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Displaying 121 –
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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 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...
A matrix in -algebra (fuzzy matrix) is called weakly robust if is an eigenvector of only if is an eigenvector of . 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 algorithm for checking the weak robustness is described.
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.
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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