Scheduling under Uncertainty Eugene Fink Jaime G Carbonell
Scheduling under Uncertainty Eugene Fink, Jaime G. Carbonell Ulas Bardak, Alex Carpentier, Steven Gardiner, Andrew Faulring, Blaze Iliev, P. Matthew Jennings, Brandon Rothrock, Mehrbod Sharifi, Konstantin Salomatin, Peter Smatana
Motivation The available knowledge is uncertain Scheduling under uncertainty We usually make decisions • Uncertain resources and based on incomplete and scheduling constraints partially inaccurate info • Search for a schedule with high expected quality
Demo
Scheduling results Manual and auto scheduling Schedule Quality 0. 78 0. 80 0. 72 0. 63 13 rooms 84 events Schedule Size Schedule Quality without uncertainty 0. 9 Auto 9 rooms 62 events Manual Auto Manual 5 rooms 32 events 0. 83 Search time 0. 8 0. 7 0. 6 with uncertainty 1 2 3 4 5 6 7 8 9 10 Time (seconds) 13 rooms 84 events
Info elicitation • Identification of critical missing info • Analysis of trade-offs between its cost and expected schedule improvements Approach • For each candidate question, estimate the probabilities of possible answers • For each possible answer, evaluate its cost and impact on the schedule • For each question, compute its overall expected impact, and select questions with highest positive impacts
Example: Initial schedule Available rooms: Room num. 1 2 3 Events: Area (feet 2) 2, 000 1, 000 Projector Yes No Yes Initial schedule: 2 Posters 1 Talk 3 Assumptions: Missing info: • Invited talk, 9– 10 am: – Needs a projector Projector need Needs a large room • Poster session, 9– 11 am: • Poster session: – Small Room room size is OK Needs a room – Needs no need projector Projector
Example: Choice of questions Initial schedule: 2 Posters 1 Talk 3 Candidate questions: Events: • Invited talk, talk: 9– 10 am: Useless info: There are no projector? × Needs a large rooms w/o a projector • Poster session, session: 9– 11 am: Useless info: There are no larger room? unoccupied larger rooms × Needs a room √ Needs a projector? Potentially useful info
Example: Improved schedule Events: • Invited talk, 9– 10 am: Needs a large room • Poster session, 9– 11 am: Needs a room Elicitation: Initial schedule: 2 Posters 1 Talk 3 New schedule: System: Does the poster session 2 Posters 1 need a projector? User: A projector may be useful, Talk 3 but not really necessary.
Elicitation results Repairing a conference schedule after a “crisis” loss of rooms. Manual and auto repair Schedule Quality Auto with Elicitation Auto w/o Elicitation After Crisis Manual Repair 0. 50 0. 61 0. 68 0. 72 Dependency of the quality on the number of questions Schedule Quality 0. 72 0. 68 10 20 30 40 50 Number of Questions
Defaults assumptions Making reasonable assumptions in the absence of specific info • Representation and use • Dynamic learning Schedule Quality 0. 72 0. 67 with default learning without learning 20 40 60 80 100 Number of Questions
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