Scheduling with uncertain resources Elicitation of additional data

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Scheduling with uncertain resources
Elicitation of additional data

• Ulas Bardak, Eugene Fink, Chris Martens, and
  Jaime Carbonell
• Carnegie Mellon University

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Problem

• Scheduling a conference under uncertainty
• Uncertain room properties
• Uncertain equipment needs
• Uncertain speaker preferences

The automated scheduler needs to collaborate
with the human user.
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Problem

• The system may not have enough data for producing
  a good schedule

• The user may be able to obtain some of the
  missing data, but not all data

The system should identify critical missing
data and ask the user only for these data.
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Initial schedule
Available rooms
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Roomnum. Size Proj-ector
123 200 100 80 YesNoYes
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3

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

• Events and constraints
• Invited talk, 910am Needs big room
• Poster session, 911am Needs a room

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

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Choice of questions
2
1
3

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

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

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Improved schedule

• Events and constraints
• 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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Architecture
Top-level control and learning
Processnew info
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Choice of questions

• For each candidate question, estimate
  theprobabilities of possible answers

• For each possible answer, compute the respective
  change of the schedule quality

• For each question, compute its expected impact on
  the schedule quality, and select questions with
  large expected impacts

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Experiments

• Scheduling of a large conference
• 14 available rooms
• 84 conference sessions
• 700 uncertain variables

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Experiments
optimal schedule
0.72
actual
0.68
Schedule Quality
estimated
0.50
0
10
30
20
40
50
Number of Questions
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Extensions

• Game-tree search for themost important questions
• Fast heuristics for pruning unimportant
  questions
• Learning new strategiesfor question selection

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Conclusions

• We have developed a system that analyzes the
  importance of missing data, identifies critical
  uncertainties, and asks the user to obtain
  related additional data.

It usually finds a near-optimal solution after
asking 2 to 6 of all potential questions.
The developed technique does not rely on
specific properties of scheduling tasks, and it
is applicable to a variety of problems that
involve optimization under uncertainty.