1. Scheduling with uncertain resources Search for a near-optimal solution
Eugene Fink, Matthew Jennings, Ulaş 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.
The motivation behind this proposal is that uncertainty in a resource planning task can be detrimental to the quality of the plan produced. It is therefore important to reduce this uncertainty through elicitation while keeping the cost of elicitation low.

3. Representation
Available rooms
Conference events
Schedule

4. Available rooms Unavailable Unavailable Unavailable Room name
Properties
Size: 1200
Stations: 10
Mikes: 5
Size: 700
Stations: 5
Mikes: 1
Size: 500
Mikes: 2
Audit- orium
Class- room
Conf. room
11:00
11:30
12:00
12:30
1:00
1:30
2:00
2:30
3:00
3:30
4:00
Distances
Dist: 400
Dist: 50
Unavailable
Availability
Auditorium
Conf. room
Unavailable
Classroom
Unavailable

5. Available rooms Unavailable Unavailable Unavailable
We represent uncertain properties and distances by intervals of possible values.
Audit- orium
Class- room
Conf. room
11:00
11:30
12:00
12:30
1:00
1:30
2:00
2:30
3:00
3:30
4:00
Unavailable
Auditorium
Conf. room
Size: 1200
Stations: 10
Mikes: 5
Size:
Stations: 5
Mikes: 2
Unavailable
Classroom
Dist:
Dist: 400
Size: 700
Stations: 5
Mikes: 1
Unavailable

6. Conference events
We specify the name and numeric importance of an event.
We also specify acceptable and preferred ranges for the following parameters:
Every room property
Start time and duration
For every other event, the distance to that event
For every other event, the start time w.r.t. that event

7. Conference events Constraints on times and room properties
Constraints on distances and relative times

8. Conference events
We represent uncertain importances and range boundaries by intervals of possible values.
Demo
Importance: 4..6
Minimal duration:
Preferred duration:
...

9. Schedule Unavailable Unavailable Unavailable For every event,
we need to select:
Room
Start time
Duration
Audit- orium
Class- room
Conf. room
11:00
11:30
12:00
12:30
1:00
1:30
2:00
2:30
3:00
3:30
4:00
Demo
Tutorial
Unavailable
Work- shop
Unavailable
Discus- sion
Unavailable
Comm-
ittee

10. 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

11. Schedule quality We compute the quality for each event.
If the specification of rooms and events includes uncertainty, we compute the expected quality:
Quality = E(Importance1) ∙ E(Quality1)
+ E(Importance2) ∙ E(Quality2)
+ …
The schedule quality is the weighted sum of event quality values.
The schedule quality is the weighted sum of event quality values:
Quality = Importance1 ∙ Quality1
+ Importance2 ∙ Quality2
+ …

12. Search Use randomized hill-climbing At each step, reschedule one event
Stop after finding a local maximum

13. Search Sort events in the decreasing order 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

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

15. Experiments: W/o uncertainty
Schedule
Quality
1.0
0.61
0.92
Manual
Automatic
0.94
0.83
0.93
0.9
0.8
0.7
0.6
5 rooms 32 events
9 rooms 62 events
14 rooms 84 events
problem size

16. Experiments: With uncertainty
Schedule
Quality
0.9
0.63
0.78
Manual
Automatic
0.8
0.72
0.83
0.8
0.7
0.6
0.5
5 rooms 32 events
9 rooms 62 events
14 rooms 84 events
problem size

17. Experiments: Search time
Schedule Quality
without
uncertainty
0.9
0.8
with
uncertainty
0.7
0.6 1 2 3 4 5 6 7 8 9 10
Time (seconds)
14 rooms
84 events

18. Conclusions
Optimization based on uncertain knowledge of available resources and scheduling constraints
Fast high-quality solutions for large real-life problems