Constraint based scheduling Paper by: Claude Le Pape Presented by: Mounir Stino

What is a scheduling problem? Input: A set of resources with given capacities. A set of activities with given processing time and resource requirements. A set of temporal constraints between activities. Output: To decide when to execute each activity. An instance of the CSP problem.

Types of scheduling problems Disjunctive vs. cumulative scheduling Non-preemptive vs. preemptive scheduling Our problem is a disjunctive non-preemptive problem, the most specific case.

Representation of constraints Constraints of activities: Two variables associated to each activity A: Start(A) and End(A).

Representation of constraints(2) Temporal constraints: Start(A) + Delay(A) < Start(B). Resource constraints: If A and B require the same resource, then A and B cannot intersect

Example: Resource-Constrained Project Scheduling Problem (RCPSP) Given: m resources R1 ... Rm with given capacities c1...cm n activities A1 ... An with given durations d1 ... dn precedence constraints between activities Task: Assign start and end date to all activities satisfying the constraints and minimizing the total duration.

Search procedure Initialize the set of selectable activities W to the complete set. If all activities have fixed start and end times, exit. Otherwise remove from W those activities which have fixed start and end times. If W is not empty, select an activity from W, create a choice point for the selected activity (to allow backtracking) and schedule the selected activity from its earliest start time to its earliest end time. If W is empty, backtrack to the most recent choice point. (If there is no choice point left, report that there is no problem solution and exit.) Upon backtracking, mark the backtracked activity as not selectable as long as its earliest start and end times have not changed. Then goto step 2.

Conclusion The paper tries to cover general scheduling problems. A lot of sections about interruptible activities, cumulative resources, state resources and energetic resources were not covered in this presentation. Not very relevant to our project.