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Extension of Rescheduling based on Minimal Graph Cut

Extension of Rescheduling based on Minimal Graph Cut. Mari án Lekavý and Pavol N ávrat. Slovak University of Technology Faculty of Informatics and Information Technologies. Presentation outline. Rescheduling RAPORT overview The rescheduling algorithm Future and Conclusions. Rescheduling.

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Extension of Rescheduling based on Minimal Graph Cut

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  1. Extension of Reschedulingbased onMinimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of TechnologyFaculty of Informatics and Information Technologies

  2. Presentation outline • Rescheduling • RAPORT overview • The rescheduling algorithm • Future and Conclusions

  3. Rescheduling • Schedule is not 100% respected • Move/shorten activities • Minimize the cost of rescheduling

  4. Rescheduling • Approaches • Enforce schedule • Include all possibilities • New schedule • Modify the old schedule

  5. Rescheduling • Modify the old schedule • RSR (Right Shift Rescheduling) • PR (Partial Rescheduling) • Unmovable deadline • Time reserves (e.g. Match-Up Rescheduling) • Shortening of activities

  6. RAPORT • Workflow system • Support formilitary exercise preparation • Tasks of the RAPORT system • Provide necessary information • Support collaboration • Adapt the schedule • Collect users’ experience

  7. RAPORT • Activities and documents in the RAPORT system

  8. The problem Increase the end time of some activity (activities) while not moving the final deadline. • Move activities • Shorten activities

  9. The problem • Input: activities • Time (start, end, minimal) • Activity dependencies (documents) • Activities which violate the schedule • Output: minimal cost rescheduling • Moved and shortened activities

  10. Rescheduling as graph cut • Rescheduling by 1 time unit • two sets of events: moved and unmoved • Graph cut • two sets of vertices divided by the graph Rescheduling can be converted to graph cut

  11. Algorithm example

  12. Algorithm example 1. Conversion to graph

  13. Algorithm example 2. Adding activity edges

  14. Algorithm example 3. Adding the final node

  15. Algorithm example 4. Edge costs

  16. Algorithm example 5. Find the minimal cut

  17. Algorithm example 6. Moving of activities

  18. Edge costs • Abort the failed activity • ∞ • Shorten an activity • 1/∞ • Shorten a dependence • 0/∞ • Move an activity • 0.001/∞ • Move the deadline • ∞

  19. Further work • Testing in NAO • Automatic cost adjusting • k-step optimal rescheduling • Combination with CPM/PERT • Resources (resource links?)

  20. Conclusions • Every rescheduling corresponds to agraph cut • New rescheduling algorithm • Minimal cost of change • Works with moving and shortening ofactivities

  21. Thank you

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