extension of rescheduling based on minimal graph cut

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