Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak...
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Transcript of Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak...
![Page 1: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/1.jpg)
Extension of ReschedulingExtension of Reschedulingbased onbased on
Minimal Graph CutMinimal Graph Cut
MariMarián Lekavýán Lekavý and Pavol N and Pavol Návratávrat
Slovak University of TechnologyFaculty of Informatics and Information Technologies
![Page 2: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/2.jpg)
Presentation outlinePresentation outline
Rescheduling RAPORT overview The rescheduling algorithm Future and Conclusions
![Page 3: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/3.jpg)
Rescheduling
Schedule is not 100% respected Move/shorten activities Minimize the cost of rescheduling
![Page 4: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/4.jpg)
Rescheduling
Approaches Enforce schedule Include all possibilities New schedule Modify the old schedule
![Page 5: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/5.jpg)
Rescheduling
Modify the old schedule RSR (Right Shift Rescheduling) PR (Partial Rescheduling)
Unmovable deadline Time reserves (e.g. Match-Up
Rescheduling) Shortening of activities
![Page 6: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/6.jpg)
RAPORT
Workflow system Support for
military exercise preparation Tasks of the RAPORT system
Provide necessary information Support collaboration Adapt the schedule Collect users’ experience
![Page 7: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/7.jpg)
RAPORT
Activities and documents in the RAPORT system
![Page 8: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/8.jpg)
The problem
Increase the end time of some activity (activities) while not moving the final deadline.
Move activities Shorten activities
![Page 9: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/9.jpg)
The problem
Input: activities Time (start, end, minimal) Activity dependencies (documents) Activities which violate the schedule
Output: minimal cost rescheduling Moved and shortened activities
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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
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Algorithm example
![Page 12: Extension of Rescheduling based on Minimal Graph Cut Marián Lekavý and Pavol Návrat Slovak University of Technology Faculty of Informatics and Information.](https://reader036.fdocuments.in/reader036/viewer/2022081515/5697bf871a28abf838c88fed/html5/thumbnails/12.jpg)
Algorithm example
1. Conversion to graph
time
A3
A5
Af1
DAY-D
A4
A6
Af2
A4
A5
A3
A6
Af2Af1
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Algorithm example
2. Adding activity edges
A4
A5
A3
A6
Af2Af1
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
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Algorithm example
3. Adding the final node
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
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Algorithm example
4. Edge costs
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
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Algorithm example
5. Find the minimal cut
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
Vunchanged
Vchanged
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Algorithm example
6. Moving of activities
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
Vunchanged
Vchanged
time
A3
A5
Af1
DAY-D
A4
A6
Af2
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Edge costs
Abort the failed activity ∞
Shorten an activity 1/∞
Shorten a dependence 0/∞
Move an activity 0.001/∞
Move the deadline ∞
Ainit
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
Afinal
ADAY-D
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Further work
Testing in NAO Automatic cost adjusting k-step optimal rescheduling Combination with CPM/PERT Resources (resource links?)
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Conclusions
Every rescheduling corresponds to agraph cut
New rescheduling algorithm Minimal cost of change Works with moving and shortening
ofactivities
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Vunchanged
VchangedA1start
A4start
A3start
A2start
A5start
A1end
A2end
A3end
A4end
A5end
Afinal
Thank you