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Scheduling with uncertain resources: Representation and utility function Ulas Bardak, Eugene Fink, and Jaime Carbonell Reflective Agent with Distributed Adaptive Reasoning RADAR
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, but also under crisis conditions Help not only in routine situations Purpose Automation of office tasks, such as scheduling and resource allocation
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Challenges Intelligent performance of office-management tasks Dealing with uncertainty and unexpected situations Collaboration with users
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Conference planning Scheduling of talks at a conference, and related allocation of rooms and equipment, in a crisis situation. Continuous stream of minor changes; for example, schedule changes and unforeseen equipment needs Unexpected major change in space availability; for example, closing of a building
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Architecture Info elicitorParserOptimizer Process new info Update resource allocation Choose and send questions Top-level control and learning Graphical user interface Administrator
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Uncertain utility Uncertainty The system allows uncertainty in the representation of all variables and functions in optimization problems. Uncertain integers Uncertain nominals
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An uncertain nominal value is either a complete unknown or a set of possible values and their probabilities. Example: We have ordered vegetarian meals, but there is a chance that we will receive meals of a wrong type. Meal-type: 0.90 chance: vegetarian 0.05 chance: regular 0.05 chance: vegan
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Uncertain integers An uncertain integer is either a complete unknown or a probability-density function represented by a set of uniform distributions. Example: An auditorium has about 600 seats. Room-size: 0.2 chance: [450..549] 0.6 chance: [550..650] 0.2 chance: [651..750] 0.002 0.004 0.006 200400600 800 Proba- bility Room Size 0 0
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Uncertain utilities An uncertain utility function may be represented in three ways. Complete unknown Piecewise-linear function with uncertain y-coordinates 0.5 1.0 200400600 800 0.0 0 Room Size Quality Set of possible piecewise-linear functions and their probabilities 0.2 chance 0.8 chance
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Optimization The optimization algorithm is based on randomized hill-climbing. At each step, reschedule one event Stop after finding a local maximum or reaching a time limit Search for a schedule with the greatest expected quality
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Experiments Manual Auto 0.83 0.72 9 rooms 62 events Manual Auto 0.83 0.63 14 rooms 84 events without uncertainty with uncertainty 10 Search time 0.8 0.9 0.7 0.6 1 2 3 4 5678 9 Schedule Quality Time (seconds) 14 rooms 84 events Manual Auto 0.78 5 rooms 32 events 0.80 Schedule Quality Manual and auto scheduling problem size
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Conclusions Optimization based on uncertain resources and constraints Collaboration with the user Results: We assume that all probability distributions are independent. Limitation: Learning of typical requirements and default user preferences Contingency scheduling Current work:
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