@article { author = {Ibrahim, Mustapha D. and Daneshvar, Sahand}, title = {Evaluating efficiency and ranking of technical efficient and inefficient units}, journal = {Annals of Optimization Theory and Practice}, volume = {2}, number = {2}, pages = {1-9}, year = {2019}, publisher = {Firouzabad Institute of Higher Education}, issn = {2588-3666}, eissn = {2588-5995}, doi = {10.22121/aotp.2019.194950.1021}, abstract = {Maintaining the efficiency score of efficient units and distinguishing between technical efficiency and efficiency are very essential topics in operations research. The Arash method is a new technique in Data Envelopment Analysis (DEA) for estimating the performance of units and ranking. The Arash method is based on additive DEA model (ADD). In this study we expand the Arash method by using facet analysis to modify the production possibility set (PPS). This modification avoids the effect of the weak part of PPS frontier which can propose a bias efficiency evaluation to DMUs placed on or compared with the weak part of the frontier. We integrated the attributes of the Arash method and modified variable return to scale model, consequently showing the true efficiency score and ranks of units associated with the weak part of the frontier, also identifying “technical efficient” and “inefficient” DMUs. The efficiency score of DMUs located at the strong part of the frontier remains the same, only those associated with the weak part are modified. A numerical example is used to show the effectiveness of the proposed model in comparison with the Arash method.}, keywords = {Efficiency,Ranking,Arash method,Facet Analysis,Data Envelopment Analysis}, url = {https://aotp.fabad-ihe.ac.ir/article_105907.html}, eprint = {https://aotp.fabad-ihe.ac.ir/article_105907_5f7c63f5634a49266c30e50250e19303.pdf} } @article { author = {Taghaodi, Rohollah}, title = {A novel solution approach for solving intuitionistic fuzzy transportation problem of type-2}, journal = {Annals of Optimization Theory and Practice}, volume = {2}, number = {2}, pages = {11-24}, year = {2019}, publisher = {Firouzabad Institute of Higher Education}, issn = {2588-3666}, eissn = {2588-5995}, doi = {10.22121/aotp.2019.198947.1022}, abstract = {In the cases that decision maker faces with uncertainty and hesitation together for determining a parameter of an optimization problem, considering intuitionistic fuzzy parameters is useful. A transportation problem with triangular intuitionistic fuzzy unit transportation costs is focused in this study. The fuzzy costs are crisped using the accuracy function of the literature. Then the algorithms e.g. the north west corner method, the least cost method, and the Vogel’s approximation method are applied to obtain an initial basic feasible solution for the crisp version of the problem. After that the modified distribution method is used to obtain the optimal solution of the problem. The performed computational experiments show the superiority of the proposed approach over those of the literature from the results’ quality and the computational difficulty point of views.}, keywords = {Triangular intuitionistic fuzzy number,Accuracy function,Intuitionistic fuzzy transportation problem of type-2,optimal solution}, url = {https://aotp.fabad-ihe.ac.ir/article_105908.html}, eprint = {https://aotp.fabad-ihe.ac.ir/article_105908_ee6bd5db37a3cc5eab39201c9db13a00.pdf} } @article { author = {Ebadizadeh, Hojjat Allah and Nazari Farikhi, Ebrahim}, title = {Simulation of the game of chaos and fractals}, journal = {Annals of Optimization Theory and Practice}, volume = {2}, number = {2}, pages = {25-33}, year = {2019}, publisher = {Firouzabad Institute of Higher Education}, issn = {2588-3666}, eissn = {2588-5995}, doi = {10.22121/aotp.2020.212629.1024}, abstract = {In this paper, the role of the iteration function system in the geometric modeling of two-dimensional and three-dimensional fractal objects is presented. We also study chaos game display technology, which is a very important and efficient tool in the biochemistry and military fields. This method provides a good template for amplified and generated sequences such as the DNA sequence. See Reference 5. The game of chaos provides many interesting patterns and is therefore a very important tool for examining the organization of units. In this paper, we investigate the game of chaos and chaotic systems, and by giving an example, we have obtained the speed of creating a system disorder by Liapanov's view.}, keywords = {fractal,absorbent,Chaos games,Random algorithm,Lyapunov view}, url = {https://aotp.fabad-ihe.ac.ir/article_105909.html}, eprint = {https://aotp.fabad-ihe.ac.ir/article_105909_03b49679fa85de1de3a5ac39e84a6d7e.pdf} } @article { author = {Nazari Farokhi, Ebrahim}, title = {Mathematical simulation of contagious virus spread}, journal = {Annals of Optimization Theory and Practice}, volume = {2}, number = {2}, pages = {35-45}, year = {2019}, publisher = {Firouzabad Institute of Higher Education}, issn = {2588-3666}, eissn = {2588-5995}, doi = {10.22121/aotp.2020.213803.1025}, abstract = {In this article we study the prevalence of contagious disease in a community. To this end, we view society as a dynamic system and apply mathematical equations and relationships to it. First, we present the history of mathematical modeling in the field of contagious diseases and the work done in this field, then find out the probability of the virus spreading in a population with a number of people with contagious disease, and finally the differential equation of disease spread. Obtain the environment and then calculate the time it took to get the disease. In addition, we also plan to provide a model to describe how a virus is transmitted. In this model, we have four boxes called susceptible individuals, virus carriers, treated individuals, and improved individuals. We obtain the differential equations of growth and decline of each of these boxes and examine the stability condition of the system.}, keywords = {Contagious Disease,susceptible,Treated,Improved}, url = {https://aotp.fabad-ihe.ac.ir/article_105912.html}, eprint = {https://aotp.fabad-ihe.ac.ir/article_105912_559e5e8ab72be2ec37f18c1a22038406.pdf} }