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On the power of randomization for job shop scheduling with k-units length tasks

Tobias Mömke (2008)

RAIRO - Theoretical Informatics and Applications

In the job shop scheduling problem k-units-Jm, there are m machines and each machine has an integer processing time of at most k time units. Each job consists of a permutation of m tasks corresponding to all machines and thus all jobs have an identical dilation D. The contribution of this paper are the following results; (i) for d = o ( D ) jobs and every fixed k, the makespan of an optimal schedule is at most D+ o(D), which extends the result of [3] for k=1; (ii) a randomized on-line approximation...

On the weak robustness of fuzzy matrices

Ján Plavka (2013)

Kybernetika

A matrix A in ( max , min ) -algebra (fuzzy matrix) is called weakly robust if A k ⊗ x is an eigenvector of A only if x is an eigenvector of A . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an O ( n 2 ) algorithm for checking the weak robustness is described.

On transitive orientations of G-ê

Michael Andresen (2009)

Discussiones Mathematicae Graph Theory

A comparability graph is a graph whose edges can be oriented transitively. Given a comparability graph G = (V,E) and an arbitrary edge ê∈ E we explore the question whether the graph G-ê, obtained by removing the undirected edge ê, is a comparability graph as well. We define a new substructure of implication classes and present a complete mathematical characterization of all those edges.

Optimal scheduling of the 3-machine assembly-type flow shop

Mohamed Haouari, Thouraya Daouas (2010)

RAIRO - Operations Research

We address the 3-Machine Assembly-Type Flowshop Scheduling Problem (3MAF). This problem is known to be NP-complete in the strong sense. We propose an exact branch and bound method based on a recursive enumeration of potential inputs and outputs of the machines. Using this algorithm, several large size instances have been solved to optimality.

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