» Hitting a certain level of renewables» Maintaining a certain distribution of people by age

within my company» Fleet management for Netjets – we would like to

maintain an even distribution of ages among the fleet (so we do not have to sell a lot of aircraft at once).

» Hitting targets for customer service» Hitting targets for inventory costs

Goals G

Expert knowledge

Knowledge tK

Information and decisions

When you are making decisions…» How are you making a decision?

• Myopic policy• Lookahead• Policy function approximation• Policy based on value function approximation

» What information are you using to make a decision?• What you know about your system now.• Forecast of exogenous events• Forecast of the impact of a decision now on the future• Forecast of a decision (plans/patterns/policies)• Forecast of an objective (goals)

Outline

The optimization challenge

Organization of information and decisions

The forward reachable setdescribes the interaction between different decision makers.

2qD1qD

Our decision function usually looks like:

bqAq xq

min cq xq( ) argq qX I

We can say that is the "IQ" of our subproblem.qI

Norfolk Southern

Decompose by “desk” (region)

System vs. “Desk”

Fleet size

System vs. “Desk”

System

Fleet size

orf 411 25 - information - princeton university...© 2013 w.b. powell slide 11 data, information and...

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