orf 411 25 - information - princeton university...© 2013 w.b. powell slide 11 data, information and...
TRANSCRIPT
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© 2013 W.B. Powell Slide 1
Outline
What is information? The evolution of information The five classes of information
» Knowledge» Forecasting» Values» Planning» Goals
The organization of information and decisions
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© 2013 W.B. Powell Slide 2
Data
What is data?
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© 2013 W.B. Powell Slide 3
Data
Data:
001100111110011100001010011100001000010010111101010000111010111110011100001010011100001000010010111101010000111010011011110101000011101001100111110011100001010011100001000010010111101011111001110000101000011101001100100111000010000100100101111100111001101100100111000101000011101011000100001001000110011111001110000101001110000100001001011110101000011101001100111110011100001010011100001000010010111101010000111010111110011100001010011100001000010010111101010000111010011011110101000011101001100111110011100001010011100001000010010111101011111001110000101000011101001100100111000010000100100101111100111001101100100111000101000011101011000100001001000110011111001110000101001110000100001001011110101000011101
Bits and bytes
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© 2013 W.B. Powell Slide 4
Information
What is data?
… information?
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© 2013 W.B. Powell Slide 5
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
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© 2013 W.B. Powell Slide 6
Information
Discussion:» What is the difference between data and information?
» What role do decisions play in defining information?
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© 2013 W.B. Powell Slide 7
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
Not
T
T
p e e
e that ( ) ( )e
p p e
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© 2013 W.B. Powell Slide 8
Information
How do we make a decision?
Our set of possible decisions is:1 Wear coat0 Do not wear coat
Our decision function is:
1 55=
0 55T
XT
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© 2013 W.B. Powell Slide 9
Information Given our decision, we can live with a simpler event space:
Temperature
Wear coat
No coat
55 1000
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© 2013 W.B. Powell Slide 10
Data, information and knowledge
What is data?
… information?
… knowledge?
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© 2013 W.B. Powell Slide 11
Data, information and 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
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© 2013 W.B. Powell Slide 12
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.
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© 2013 W.B. Powell Slide 13
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?
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© 2013 W.B. Powell Slide 14
Data, information and knowledge
Example» Commodities prices
» Assume that we derive the functional relationship:
Old prices 0Current price 0Future prices 0
t
tP t
t
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
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© 2013 W.B. Powell Slide 15
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:
Like
lihoo
d
Price
Price
Like
lihoo
d
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© 2013 W.B. Powell Slide 16
Forecasting wind to make energy commitments» How do we classify current wind, the forecast of wind,
and the forecast model?
Information
Forecast
Forecast distribution
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© 2013 W.B. Powell Slide 17
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
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© 2013 W.B. Powell Slide 18
Forecasting wind to make energy commitments» Using a better model
Information
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© 2013 W.B. Powell Slide 19
Data, information and knowledge
Dilbert on knowledge
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© 2013 W.B. Powell Slide 20
Outline
What is information? The evolution of information The five classes of information
» Knowledge» Forecasting» Values» Planning» Goals
The organization of information and decisions
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© 2013 W.B. Powell Slide 21
The evolution of information
Systems evolve through a cycle of exogenous and endogenous information
Time
1W 2W 3W 4W 5W 6W
1x 2x 3x 4x 5x 6x
The information that arrives can depend on the decisions you make!
0x
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© 2013 W.B. Powell Slide 22
The evolution of information
'
1
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
t tt
t
t t
t
t
S fx
x X S
xW
1 1
our state
, ,
Repeat endlessly.
Mt t t tS S S x W
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© Bill Watterson
© 2013 W.B. Powell Slide 23
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© 2013 W.B. Powell Slide 24
The evolution of information
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.
