Scheduling with uncertain resources Search for a near-optimal solution

1
Scheduling with uncertain resources Search
for a near-optimal solution
Eugene Fink, Matthew Jennings, Ulas Bardak,Jean
Oh, Stephen Smith, and Jaime Carbonell Carnegie
Mellon University
2
Problem

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

We need to build a schedule with high expected
quality.
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Representation

• Available rooms
• Conference events
• Schedule

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Available rooms

• Room name

Audit-orium Class-room Conf.room
1100
1130
1200
1230
100
130
200
230
300
330
400
Unavailable

• Availability

Auditorium
Conf. room
Unavailable
Classroom
Unavailable
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Available rooms

• We represent uncertain properties and
  distances by intervals of possible values.

Audit-orium Class-room Conf.room
1100
1130
1200
1230
100
130
200
230
300
330
400
Unavailable
Auditorium
Conf. room
Size 1200 Stations 10 Mikes 5
Size 500..750 Stations 5 Mikes 2
Unavailable
Classroom
Dist50..70
Dist400
Size 700 Stations 5 Mikes 1
Unavailable
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Conference events
We specify the name and numeric importance of
an event.
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Conference events
Constraints on times and room properties
Constraints on distances and relative times
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Conference events
We represent uncertain importances and range
boundaries by intervals of possible values.
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Schedule

• For every event,
• we need to select
• Room
• Start time
• Duration

Audit-orium Class-room Conf.room
1100
1130
1200
1230
100
130
200
230
300
330
400
Demo
Tutorial
Unavailable
Work-shop
Unavailable
Discus-sion
Unavailable
Comm- ittee
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Schedule quality
We compute the quality for each event.

• If start time, duration, room properties,
  distances, or relative times are outside their
  acceptable ranges, the quality is 0.0

• If all these values are within their preferred
  ranges, the quality is 1.0

• If all these values are acceptable, but some are
  not preferred, the quality is between 0.0 and 1.0

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Schedule quality
We compute the quality for each event.
The schedule quality is the weighted sum of
event quality values Quality Importance1
Quality1 Importance2 Quality2

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Search

• Use randomized hill-climbing

• At each step, reschedule one event

• Stop after finding a local maximum

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Search

• Sort events in the decreasingorder of their
  importances

• For each event- Consider all possible
  placements, i.e. rooms, start times, and
  durations- Select the placement with the
  highest expected quality

• If found any new placements,repeat from the
  beginning

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Experiments

• Scheduling of a large conference
• Eighty-four events
• Four days, fourteen rooms
• 2500 numeric values

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Experiments W/o uncertainty
Schedule Quality
1.0
0.9
0.8
0.7
0.6
14 rooms84 events
5 rooms32 events
9 rooms62 events
problem size
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Experiments With uncertainty
Schedule Quality
0.9
0.8
0.7
0.6
0.5
14 rooms84 events
5 rooms32 events
9 rooms62 events
problem size
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Experiments Search time
ScheduleQuality
without uncertainty
0.9
0.8
with uncertainty
0.7
0.6
1
3
4
9
10
2
5
6
7
8
Time (seconds)
14 rooms 84 events
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Conclusions

• Optimization based on uncertainknowledge of
  available resourcesand scheduling constraints
• Fast high-quality solutions forlarge real-life
  problems