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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
Presentation outlinePresentation outline
Rescheduling RAPORT overview The rescheduling algorithm Future and Conclusions
Rescheduling
Schedule is not 100% respected Move/shorten activities Minimize the cost of rescheduling
Rescheduling
Approaches Enforce schedule Include all possibilities New schedule Modify the old schedule
Rescheduling
Modify the old schedule RSR (Right Shift Rescheduling) PR (Partial Rescheduling)
Unmovable deadline Time reserves (e.g. Match-Up
Rescheduling) Shortening of activities
RAPORT
Workflow system Support for
military exercise preparation Tasks of the RAPORT system
Provide necessary information Support collaboration Adapt the schedule Collect users’ experience
RAPORT
Activities and documents in the RAPORT system
The problem
Increase the end time of some activity (activities) while not moving the final deadline.
Move activities Shorten activities
The problem
Input: activities Time (start, end, minimal) Activity dependencies (documents) Activities which violate the schedule
Output: minimal cost rescheduling Moved and shortened activities
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
Algorithm example
Algorithm example
1. Conversion to graph
time
A3
A5
Af1
DAY-D
A4
A6
Af2
A4
A5
A3
A6
Af2Af1
Algorithm example
2. Adding activity edges
A4
A5
A3
A6
Af2Af1
A4start
A5start
A3start
A6start
A3end
A5end
A4end
A6end
Af2Af1
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
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
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
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
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
Further work
Testing in NAO Automatic cost adjusting k-step optimal rescheduling Combination with CPM/PERT Resources (resource links?)
Conclusions
Every rescheduling corresponds to agraph cut
New rescheduling algorithm Minimal cost of change Works with moving and shortening
ofactivities
Vunchanged
VchangedA1start
A4start
A3start
A2start
A5start
A1end
A2end
A3end
A4end
A5end
Afinal
Thank you