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An Information Theoretic Approach
to Dynamic Resource Management
© 1999 Warren B. Powell, Princeton University
Overview
 Modeling complex operations  an information theoretic perspective
 Managing the control of information
 Adding value to the information set
 What to do about head knowledge?
© 1998 Warren B. Powell, Princeton University
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Burlington Motor Carriers
© 1999 Warren B. Powell, Princeton University
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© 1999 Warren B. Powell, Princeton University
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Norfolk Southern Railroad
© 1999 Warren B. Powell, Princeton University
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© 1999 Warren B. Powell, Princeton University
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Air Products and Chemicals
© 1999 Warren B. Powell, Princeton University
The subproblem
 Through coupling, we pick up attribute layers:
Airlift Mobility Command
 1980’s
 LTL trucking, truckload trucking rail, air freight, chemical distribution
 19901996
 Managing resources and tasks
 19971998  The Dynamic Resource Transformation Problem
 Resources  Processes  Controls
 199899
 Objects  Processes  Controls
 March 1999  ????
 Information  Processes  Controls
 So, just what kind of problem am I working on?
Problem representation
 A Dynamic Resource Transformation Problem consists of:
Information  Processes  Controls

 Information: Information entities representing natural groupings of information.
 Processes: The physical laws that govern the transformation of resources over time.
 Controls: The means by which endogenous decisions modify the system.
Since “DRTP” is hard to pronounce, we call these “DRiPs”.
This problem has been captured in a new Javabased
library that we call “DRiP Java.”
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New Modeling Language Captures
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Information entities
 Information:
 I.1) Information classes
 What types of information are available?
 I.2) Attribute space
 What are the relevant attributes of each class?
 How can entities be grouped?
 I.3) Aggregation
 What information is useful?
 What details can we ignore?
What is information?
Information
Problem representation
R.1) Object classes
What is a resource?
 What is a resource?


Resource, a.k.a. asset, a.k.a. commodity, is an
endogenously controllable information class
that constrains the system over time.
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Air Products and Chemicals
Information entities
 Through coupling, we pick up attribute layers:
Information entities
 Through coupling, we pick up attribute layers:
Problem representation
 A fully layered resource now takes on new behaviors: the ability to deliver product to customers.
Information entities
Information entities
Processes
 Processes:
 P1) Information processes
 Exogenous (external events)
 Endogenous (decisions)
 P.2) System dynamics
 Evolution of information over time
 P.3) Constraints
 Flow conservation
 A resource can only be in one place at one time
 A demand can be covered by only one driver
 Rate of process transformation
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Exogenous information looks like:
 Exogenous information looks like:
 Endogenous information looks like:
Processes
 I.1) Information processes
 Exogenous information processes (events)




 Endogenous information processes (decisions)
Both kinds of information evolve over time:
 Both kinds of information evolve over time:
A plan is a forecast of a decision.
Processes
 We can’t always predict the future...
be the set of possible events in the future.
W is the new information that will become available in the future.
Processes
 Constructing the information stream:

