Scheduling with uncertain resources: Representation and utility function Ulas Bardak, Eugene Fink, and Jaime Carbonell Reflective Agent with Distributed Adaptive Reasoning RADAR

, but also under crisis conditions Help not only in routine situations Purpose Automation of office tasks, such as scheduling and resource allocation

Challenges Intelligent performance of office-management tasks Dealing with uncertainty and unexpected situations Collaboration with users

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

Architecture Info elicitorParserOptimizer Process new info Update resource allocation Choose and send questions Top-level control and learning Graphical user interface Administrator

Uncertain utility Uncertainty The system allows uncertainty in the representation of all variables and functions in optimization problems. Uncertain integers Uncertain nominals

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

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: [ ] 0.6 chance: [ ] 0.2 chance: [ ] Proba- bility Room Size 0 0

Uncertain utilities An uncertain utility function may be represented in three ways. Complete unknown Piecewise-linear function with uncertain y-coordinates Room Size Quality Set of possible piecewise-linear functions and their probabilities 0.2 chance 0.8 chance

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

Experiments Manual Auto rooms 62 events Manual Auto rooms 84 events without uncertainty with uncertainty 10 Search time Schedule Quality Time (seconds) 14 rooms 84 events Manual Auto rooms 32 events 0.80 Schedule Quality Manual and auto scheduling problem size

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: