جستجوی مقالات مرتبط با کلیدواژه « Cross-efficiency » در نشریات گروه « ریاضی »

In the dynamic world of financial investment, crafting an optimal stock portfolio that judiciously balances risk, return, and efficiency emerges as a critical challenge. Despite the wealth of research on financial portfolio optimization, prevailing methodologies predominantly emphasize either risk minimization or return maximization, often overlooking the imperative for a holistic strategy that simultaneously boosts efficiency and effectiveness. Addressing this gap in the literature, this study introduces an innovative four-objective model that intricately blends risk, return, and efficiency considerations for the strategic selection of stock portfolios. This model ingeniously integrates the foundational principles of Markowitz's mean-variance analysis with the sophisticated network data envelopment analysis (NDEA) techniques, significantly refining the portfolio selection methodology. It further distinguishes itself by incorporating returns represented as trapezoidal intuitionistic fuzzy numbers, adeptly capturing the inherent uncertainties in financial returns. Additionally, the model employs the network data envelopment analysis's cross-efficiency principle, providing a nuanced measure of company performance. To effectively navigate the complexities of this model, we deploy the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a multi-objective genetic algorithm, demonstrating the model's capability to unearth optimal solutions efficiently. The comparative analysis highlights that the proposed model significantly outperforms the efficiency and effectiveness of existing models, marking a substantial advancement in portfolio optimization strategies.

Cross-efficiency is a frequently used method for ranking decision-making units in Data Envelopment Analysis (DEA). A fundamental weakness of this method which has been quite problematic is the presence of multiple optimal weights along with selection of zero values by many of these multiple weights in calculating cross-efficiency. In the current paper it is tried to provide a method which through utilizing fair distribution of weights resolve the mentioned problems and in this way give more validity to the cross-efficiency method in raking decision-making units.

This study combines Data Envelopment Analysis (DEA) with machine learning clustering method in datamining for finding the most efficient Decision Making Unit (DMU) and the best clustering algorithm, respectively. The problem of assessment of units by using DEA may not be straightforward due to the data uncertainty. Several scholars have been attracted to develop methods which incorporate uncertainty into input/output values in the DEA literature. On the other hand, in many real world applications, the data is reported in the form of intervals. This means that each input/output value is selected from a symmetric box. In the DEA literature, this type of uncertainty has been addressed as Interval DEA approaches. The main goal of this study is to evaluate the efficiency of banks in the case of data uncertainty with cross-efficiency method in the DEA literature. For this purpose, we consider the BCC-CCR and CCR-BCC models in the presence of uncertain data to find the superior model. After applying the optimization models, in machine learning step, clustering method is applied. Clustering is a procedure for grouping similar items together which this group is called the cluster. Also, the different clustering algorithms can be used according to the behavior of data. In this study, we apply the farthest first and expectation maximization algorithms and show that, in the case of data uncertainty, the BCC-CCR and farthest first algorithms are as a superior optimization model and machine learning algorithm, respectively.

When we use the CCR model in the input-oriented with fuzzy data for ranking with the help of cross-efficiency, there is a possibility that the model will find a different optimal answer. This means that the ranking is not unique, that is, a decision-making unit may be assigned several ranks. Here, the judgment regarding the ranking faces a problem. To solve this problem, a secondary objective is determined for weight selection. According to that secondary objective, a suitable weight is selected from among the optimal solutions. In this article, the secondary goal of the concept of symmetrizing the weights plays a fundamental role in solving the mentioned problem. The model selects weights that are symmetrical, the act of choosing symmetrical weights causes many weights that are not useful to be removed from the set. The decision-making unit that selects symmetrical weights for all indicators, has a better performance than the decision-making unit that does not use symmetrical weights and covers its weak points with low weight and highlights its strong points with high weight. The model along with the mentioned secondary objective is used to evaluate decision-making units with fuzzy input and output, by choosing the optimal weight, a cross-efficiency table is formed. By using the cross-efficiency table, the efficiency of each unit is determined and ranked compared to other units. Units are done.

