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The complexity of short schedules for uet bipartite graphs

Evripidis Bampis (2010)

RAIRO - Operations Research

We show that the problem of deciding if there is a schedule of length three for the multiprocessor scheduling problem on identical machines and unit execution time tasks in -complete even for bipartite graphs, i.e. for precedence graphs of depth one. This complexity result extends a classical result of Lenstra and Rinnoy Kan [5].

Timed Petri-net based formulation and an algorithm for the optimal scheduling of batch plants

Tianlong Gu, Parisa Bahri, Guoyong Cai (2003)

International Journal of Applied Mathematics and Computer Science

The effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and an optimal solution algorithm are the main issues of study. Petri nets have proven to be a promising technique for solving many difficult problems associated with the modelling, formal analysis, design and coordination control of discrete-event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioural...

Tolerance problems for generalized eigenvectors of interval fuzzy matrices

Martin Gavalec, Helena Myšková, Ján Plavka, Daniela Ponce (2022)

Kybernetika

Fuzzy algebra is a special type of algebraic structure in which classical addition and multiplication are replaced by maximum and minimum (denoted and , respectively). The eigenproblem is the search for a vector x (an eigenvector) and a constant λ (an eigenvalue) such that A x = λ x , where A is a given matrix. This paper investigates a generalization of the eigenproblem in fuzzy algebra. We solve the equation A x = λ B x with given matrices A , B and unknown constant λ and vector x . Generalized eigenvectors have interesting...

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