Iranian Journal of Optimization: 1 (1)

Open Access Article

1 - Numerical solution of Fredholm and Volterra integral equations using the normalized Müntz−Legendre polynomials
فرشته صائمی حمیده ابراهیمی محمود شفیعی

The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operationa More

The current research approximates the unknown function based on the normalized Müntz−Legendre polynomials (NMLPs) in conjunction with a spectral method for the solution of nonlinear Fredholm and Volterra integral equations. In this method, by using operational matrices, a system of algebraic equations is derived that can be readily handled through the use of the Newton scheme. The stability, error bound, and convergence analysis of the method are discussed in detail by preparing some theorems. Several illustrative examples are provided formally to show the efficiency of the proposed method. Manuscript profile

Open Access Article

2 - A Bounded Additive Model for Efficiency Evaluation in Two-Stage Production Systems With Negative Data
حمیدرضا بابائی اصیل رضا کاظمی متین محسن خون سیاوش زهره مقدس

Data Envelopment Analysis (DEA) is a method for assessing the efficiency of Decision Making Units (DMUs). Traditional DEA models do not examine the potential differences between two stages caused by intermediate operations. As a result, DEA has been extended to evaluate More

Data Envelopment Analysis (DEA) is a method for assessing the efficiency of Decision Making Units (DMUs). Traditional DEA models do not examine the potential differences between two stages caused by intermediate operations. As a result, DEA has been extended to evaluate the efficiency of two-stage processes. In these processes, all outputs of the first stage are intermediate operations that comprise the inputs of the second stage. The input data in real-world applications may have negative values. In this study, considering the importance of network production processes, we deal with the efficiency evaluation of two-stage production units with negative data. Also, we extend CRS (constant returns to scale) bounded additive model for the efficiency evaluation of the two-stage units in the presence of negative data. For illustration, we evaluate the efficiency and ranking of 36 airlines by applying the new model. Manuscript profile

Open Access Article

3 - On the Picard-Mann approach for hybridizing the double direction method for solving a system of nonlinear equations.
Abubakar Halilu Aliyu kiri Mohammed Waziri

In this article, the improvement of the numerical performance of the iterative scheme presented by Halilu and Waziri in [5] is considered. This is made possible by hybridizing it with Picard-Mann hybrid iterative process. In addition, the step length is calculated using More

In this article, the improvement of the numerical performance of the iterative scheme presented by Halilu and Waziri in [5] is considered. This is made possible by hybridizing it with Picard-Mann hybrid iterative process. In addition, the step length is calculated using the inexact line search technique. Under the preliminary conditions, the proposed method's global convergence is established. The numerical experiment shown in this paper depicts the efficiency of the proposed method, which improved the results than the double direction method [5], existing in the literature. Manuscript profile

Open Access Article

4 - An Entropy Based Shapley Value for Ranking in Data Envelopment Analysis
رضا فلاح نژاد ساناز اسدی رحمتی کیوان مرادی پور

In traditional DEA, DMUs are divided into Efficient and inefficient, but the score of all efficient units are equal to one and there is no discrimination between them. Thus many ranking methods are proposed to increase discrimination power. This paper proposes an integr More

In traditional DEA, DMUs are divided into Efficient and inefficient, but the score of all efficient units are equal to one and there is no discrimination between them. Thus many ranking methods are proposed to increase discrimination power. This paper proposes an integrated framework of cooperative games and entropy to rank efficient units by considering efficient units as players in a cooperative game, A subset of these players is defined as the coalition of S. The sum of the efficiency of inefficient DMUs with respect to the frontier of production possibility set contain inefficient DMUs and the member of coalition S is defined as the characteristic function of the coalition S, which is used to determine the marginal effect of efficient DMUs. Then, a new Shapley Value resulted from aggregating the marginal effects of efficient DMUs weighted by Shannon entropy is used for ranking efficient DMUs. For the first time, we use the entropy to create a Shapley value for calculating the rank of efficient units.. Two examples are provided to illustrate the applicability of proposed model. Manuscript profile

Open Access Article

5 - meta-heuristic algorithms to solve the problem of terminal facilities on a real scale
مهدی فضلی فرزین مدرس خیابانی بهروز دانشیان

a b s t r a c tOur main goal in this article is to arrange terminal facilities, place different departments, stores and units in predefined areas in such a way as to minimize the cost of moving customers and transportation staff. Especially in large-scale terminals with More

a b s t r a c tOur main goal in this article is to arrange terminal facilities, place different departments, stores and units in predefined areas in such a way as to minimize the cost of moving customers and transportation staff. Especially in large-scale terminals with several different transport segments, it is important for terminal performance to be close to interactive units. Today, meta-heuristic methods are often used to solve optimization problems such as facility design. in this study; The design of the various units, stores, and rooms of a large-scale real terminal was organized using three meta-heuristic algorithms: Migratory Bird Optimization (MBO), Taboo Search (TS), and Simulated Simulation (SA). The results were compared with the existing terminal design. As a result, MBO and SA metaheuristic algorithms have provided the best results, which improve the efficiency of the existing terminal design to an acceptable level. Manuscript profile

Open Access Article

6 - Grading of Decision-Making Units with Multi-Period Two-Stage Network Structure: a Method Based on Relative Data Envelopment Analysis
مقصود احمد خانلو قراخانلو نیما آذرمیر شتربانی قاسم توحیدی شبنم رضویان روح اله عباسی

Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. De More

Data envelopment analysis is always considered as a non-parametric method for measuring the efficiency of a set of decision units. The efficiency number obtained from standard models is a criterion for comparing the performance of each decision unit with other units. Despite the many strengths of these models, one of their weaknesses is the lack of distinction between efficient units. Also, these models do not pay attention to the internal structure of the units and have a black box view. To solve these problems, relational data envelopment analysis models are used, which are much more cost-effective in terms of time and cost; But these models are static and do not take time into evaluation. In this paper, a method has been proposed for grading of the decision making units with multi- period two stages network structure using relative data envelopment analysis. Three different perspective are introduced for assessment of efficiency in time periods via relative data envelopment analysis. Proportionate with each perspective, an efficiency number is obtained for any decision making unit. Then three efficiency numbers obtained in the mentioned method is combined with Shannon entropy method and a total efficiency criterion is defined for each unit. Finally, this measure is considered as the main indicator for the units grading. The results of implementation of the mentioned algorithm on the real example and comparison with the similar methods clarify the strength of this algorithm. Manuscript profile

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