Hasan Bal

Improving the discrimination power and weights dispersion in the data envelopment analysis

Data envelopment analysis (DEA) has been a very popular method for measuring and benchmarking relative efficiency of peer decision making units (DMUs) with multiple input and outputs. Beside of its popularity, DEA has some drawbacks such as unrealistic input-output weights and lack of discrimination among efficient DMUs. In this study, two new models based on a multi-criteria data envelopment analysis (MCDEA) are developed to moderate the homogeneity of weights distribution by using goal programming (GP). These goal programming data envelopment analysis models, GPDEA-CCR and GPDEA-BCC, also improve the discrimination power of DEA.

Comparing performances of backpropagation and genetic algorithms in the data classification

Artificial neural networks (ANN) have a wide ranging usage area in the data classification problems. Backpropagation algorithm is classical technique used in the training of the artificial neural networks. Since this algorithm has many disadvantages, the training of the neural networks has been implemented with the binary and real-coded genetic algorithms. These algorithms can be used for the solutions of the classification problems. The real-coded genetic algorithm has been compared with other training methods in the few works. It is known that the comparison of the approaches is as important as proposing a new classification approach. For this reason, in this study, a large-scale comparison of performances of the neural network training methods is examined on the data classification datasets. The experimental comparison contains different real classification data taken from the literature and a simulation study. A comparative analysis on the real data sets and simulation data shows that the real-coded genetic algorithm may offer efficient alternative to traditional training methods for the classification problem.

A new method based on the dispersion of weights in data envelopment analysis

One of the drawbacks of the data envelopment analysis (DEA) is the problem of lack of discrimination among efficient decision making units (DMUs) and hence yielding many numbers of DMUs as efficient. The main purpose of this study is to overcome this inability. In the case in which the minimization of the coefficient of variation (CV) for input-output weights is added to the DEA model, more reasonable and more homogeneous input-output weights are obtained. For this new proposed model based on the CV it is observed that the number of efficient DMUs is reduced, improving the discrimination power. When this new approach is applied to two well-known examples in the literature, and a real-world data of OECD countries, it has been seen that the new model yielded a more balanced dispersion of input-output weights and reduced the number of efficient DMUs. In addition, the applicability of the new model is tested by a simulation study.

Goal programming approaches for data envelopment analysis cross efficiency evaluation

Abstract Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.

An experimental comparison of the new goal programming and the linear programming approaches in the two-group discriminant problems

The aim of this article is to consider a new linear programming and two goal programming models for two-group classification problems. When these approaches are applied to the data of real life or of simulation, our proposed new models perform well both in separating the groups and the group-membership predictions of new objects. In discriminant analysis some linear programming models determine the attribute weights and the cut-off value in two steps, but our models determine simultaneously all of these values in one step. Moreover, the results of simulation experiments show that our proposed models outperform significantly than existing linear programming and statistical approaches in attaining higher average hit-ratios.

A new mathematical programming approach to multi-group classification problems

In this paper we introduce a goal programming formulation for the multi-group classification problem. Although a great number of mathematical programming models for two-group classification problems have been proposed in the literature, there are few mathematical programming models for multi-group classification problems. Newly proposed multi-group mathematical programming model is compared with other conventional multi-group methods by using different real data sets taken from the literature and simulation data. A comparative analysis on the real data sets and simulation data shows that our goal programming formulation may suggest efficient alternative to traditional statistical methods and mathematical programming formulations for the multi-group classification problem.

A modification of a mixed integer linear programming (MILP) model to avoid the computational complexity

Having multiple optimal solutions to weights affects to a great extent the consistency of operations related to weights. The cross efficiency method is the most frequently studied topic in data envelopment analysis (DEA) literature. Originally, the cross efficiency method included the efficiency evaluations that were obtained for a decision making unit (DMU) by the classical DEA for the reuse of optimal weights in other DMUs. As the optimal weights in classical DEA solutions usually have multiple solutions, this reduces the usefulness of the cross evaluation. Lam (J Oper Res Soc 61:134–143, 2010) proposed a mixed-integer linear programming (MILP) formulation based on linear discriminant analysis and super efficiency method to choose suitable weight sets to be used in cross efficiency evaluation. In this study, Lam’s MILP model has been modified to reduce the steps during the solution process. The model also becomes a linear programming model after the modification to make it easier to use and to reduce the computational complexity. Numerical examples indicate that the proposed weight determination model both reduces the steps and minimizes computational complexity. Furthermore, it has similar performance with Lam’s MILP model for the cross efficiency evaluation.

An Archimedean Copula Family with Hyperbolic Cotangent Generator

Hyperbolic cotangent function is proposed as a generator of new Archimedean copula family and several properties are revealed. To show performance in real data analysis, application to modeling dep...

Additive generators of copulas

In this study, we discuss additive generators of copulas with a fixed dimension n ? 2 and additive generators that yield copulas for any dimension n ? 2 . We review the reported methods used to construct additive generators of copulas, and we introduce and exemplify some new construction methods.

Ranking the airports in Turkey with data envelopment analysis and principal component analysis

Data envelopment analysis (DEA) is a linear programming (LP) technique for measuring the relative efficiency of peer decision making units(DMUs) when multiple inputs and outputs are present. This objective method was originated by Charnes et al. (1978). DEA can be used, not only for estimating the performance of units, but also for solving other problems of management such as aggregating several preference rankings into single ranking. Data Envelopment Analysis (DEA) model selection is an important step and problematic. Efficiency values for decision making units are connected to input and output data. It also depends on the number of outputs plus inputs. A new method for model selection is proposed in this study. Efficiencies are calculated for all possible DEA model specifications. It is shown that model equivalence or dissimilarity can be easily assessed using this approach. The results are analysed using Principal Component Analysis.