eng
Firouzabad Institute of Higher Education
Annals of Optimization Theory and Practice
2588-3666
2588-5995
2019-09-01
2
2
1
9
10.22121/aotp.2019.194950.1021
105907
Original Article
Evaluating efficiency and ranking of technical efficient and inefficient units
Mustapha D. Ibrahim
mibrahim1@hct.ac.ae
1
Sahand Daneshvar
sahand.daneshvar@emu.edu.tr
2
Industrial Engineering Technology, Higher Colleges of Technology, UAE
Department of Industrial Engineering, Eastern Mediterranean University, Famagusta, North Cyprus, via Mersin 10, Turkey
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.
https://aotp.fabad-ihe.ac.ir/article_105907_5f7c63f5634a49266c30e50250e19303.pdf
Efficiency
Ranking
Arash method
Facet Analysis
Data Envelopment Analysis
eng
Firouzabad Institute of Higher Education
Annals of Optimization Theory and Practice
2588-3666
2588-5995
2019-09-01
2
2
11
24
10.22121/aotp.2019.198947.1022
105908
Original Article
A novel solution approach for solving intuitionistic fuzzy transportation problem of type-2
Rohollah Taghaodi
taghaode@yahoo.com
1
Department of Mathematics, Kashan Branch, Islamic Azad University, Kashan, Iran
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.
https://aotp.fabad-ihe.ac.ir/article_105908_ee6bd5db37a3cc5eab39201c9db13a00.pdf
Triangular intuitionistic fuzzy number
Accuracy function
Intuitionistic fuzzy transportation problem of type-2
optimal solution
eng
Firouzabad Institute of Higher Education
Annals of Optimization Theory and Practice
2588-3666
2588-5995
2019-09-01
2
2
25
33
10.22121/aotp.2020.212629.1024
105909
Original Article
Simulation of the game of chaos and fractals
Hojjat Allah Ebadizadeh
ebadizadeh.h@gmail.com
1
Ebrahim Nazari Farikhi
e60_itmgtn@yahoo.com
2
Faculty of Basic Sciences, Imam Ali University, Tehran, Iran
IT Management, Imam Ali University, Tehran, Iran
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.
https://aotp.fabad-ihe.ac.ir/article_105909_03b49679fa85de1de3a5ac39e84a6d7e.pdf
fractal
absorbent
Chaos games
Random algorithm
Lyapunov view
eng
Firouzabad Institute of Higher Education
Annals of Optimization Theory and Practice
2588-3666
2588-5995
2019-09-01
2
2
35
45
10.22121/aotp.2020.213803.1025
105912
Original Article
Mathematical simulation of contagious virus spread
Ebrahim Nazari Farokhi
e60_itmgtn@yahoo.com
1
IT Management, Imam Ali University, Tehran, Iran
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.
https://aotp.fabad-ihe.ac.ir/article_105912_559e5e8ab72be2ec37f18c1a22038406.pdf
Contagious Disease
susceptible
Treated
Improved