Scheduling with Uncertain Resources

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Scheduling with Uncertain Resources
Eugene Fink, Jaime G. Carbonell, Ulas Bardak,
Alex Carpentier, Steven Gardiner,Andrew
Faulring, Blaze Iliev, P. Matthew
Jennings,Brandon Rothrock, Mehrbod
Sharifi,Konstantin Salomatin, Peter Smatana
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Motivation
The available knowledgeis inherently uncertain.
We usually make decisionsbased on incomplete and
partially inaccurate data.
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Challenges

• Representation of uncertainty

• Fast reasoning based on uncertain knowledge

• Elicitation of criticaladditional data

• Learning of reasonable defaults

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RADAR project
Scheduling and resource allocation under
uncertainty.
Part of the RADAR project,aimed at building an
intelligent assistant for an office manager.
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Demo
Planning a conferencebased on uncertain
dataabout available resources and scheduling
constraints.
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Outline

• Representation of uncertainty
• Reasoning based on uncertain knowledge
• Elicitation of missing data
• Default assumptions

Representation of uncertainty
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Alternative representations

• Approximations
• Marys weight is about 150. Marys cell
  phone is probably in her purse.

• Ranges or sets of possible values
• Marys weight is between 140 and 160.
  Marys cell phone may be in her purse,
  office, home, or car.

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Approximations
Simple and intuitive approach, which usually does
not require changes to standard algorithms.
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Approximations
Example Selecting an amount of medication.
Since small input changes translate intosmall
output changes, we can use anapproximate weight
value.
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Approximations
Example Loading an elevator.
We can adapt this procedure to the useof
approximate weights by subtracting asafety
margin from the weight limit.
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Approximations
Example Playing the exact weight game.
If we use approximate weight values, we cannot
determine the chances of winning.
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Ranges or sets of possible values

• Explicit representation of a margin of error
• Moderate changes to standard algorithms

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Ranges or sets of possible values
Example Loading an elevator.
We identify the danger of overloading, but we
cannot determine its probability.
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Ranges or sets of possible values
Example Playing the exact weight game.
We still cannot determine the chances of winning.
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Probability distributions
Accurate analysis of possible values and their
probabilities.
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Probability distributions
Example Playing the exact weight game.
prize
player weight
We can determine possible outcomes and evaluate
their probabilities.
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Proposed approach
ranges or sets of values
ranges or setswith probabilities
probability distributions
We approximate a probability density function by
a set of uniform distributions, and represent it
as a set of ranges with probabilities.
Weight 0.1 chance 140..145 0.8 chance
145..155 0.1 chance 155..160
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Uncertain data

• Nominal values

An uncertain nominal value is a set of possible
values and their probabilities.
Phone location 0.95 chance purse 0.02
chance home 0.02 chance office 0.01 chance
car
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Uncertain data

• Nominal values
• Integers and reals

An uncertain numeric value is a
probability-density function represented by a set
of uniform distributions.
Weight 0.1 chance 140..145 0.8 chance
145..155 0.1 chance 155..160
probabilitydensity
140
160
150
weight
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Uncertain data

• Nominal values
• Integers and reals
• Functions

An uncertain function is apiecewise-linear
function with uncertain coordinates
amount ofmedication
patient weight
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Outline

• Representation of uncertainty
• Reasoning based on uncertain knowledge
• Elicitation of missing data
• Default assumptions

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Uncertainty arithmetic
We have developed a library of basic operations
on uncertain data, which input and output
uncertain values.
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Uncertainty arithmetic

• Allows extension of standard algorithms to
  reasoning with uncertain values

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RADAR application
Scheduling and resource allocation based on
uncertain knowledge of resources and constraints.

• Uncertain room and event properties
• Uncertain resource availability and prices

We use an optimizer that searches for a schedule
with the greatest expected quality.
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RADAR results
Scheduling of conference events.
without uncertainty
with uncertainty
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Outline

• Representation of uncertainty
• Reasoning based on uncertain knowledge
• Elicitation of missing data
• Default assumptions

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Elicitation challenge

• Identification of critical missing data
• Analysis of the trade-off between the cost of
  data acquisition and the expected performance
  improvements

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Proposed approach

• For each candidate question, estimate the
  probabilities of possible answers

• For each possible answer, compute its cost, as
  well as its impact on the optimization utility

• For each question, compute its expected impact on
  the overall utility, and select questions with
  highest expected impacts

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RADAR example Initial schedule
Available rooms
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Roomnum. Area(feet2) Proj-ector
123 2,0001,0001,000 YesNoYes
1
3

• Missing info
• Invited talk Projector need
• Poster session Room size Projector
  need

• Assumptions
• Invited talk Needs a projector
• Poster session Small room is OK
  Needs no projector

• Events
• Invited talk, 910am Needs a large room
• Poster session, 911am Needs a room

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RADAR example Choice of questions
Initial schedule
2
1
Posters
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Talk

• Candidate questions
• Invited talk Needs a projector?
• Poster session Needs a larger room? Needs
  a projector?

• Events
• Invited talk, 910am Needs a large room
• Poster session, 911am Needs a room

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RADAR example Improved schedule

• Events
• Invited talk, 910am Needs a large room
• Poster session, 911am Needs a room

Info elicitation
System Does the poster sessionneed a projector?
Posters
UserA projector may be useful,but not really
necessary.
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RADAR results
Repairing a conference schedule after a crisis
loss of rooms.
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Outline

• Representation of uncertainty
• Reasoning based on uncertain knowledge
• Elicitation of missing data
• Default assumptions

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Defaults assumptions
Learning to make reasonable common-sense
assumptions in the absence of specific data.
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Defaults assumptions
Learning to make reasonable common-sense
assumptions in the absence of specific data.

• Representation of general and context-specific
  assumptions
• Dynamic learning of assumptions
• Integration with data elicitation

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RADAR results
Dependency of the schedule quality on the number
of questions.
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Reasoning under
Uncertainty