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Outline
What is information? The evolution of information The five classes of information
» Knowledge» Forecasting» Values» Planning» Goals
The organization of information and decisions
© 2013 W.B. Powell Slide 25
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© 2013 W.B. Powell Slide 26
Air Mobility Command
AirMobility
Command
Fuel
Cargo HandlingRamp Space
Maintenance
Cargo Holding
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© 2013 W.B. Powell Slide 27
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© 2013 W.B. Powell Slide 28
Outputs of optimizing simulator
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© 2013 W.B. Powell Slide 29
Goals G
Expert knowledge
The five information classes
Forecasts of impacts on others tV
tForecasts of exogenous events
Knowledge tK
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© 2013 W.B. Powell Slide 30
The five information classes
Knowledge tK
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© 2013 W.B. Powell Slide 31
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
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© 2013 W.B. Powell Slide 32
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.
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© 2013 W.B. Powell Slide 33
Modeling information: Knowledge
Information arrives over time
Time
KnowledgetK
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© 2013 W.B. Powell Slide 34
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.
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© 2013 W.B. Powell Slide 35
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.
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© 2013 W.B. Powell Slide 36
Knowledge
Cost based: one requirement and multiple aircraft
California
Germany
New Jersey
Colorado
Taiwan
England
New Jersey
Aircraft Requirements
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© 2013 W.B. Powell Slide 37
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.
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© 2013 W.B. Powell Slide 38
Knowledge
Cost based: multiple requirements and aircraft
California
Germany
New Jersey
Colorado
Taiwan
England
New Jersey
Aircraft Requirements
If we have costs, finding the best combination of assigning aircraft to requirements is easily solved as a linear program.
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© 2013 W.B. Powell Slide 39
The five information classes
tForecasts of exogenous events
Knowledge tK
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© 2013 W.B. Powell Slide 40
Forecasts of exogenous information
California
Germany
New Jersey
Colorado
Taiwan
England
New Jersey
( ) involves solving a linear program/network model.X I
Aircraft Requirements
Resources that are known now…
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© 2013 W.B. Powell Slide 41
Forecastt
Modeling information: Forecasts
Information arrives over time
KnowledgetK
Time
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© 2013 W.B. Powell Slide 42
Forecasts of exogenous information
Aircraft Requirements
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
Aircraft Requirements
Resources that are known now…
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© 2013 W.B. Powell Slide 43
Forecasts of exogenous information
Aircraft Requirements California
Germany
New Jersey
Colorado
TaiwanEngland
New Jersey
… and are forecasted for the future.
Kno
wn
now
CaliforniaGermany
New Jersey
Colorado
Taiwan
England
New Jersey
Fore
cast
ed
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© 2013 W.B. Powell Slide 44
The five information classes
Forecasts of impacts on others tV
tForecasts of exogenous events
Knowledge tK
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© 2013 W.B. Powell Slide 45
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.
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© 2013 W.B. Powell Slide 46
Approximate dynamic programming
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
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© 2013 W.B. Powell Slide 47
Start with a trucker in Texas
Nomadic trucker illustration
1 ( )=( )
xt
Location TXS
Time avail t
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© 2013 W.B. Powell Slide 48
Learns new information: four loads out of Texas
$300
$150
$350
$450
Nomadic trucker illustration
ˆ( , )t t
TXS D
t
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© 2013 W.B. Powell Slide 49
Need to estimate the value of being at each destination
0 ( ) 0V CO
0 ( ) 0V MN
$300
$150
$350
$4500 ( ) 0V CA
0 ( ) 0V NY
Nomadic trucker illustration
ˆ( , )t t
TXS D
t
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© 2013 W.B. Powell Slide 50
We choose to go to NY
$300
$150
$350
$450
0 ( ) 0V CO
0 ( ) 0V CA
0 ( ) 0V NY
Nomadic trucker illustration
( )1
xt
NYS
t
0 ( ) 0V MN
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© 2013 W.B. Powell Slide 51
Update the value of being in Texas.