Cross-efficiency is a ranking technique based on the peer-evaluation that can increase the discriminating power between efficient decision-making units. This paper intends to assess the two-stage processes consisting of undesirable outputs by applying the cross-efficiency evaluation. Given undesirable outputs, the directional distance function under the weak disposability assumption is utilized. The proposed model under variable returns to scale is designed, which makes it different from the previous models. Furthermore, it can reduce the zero optimal coefficients. By measuring the inputs and outputs inefficiency, the whole system and each of its two stages rank, simultaneously. To analyze the suggested method, an application on the industrial productions of 30 regions of China is used.

Cross-efficiency method is a useful tool for efficiency evaluation of decision-making units in data envelopment analysis. The issue of non-uniqueness of optimal weights in the cross-efficiency evaluation has reduced the usefulness of this powerful method. This paper introduces a new method for selection of weights profiles as the secondary goal in cross-efficiency with stochastic data. The issue of zero-weight which implies the exclusion of some variables from the assessments, is also addressed in the new proposed method. The provided weights selection method also reduces the weight disparity in the achieved weights profile. In the peer-restricted stochastic cross-efficiency evaluation, the new approach guarantees that different DMUs should not attach very different weights to the same variables. As the result, a common set of weights using the idea of similarity between sets of weights is achieved in the proposed computation method. Some numerical examples are also used for illustration and comparison purposes.

In traditional data envelopment analysis (DEA), the efficiency and productivity changes computations are based on an optimistic perspective and an efficient unit may perform rather poorly when the realist weights are assigned to inputs and outputs. Hence, the results of productivity change of decision making units (DMUs) between two time periods may change from progress to regress or vice versa when the weights are modified. Because of the cross efficiency merits, we use it to obtain a common set of weights so called common set of cross weights. On the other hand, we need a base for comparing the productivity change of DMUs. To this end, the common set of cross weights are used to approximate the cross efficient frontier as a base for determining cross Malmquist (CM) index for evaluating the productivity change. This leads to introduce a new efficiency, weight efficiency, and the decomposition of the cross efficiency. Some DEA and cross efficiency models are modified to find the value of the proposed CM index and its components. An empirical example is used to compare the proposed method and the technical Malmquist index.

The purpose of the current paper is to propose a new model for the secondary goal in DEA by introducing secondary objective function. The proposed new model minimizes the average of the absolute deviations of data points from their median. Similar problem is studied in a related model by Liang et al. (2008), which minimizes the average of the absolute deviations of data points from their mean. By using two well known data sets, which are also used by Liang et al.(2008), and Greene (1990)  we compare the results of the proposed new model and several other models.

One way to rank DMUs in DEA is the cross efficiency method. In this method, the efficiency of each DMU is calculated by other DMUs optimum weights, which makes the ranking more acceptable for managers. Existing alternative optimum weights in cross efficiency method lead to several ranks for DMUs. Several secondary goals have introduced to avoid this problem, till now. In this paper, a new model is presented, that would be satisfying and acceptable for all DMUs. Therefore, by solving this model, the optimum weights are agreeable and fairy for DMUs.

Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problems to overcome the problem of determining weights. In this study, a membership function was defined base on the results of CCR model and cross efficiency, and by using this membership function in a proposed model, we obtained a common set of weights for all DMUs. Finally, by solving a sample problem, the proposed algorithm was explained.

The cross efficiency evaluation is used to performance measurement of decision making units in data envelopment analysis concept. One of the most important shortcoming of this method is existing alternative optimal solution and therefore, the efficiency scores are not unique. We are going to summarize the pervious models proposed by researchers and suggest an alternative secondary goal approach to modify them to remove the shortcomings and difficulties of basic cross efficiency method. Also we tried the presented model to rank the efficient units.

Because of the piecewise linear nature of the data envelopment analysis (DEA) frontier, the optimal multipliers of the DEA models may not be unique. Choosing weights from alternative optimal solutions of dual multiplier models is one of the most frequently studied subjects in the context of DEA. In this paper, the authors have been inspired by the idea of Cooper et al. (2011) to propose a linear programming problem in which a specific decision making unit chooses the optimal solution of a linear program as the profile of weights for use in the cross-efficiency calculation. The approach proposed in this paper to determine input/output weights, prohibit the large differences in weights in cross efficiency evaluation. A real case on Chinese cities and special economic zones is given to illustrate the applicability of the proposed approach.