## 00-14

#### How Many Sequences Solve an Open Shop Problem?

by Tautenhahn, T.; Willenius, P.

**Preprint series:** 00-14, Preprints

**Abstract:** We consider the classical open shop problem to minimize makespan. For this problem, a feasible combination of all job ordes and machine orders is called a sequence. Structural investigations lead to a dominance relation between sequences in the sense that if a sequence A dominates a sequence B then the makespan of A is smaller than or equal to the makespan of B independently of the given processing times. In this paper we generalize this concept by examination a dominance relation between sets of sequences. We give several necessary and sufficient conditions for a sequence to be dominated by a set of other sequences. Moreover, we show that this relation can be formulated as a mixed integer program. Using these results, for some small formats we are able to compute a minimal set of sequences with the property that for any choise of processing times this set contains at least one optimal sequence.

**Keywords:** open shop

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