1( ) 450V TX
$300
$150
$350
$450
0 ( ) 0V CO
0 ( ) 0V CA
0 ( ) 0V NY
Nomadic trucker illustration
( )1
xt
NYS
t
0 ( ) 0V MN
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© 2013 W.B. Powell Slide 52
Repeat the process in NY – choose to go to CA
$600
$400
$180
$125
0 ( ) 0V CO
0 ( ) 0V CA
0 ( ) 0V NY
1( ) 450V TX
Nomadic trucker illustration
1 1ˆ( , )
1t t
NYS D
t
0 ( ) 0V MN
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© 2013 W.B. Powell Slide 53
Update value of being in NY
0 ( ) 600V NY
$600
$400
$180
$125
0 ( ) 0V CO
0 ( ) 0V CA
1( ) 450V TX
Nomadic trucker illustration
1 ( )2
xt
CAS
t
0 ( ) 0V MN
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© 2013 W.B. Powell Slide 54
Repeat the process in CA – choose to go to TX
$150
$400
$200
$350
0 ( ) 0V CA
0 ( ) 0V CO
1( ) 450V TX
Nomadic trucker illustration
0 ( ) 600V NY
2 2ˆ( , )
2t t
CAS D
t
0 ( ) 0V MN
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© 2013 W.B. Powell Slide 55
Update the value of being in CA
$150
$400
$200
$350
0 ( ) 800V CA
0 ( ) 0V CO
1( ) 450V TX
0 ( ) 600V NY
Nomadic trucker illustration
3 ( )3
xt
TXS
t
0 ( ) 0V MN
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© 2013 W.B. Powell Slide 56
Energy resource modeling
oiltx
2008
oiltR ˆ oil
tD ˆ oiltˆ oil
tRNew information 2009
1oiltR 1
oiltx 1
ˆ oiltD 1ˆ oil
t 1ˆ oil
tR
New information
windtxwind
tR ˆ windtD ˆ wind
tˆ windtR 1
windtR 1
windtx 1
ˆ windtD 1ˆ wind
t 1ˆ wind
tR
coaltxcoal
tR ˆ coaltD ˆ coal
tˆ coaltR 1
coaltR 1
coaltx 1
ˆ coaltD 1ˆ coal
t 1ˆ coal
tR
corntxcorn
tR ˆ corntD ˆ corn
tˆ corntR 1
corntx 1
corntR 1
ˆ corntD 1ˆ corn
t ˆ corn
tR
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© 2013 W.B. Powell Slide 57
We have to allocate resources before we know the demands for different types of energy in the future:
Energy resource modeling
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© 2013 W.B. Powell Slide 58
We use value function approximations of the future to make decisions now:
Energy resource modeling
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© 2013 W.B. Powell Slide 59
,,1x ntR
,,2x ntR
,,3x ntR
,,4x ntR
,,5x ntR
This determines how much capacity to provide:
Energy resource modeling
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© 2013 W.B. Powell Slide 60
,1ˆ ( )ntv
,2ˆ ( )ntv
,3ˆ ( )ntv
,4ˆ ( )ntv
,5ˆ ( )ntv
Marginal value:
,,1x ntR
,,2x ntR
,,3x ntR
,,4x ntR
,,5x ntR
Energy resource modeling
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© 2013 W.B. Powell Slide 61
1, 1,( )xt j t jV R
,1,
x nt jR
Using the marginal values, we iteratively estimate piecewise linear functions.
Energy resource modeling
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© 2013 W.B. Powell Slide 62
( ),ˆ n
t jv( )
,ˆ nt jv
Right derivativeLeft derivative
1, 1,( )xt j t jV R
,( )1,
x nt jR
Using the marginal values, we iteratively estimate piecewise linear functions.
Energy resource modeling
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© 2013 W.B. Powell Slide 63
( 1),ˆ n
t jv ( 1)
,ˆ nt jv
1, 1,( )xt j t jV R
,( 1)1,
x nt jR
Using the marginal values, we iteratively estimate piecewise linear functions.
