Multistage Open-Shop-Problem: Schedules for N Tasks on K Machines with Different Technical Characteristics for an Arbitrary order of Tasks

2021 ◽  
Vol 27 (5) ◽  
pp. 249-258
Author(s):  
Yu. A. Zack ◽  
Keyword(s):  
Arbitrary Order ◽  
Open Shop ◽  
Time Range ◽  
Approximate Methods ◽  
Numerical Examples ◽  
Multi Stage ◽  
Open Shop Problem ◽  
Exact And Approximate Methods ◽  
Definition Of ◽  
End Times

The statements and mathematical models of the open — shop-problem are considered: performing N tasks on K machines with an arbitrary order of processing each task on all machines. Unlike most publications on solving this problem, the task posed is solved in a multi-stage formulation under the conditions of a sequential chain of sections and workshops of the enterprise, as well as in the presence of restrictions on the start and end times of tasks and the permissible operating times of machines. In addition, for scheduling systems of enterprises, it is extremely important to consider this task in a multi-stage setting, i.e. in a sequential chain of plots and workshops. The properties of admissible and optimal schedules, as well as algorithms of exact and approximate methods for solving these problems by successive optimization algorithms are investigated. At the early stages of solving the problem, the fact of incompatibility of the system of constraints of the task and the definition of a subset of tasks or resources, the time range of which should be expanded, is established. The described algorithms for solving the problem are illustrated by numerical examples.

Multiprocessor open shop problem: literature review and future directions

2020 ◽  
Vol 40 (2) ◽  
pp. 547-569
Author(s):  
Zeynep Adak ◽  
Mahmure Övül Arıoğlu Akan ◽  
Serol Bulkan
Keyword(s):  
Literature Review ◽  
Open Shop ◽  
Future Directions ◽  
Open Shop Problem ◽  
Multiprocessor Open Shop

Edges of Regression and Limit Normal Point of Conjugate Surfaces1

1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen
Keyword(s):  
Differential Geometry ◽  
Contact Boundary ◽  
Boundary Line ◽  
Tangent Point ◽  
Common Tangent ◽  
Numerical Examples ◽  
Envelope Surface ◽  
The Common ◽  
Conjugate Surfaces ◽  
Definition Of

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

Presentation of the Comprehensive and Brief International Classification of Functioning, Disability and Health Core Sets (ICF-CS) for schizophrenia

2016 ◽  
Vol 33 (S1) ◽  
pp. S365-S365
Author(s):  
O. Pino ◽  
G. Guilera ◽  
E. Rojo ◽  
J. Gómez-Benito
Keyword(s):  
Consensus Conference ◽  
International Classification Of Functioning ◽  
International Consensus ◽  
Multi Stage ◽  
Core Set ◽  
Core Sets ◽  
Competing Interest ◽  
Persons With Schizophrenia ◽  
Definition Of ◽  
Icf Core Sets

ObjectiveThe aim this presentation is present the results of the preparatory studies were presented at an international consensus conference, a multi-stage, iterative, decision-making and consensus process that took place 12–14 May 2015 in Barcelona, Spain. At this consensus conference, schizophrenia experts from different countries worldwide and working in a broad range of professions decided which ICF categories should be included in the first version of the ICF Core Sets for schizophrenia.MethodFour preliminary studies intend to capture the researcher's perspective, the patient's perspective, the expert's perspective and the clinician's perspective, respectively, on the most relevant aspects of functioning of persons living with schizophrenia. The final definition of ICF Core Sets for schizophrenia have been determined by integrating the results of preliminary studies in a consensus conference with international expert.ResultThe experts included 97 categories in the Comprehensive ICF Core Set and 25 categories in the Brief ICF-CS. The specific categories of each ICF-CS are shown in this presentation. The Comprehensive ICF-CS can guide multidisciplinary assessments of functioning in persons with schizophrenia, and the brief version is ideal for use in both clinical and epidemiological research, since it includes a small and practical number of categories, but sufficiently wide for finding utility in clinical assessments.ConclusionICF-CS are being designed with the goal of providing useful standards for research, clinical practice and teaching, and it will stimulate research and will improve understanding of functioning, health and environmental factors in schizophrenia.Disclosure of interestThe authors have not supplied their declaration of competing interest.

scholarly journals The effect of the application of the exact and approximate methods on values of selected ecological indices

2014 ◽  
Vol 67 (1) ◽  
pp. 39-46
Author(s):  
Maria Ługowska ◽  
Zofia Rzymowska
Keyword(s):  
Wiener Index ◽  
Ecological Indices ◽  
Exact Methods ◽  
Approximate Methods ◽  
Winter Cereals ◽  
Spring Cereals ◽  
Phytosociological Relevés ◽  
Exact And Approximate Methods ◽  
Potato Crops ◽  
Tuber Crops

<p>The work presents the results of a study on the biodiversity of agrocenoses using ecological indices. In order to calculate the measures, phytosociological relevés were made and exact methods were applied in winter cereals, spring cereals, tuber crops and stubble fields. The objective of the work was to compare ecological indices (Simpson’s index of dominance <em>C</em>, Simpson’s index of species richness <em>D,</em> and Shannon-Wiener index of biodiversity <em>H</em>’) calculated using the number of plants and their cover determined based on the degree of presence. Moreover, correlation analysis was conducted between the indices computed using the two approaches applied.</p><p>The results of the study revealed significant differences between all the indices calculated using the exact and approximate methods. In turn, comparisons of the measures computed for individual crops showed significant differences only for potato crops and winter cereals. No significant differences were found between the indicators calculated for spring cereals and stubble fields.</p>

Scheduling the two-machine open shop problem under resource constraints for setting the jobs

2013 ◽  
Vol 211 (1) ◽  
pp. 333-356 ◽  
Author(s):  
Ammar Oulamara ◽  
Djamal Rebaine ◽  
Mehdi Serairi
Keyword(s):  
Resource Constraints ◽  
Open Shop ◽  
Open Shop Problem
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