Part 10: Disjunctive Scheduling

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Theoretical Questions

Decomposing the Disjunctive Constraint

Your task is to make the Disjunctive constraint more efficient than by using the Cumulative constraint with unit capacity:

  • Implement the constraint for the reification b iff x <= y, where b, x, and y are variables. This will be useful for implementing the decomposition of the Disjunctive constraint.

  • Test your implementation in

  • Implement the decomposition with reified constraints for

  • Make sure your implementation passes all the tests except testOverloadChecker, testDetectablePrecedence, and testNotLast (those are for the programming exercise below) in

  • Test whether, as expected, this decomposition prunes more than the formulation with timetable filtering for the Cumulative constraint. For example, observe on that the number of backtracks is reduced with the decomposition compared to the formulation with Cumulative. Test for instance on the small instance data/jobshop/sascha/jobshop-4-4-2 with 4 jobs, 4 machines, and 16 activities.

The Global Disjunctive Constraint: Overload Checker, Detectable Precedence, and Not-First-Not-Last

  • Read and make sure you understand the implementation Some unit tests are implemented in To make sure you understand it, add a unit test with 4 activities and compare the results with a manual computation.

  • Overload checking, detectable precedences, not-first-not-last, and edge finding only filter one side of the activities. To get the symmetrical filtering, implement the mirroring activities trick similarly to

  • Implement the overload checker in

  • The overload checker should already make a big difference to prune the search tree. Make sure that larger job-shop instances are now solved faster; for instance, data/jobshop/sascha/jobshop-6-6-0 should now become easy to solve.

  • Implement detectable precedences in

  • Implement not-first-not-last in

  • Make sure your implementation passes the tests

  • (optional) Implement edge finding in (you will also need to implement the ThetaLambdaTree data structure).