Energy resource modeling
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© 2013 W.B. Powell Slide 64
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
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© 2013 W.B. Powell Slide 65
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
R r
Two-stage stochastic programming
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© 2013 W.B. Powell Slide 66
Simulating a myopic policy
Approximate dynamic programming
t
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© 2013 W.B. Powell Slide 67
Simulating a myopic policy
Approximate dynamic programming
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© 2013 W.B. Powell Slide 68
Using value functions to anticipate the future
Approximate dynamic programming
t
“Here and now” Downstream impacts
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© 2013 W.B. Powell Slide 69
Approximate dynamic programming
Using value functions to anticipate the future
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© 2013 W.B. Powell Slide 70
Approximate dynamic programming
Using value functions to anticipate the future
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© 2013 W.B. Powell Slide 71
Approximate dynamic programming
Using value functions to anticipate the future
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© 2013 W.B. Powell Slide 72
Expert knowledge
The five information classes
Forecasts of impacts on others tV
tForecasts of exogenous events
Knowledge tK
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© 2013 W.B. Powell Slide 73
Expert knowledge
Old modeling approach: Engineering costs
0, :Subject tominarg*
xbAxcxx
Objectives
“Physics”
“Behavior”
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© 2013 W.B. Powell Slide 74
Flows from history
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© 2013 W.B. Powell Slide 75
Flows from history
Flows from the model
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© 2013 W.B. Powell Slide 76
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
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© 2013 W.B. Powell Slide 77
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.
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Expert knowledge
Expressing “forecasts of decisions” in English
© 2013 W.B. Powell Slide 78
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© 2013 W.B. Powell Slide 79
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
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© 2013 W.B. Powell Slide 80
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.
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© 2013 W.B. Powell Slide 81
Flows from history
Flows from the model
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© 2013 W.B. Powell Slide 82
Flows from history
Flows from the model
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© 2013 W.B. Powell Slide 83
Expert knowledge
Patterns can come from history:
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© 2013 W.B. Powell Slide 84
Expert knowledge… or an expert:
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© 2013 W.B. Powell Slide 85
Goals G
Expert knowledge
The five information classes
Forecasts of impacts on others tV
tForecasts of exogenous events
Knowledge tK
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© 2013 W.B. Powell Slide 86
Goals
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
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© 2013 W.B. Powell Slide 87
Goals G
Expert knowledge
The five information classes
Forecasts of impacts on others tV
tForecasts of exogenous events
Knowledge tK
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© 2013 W.B. Powell Slide 88
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)
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© 2013 W.B. Powell Slide 89
Outline
What is information? The evolution of information The five classes of information
» Knowledge» Forecasting» Values» Planning» Goals
The organization of information and decisions
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© 2013 W.B. Powell Slide 90
The optimization challenge
qDqD
qDqD
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© 2013 W.B. Powell Slide 91
Organization of information and decisions
qD
3qD
The forward reachable setdescribes the interaction between different decision makers.
q
2qD1qD
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© 2013 W.B. Powell Slide 92
Our decision function usually looks like:
0xq
bqAq xq
min cq xq( ) argq qX I
qI
We can say that is the "IQ" of our subproblem.qI
Organization of information and decisions
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© 2013 W.B. Powell Slide 93
qD
qDqD
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© 2013 W.B. Powell Slide 94
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© 2013 W.B. Powell Slide 95
Norfolk Southern
qDqD
qDqD
qD
qD
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© 2013 W.B. Powell Slide 96
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© 2013 W.B. Powell Slide 97
t
Decompose by “desk” (region)
Organization of information and decisions
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© 2013 W.B. Powell Slide 98
System vs. “Desk”
Desk
Del
ay h
ours
/day
Fleet size
Organization of information and decisions
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© 2013 W.B. Powell Slide 99
System vs. “Desk”
System
Desk
Del
ay h
ours
/day
Fleet size
Organization of information and decisions