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By Toan Phan Huy

This e-book offers an intensive research of scheduling difficulties that come up in a versatile production atmosphere with scarce source provide. Generalizations of the well-known activity store scheduling challenge are mentioned. As a easy and customary strategy for fixing those difficulties constraint propagation is utilized in a variety of answer equipment. The effectiveness of constraint propagation is verified via the answer of a excessive variety of benchmark challenge situations.

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LLRS93], Blazewicz et al. [BEP+96] and Drozdowski [Dro96]. 2. 2 Disjunctive Clique Decompositions The representation of a DSP instance as a disjunctive graph naturally induces a decomposition into disjunctive cliques. From a model theoretic point of view, this decomposition is apparently redundant, since it basically defines a partition of the set of disjunctive constraints in some particular way. With regard to the algorithmic treatment and solution of the DSP, however, clique structures playa crucial role, as they allow the deduction of the sequencing order of sets of operations.

For further complexity results of the DSP and its subclasses, we refer to Rinnooy Kan [Rin76], Lenstra et al. [LKB77], Lawler et al. [LLRS93], Blazewicz et al. [BEP+96] and Drozdowski [Dro96]. 2. 2 Disjunctive Clique Decompositions The representation of a DSP instance as a disjunctive graph naturally induces a decomposition into disjunctive cliques. From a model theoretic point of view, this decomposition is apparently redundant, since it basically defines a partition of the set of disjunctive constraints in some particular way.

Since (i, j) E D implies (j, i) ED, we will write i f-t JED. Finally, let P = {Pi liE O} be the set of processing times. , ... ,stn )} st; E V(st;) = No (i) st; + p; stj (ii) st; + p; stj V stj :s :s + Pj :s st; i E 0, i -+ j E C, i f-t JED. A schedule is an assignment ST = (sh, ... ,stn) E V(stt} x ... x V(st n ) of all start time variables. For the sake of simplicity, we will use the same notation for variables and their assignments. A schedule ST is feasible if it satisfies all conjunctive constraints (i) and all disjunctive constraints (ii).

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