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

The available knowledge is uncertain Motivation The available knowledge is uncertain Scheduling under uncertainty Uncertain resources and scheduling constraints Search for a schedule with high expected quality We usually make decisions based on incomplete and partially inaccurate info

Demo

Scheduling results Manual and auto scheduling Search time Schedule Quality Manual and auto scheduling Schedule Size 10 Search time 0.8 0.9 0.7 0.6 1 2 3 4 5 6 7 8 9 Schedule Quality Time (seconds) 13 rooms 84 events Manual Auto 0.78 5 rooms 32 events 0.80 Manual Auto 0.83 0.72 9 rooms 62 events Manual Auto 0.83 0.63 13 rooms 84 events without uncertainty with uncertainty

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: Initial schedule: Talk Posters Room num. Area (feet2) Proj- ector 1 2 3 2,000 1,000 1,000 Yes No Yes 1 2 3 Events: Invited talk, 9–10am: Needs a large room Poster session, 9–11am: Needs a room Assumptions: Invited talk: – Needs a projector Poster session: – Small room is OK – Needs no projector Missing info: Invited talk: – Projector need Poster session: – Room size – Projector need

Example: Choice of questions Initial schedule: 1 2 Posters 3 Talk Candidate questions: Invited talk: Needs a projector? Poster session: Needs a larger room? Needs a projector? Events: Invited talk, 9–10am: Needs a large room Poster session, 9–11am: Needs a room Useless info: There are no large rooms w/o a projector × Useless info: There are no unoccupied larger rooms × Potentially useful info √

Example: Improved schedule Events: Invited talk, 9–10am: Needs a large room Poster session, 9–11am: Needs a room 1 2 3 Initial schedule: Talk Posters Elicitation: 1 2 3 New schedule: Talk System: Does the poster session need a projector? Posters User: A projector may be useful, but not really necessary.

Dependency of the quality on the number of questions Elicitation results Repairing a conference schedule after a “crisis” loss of rooms. 0.68 0.72 Schedule Quality 10 30 20 40 50 Number of Questions Dependency of the quality on the number of questions Schedule Quality Manual and auto repair Auto with Elicitation 0.72 Auto w/o Elicitation 0.68 Manual Repair 0.61 After Crisis 0.50

Making reasonable assumptions in the absence of specific info Defaults assumptions Making reasonable assumptions in the absence of specific info Representation and use Dynamic learning 0.67 0.72 Schedule Quality 20 60 40 80 100 Number of Questions with default learning without learning