Automata, Languages and Programming: 12th Colloquium by L. Lovász (auth.), Wilfried Brauer (eds.)

By L. Lovász (auth.), Wilfried Brauer (eds.)

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Extra info for Automata, Languages and Programming: 12th Colloquium Nafplion, Greece, July 15–19, 1985

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In this paper, we invented new pruning rules for weighted sums where the summands are the weighted start times of tasks to be serialized. Then, the presented theoretical results are adopted for their practical application in constraint programming. Further, their adequacy was practically shown in a real-world application domain: the optimal sequencing of surgeries in hospitals. There, in contrast to the original rules the new pruning rules behave in very robust way, especially in real scheduling problems.

Solution computation of all solutions n time/msec. # choices # backtracks time/msec. # combinations n! 8 11 8 0 31 40320 9 15 9 0 313 362880 10 15 10 0 2648 3628800 11 17 11 0 27737 39916800 12 17 12 0 279418 479001600 Fig. 7. )) are necessary if we use WeightedSum either together with SingleResource or any other, even specialized constraint for scheduling equal length tasks8 (cf. [1]). However, WeightedTaskSum requires the least number of choices to find an optimal solution: n for the finding and proving the optimality where n is the number of surgeries.

Furthermore, each task ti ∈ T has a fixed positive priority αi ∈ Q. , a machine, an employee, etc. or especially an operating room). , for setting-up the used machine. e. some start times s1 ∈ S1 , . . e. it minimizes the sum i=1 αi · si such that for any other n solution s1 ∈ S1 , . . , sn ∈ Sn it holds: i=1 αi · si ≤ ni=1 αi · si . In the following, we call this problem, which is characterized by a task set T , the Prioritized Task Scheduling Problem of T , or PTSP(T ) for short. Furthermore, we call a PTSP(T ) solvable if a (minimal) solution exists.

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