Realization of an Optimal Schedule for the Two-machine Flow-Shop with Interval Job Processing Times

Non-preemptive two-machine flow-shop scheduling problem with uncertain processing times of n jobs is studied. In an uncertain version of a scheduling problem, there may not exist a unique schedule that remains optimal for all possible realizations of the job processing times. We find necessary and sufficient conditions (Theorem 1) when there exists a dominant permutation that is optimal for all possible realizations of the job processing times. Our computational studies show the percentage of the problems solvable under these conditions for the cases of randomly generated instances with n ≤ 100 . We also show how to use additional information about the processing times of the completed jobs during optimal realization of a schedule (Theorems 2 – 4). Computational studies for randomly generated instances with n ≤ 50 show the percentage of the two- machine flow-shop scheduling problems solvable under the sufficient conditions given in Theorems 2 – 4.

Stability of an Optimal Schedule for a Job-Shop Problem with Two Jobs

The usual assumption that the processing times of the operations are known in advance is the strictest one in scheduling theory. This assumption essentially restricts practical aspects of deterministic scheduling theory since it is not valid for the most processes arising in practice. The paper is devoted to a stability analysis of an optimal schedule, which may help to extend the significance of scheduling theory for decision-making in the real-world applications. The term stability is generally used for the phase of an algorithm, at which an optimal solution of a problem has already been found, and additional calculations are performed in order to study how solution optimality depends on variation of the numerical input data.

Digital Art and Design

The desire to create unique things and give free rain to one's imagination served as a powerful impetus to the development of digital art and design software. The commoner was the use of computers the wider variety of professional software was developed. Nowadays the creators and computer designers are receiving more and more new and advanced programs that allow their ideas becoming virtual reality. This research paper looks at the history of the development of graphic editors from the simplest to the most modern and advanced. This brief survey includes the history of different graphic editors’ creation, their features and abilities. This paper highlights the two basic branches of graphic editors – these that are in free use and commercial graphic editors design software. The researcher selected the most powerful and influential graphic editors design software brands like Paint.NET and GIMP among free software and commercial Adobe Photoshop. This paper also dwells upon the way digital art transferred from the exclusively professional business into the hobby for ordinary users. This research paper bears implications for those who are interested in features and potentiality of most popular graphic editors design software.