 Possible forecasting options:
Processes
Problem representation
a) Use expected demands (send a fraction of a vehicle
b) Randomly sample demands (send vehicle to a random city)
Processes
Information about boxcars to depart on train 148H
As time passes, we know more about what will happen on Wednesday.
Processes
Departs Dallas, eta Chicago is 3pm Wednesday
Processes
Processes
Planning Tuesday’s schedule on Monday . . .
Schedule “edits” and overrides from the planner:
Because of the rapid flow of updates from schedulers as the plan
is being made, we actually have a highly dynamic system!
P.2) System dynamics:
 P.2) System dynamics:
 Evolution due to exogenous information processes
… But this assumes that we never forget anything!
Better notation:
When exogenous information arrives, the update is usually pretty simple:
 When exogenous information arrives, the update is usually pretty simple:
So how does a decision xt change the system?
What does a decision look like?
 What does a decision look like?
Processes
 The effect of a decision is captured through the “modify” function:
The modify function captures all the “physics” of our operation.
Processes
Controls
 Controls  dimensions
C.1) Types of controls
 How do we control a system?
C.2) The control structure
C.3) The decision function
 How are decisions made?
 And with what information?
C.4) Measurement and evaluation
 How do we determine when one solution is better than another?
Controls
 C.1) Types of controls
 Direct controls  Those that change the attributes of a resource
 Couple
 Uncouple
 Modify
 Hold (or other default “do nothing” action)
 “Enter” or “Leave” the system.
 “Move” (change location)
 Indirect controls:
 Those that change the parameters that affect a decision.
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© 1999 Warren B. Powell, Princeton University
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Controls
Informational decomposition
The forward reachable set.
Problem representation
 Our decision function usually looks like:
In a normal optimization problem, we want to find the best decisions:
 In a normal optimization problem, we want to find the best decisions:
 In our problem, we want to find the best function:
But what does this mean???
Overview
 Managing the control of information
© 1999 Warren B. Powell, Princeton University
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 How do we optimize systems like this?
Normally, we would formulate a big optimization problem:
 Normally, we would formulate a big optimization problem:
Normally, we would formulate a big optimization problem:
 Normally, we would formulate a big optimization problem:
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Returning to our optimization problem:
 Returning to our optimization problem:
How do we optimize … Harry?
 How do we optimize … Harry?
Controls
 How do I control an operation?
The information optimization problem:
 The information optimization problem:
The information flow problem:
 The information flow problem:
The information cost functions:
 The information cost functions:
The information optimization problem is now:
 The information optimization problem is now:
Subject to system dynamics.
In many ways, the economics of moving information is very similar to moving flow:
 In many ways, the economics of moving information is very similar to moving flow:
 The function may be linear:
In many ways, the economics of moving information is very similar to moving flow:
 In many ways, the economics of moving information is very similar to moving flow:
 It may have a fixed charge:
Cost of constructing databases, screens,
In many ways, the economics of moving information is very similar to moving flow:
 In many ways, the economics of moving information is very similar to moving flow:
In many ways, the economics of moving information is very similar to moving flow:
 In many ways, the economics of moving information is very similar to moving flow:
In many ways, the economics of moving information is very similar to moving flow:
 In many ways, the economics of moving information is very similar to moving flow:
 It may be separable:





 or highly nonseparable. There are joint economies of production, just as in discrete parts manufacturing.
But there is one way in which the flow of information is very different from the flow of resources...
 But there is one way in which the flow of information is very different from the flow of resources...
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Overview
 Adding value to the information set
© 1999 Warren B. Powell, Princeton University
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 We need to make Harry make smarter decisions. . .
Adding intelligence
 How do we make decision makers smarter?
How do we increase ?
How do we increase ?
A algorithmic metastrategy
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Percent of posterior bound
Deterministic, rolling horizon
Informational decomposition
 Consider how we normally solve big optimization problems:
Informational decomposition
 Real problems are decomposed over space . . .
Informational decomposition
Informational decomposition
 We use approximations of subproblems to model interactions:
Informational decomposition
 … and then approximate the problem we just solved...
Informational decomposition
 … so other people can understand how their decisions impact us!
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 Optimizing flows at BNSF railroad:
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This is how we are solving the locomotive problem at BNSF:
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This is how we are solving the locomotive problem at BNSF:
How do we increase ?
 How do we increase ?
 We need to add the impact of decisions on other subproblems:





 Popular techniques:
 Discrete dynamic programming (Bertsekas and Tsitsiklis)
 Nested Bender’s decomposition (Birge, Higle and Sen)
 Nested stochastic optimization techniques
 Functional approximations
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Percent of posterior bound
Deterministic, rolling horizon
Adaptive dynamic programming
V’s to the information set.
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Overview
 What to do about head knowledge?
© 1999 Warren B. Powell, Princeton University
Patterns
Information can be divided between:
Patterns
 What is head knowledge”
 Data known by a human that is not in the computer, but should be.
 Larger patterns of behavior that reflect an understanding of the complete system.
The information wall:
The evolution of coordination
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Patterns
 The second form of head knowledge is patterns  standard actions given the state of the system.
Patterns
 Concept: pattern matching
 Old modeling approach: Bottom up modeling


To get the right “behavior” we have to specify the right costs and the right constraints.
If you don’t like the behavior, you have to fix the data!
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Patterns
 Concept: pattern matching
 New modeling approach: Top down, bottom up modeling


Learning operating patterns
The flows are not the same, but they have the same pattern.