A hybrid radial basis function and data envelopment analysis neural network for classification

We propose a hybrid radial basis function network-data envelopment analysis (RBFN-DEA) neural network for classification problems. The procedure uses the radial basis function to map low dimensional input data from input space ℜ to a high dimensional ℜ⁺ feature space where DEA can be used to learn the classification function. Using simulated datasets for a non-linearly separable binary classification problem, we illustrate how the RBFN-DEA neural network can be used to solve it. We also show how asymmetric misclassification costs can be incorporated in the hybrid RBFN-DEA model. Our preliminary experiments comparing the RBFN-DEA with feed forward and probabilistic neural networks show that the RBFN-DEA fares very well.     

A robust optimization approach for imprecise data envelopment analysis

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it’s supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.     

Ranking efficient decision-making units in data envelopment analysis using fuzzy concept

This paper introduces a new mathematical method for improving the discrimination power of data envelopment analysis and to completely rank the efficient decision-making units (DMUs). Fuzzy concept is utilised. For this purpose, first all DMUs are evaluated with the CCR model. Thereafter, the resulted weights for each output are considered as fuzzy sets and are then converted to fuzzy numbers. The introduced model is a multi-objective linear model, endpoints of which are the highest and lowest of the weighted values. An added advantage of the model is its ability to handle the infeasibility situation sometimes faced by previously introduced models.     

Common weights data envelopment analysis with uncertain data: A robust optimization approach

One of the primary issues on data envelopment analysis (DEA) models is the reduction of weights flexibility. There are literally several studies to determine common weights in DEA but none of them considers uncertainty in data. This paper introduces a robust optimization approach to find common weights in DEA with uncertain data. The uncertainty is considered in both inputs and outputs and a suitable robust counterpart of DEA model is developed. The proposed robust DEA model is solved and the ideal solution is found for each decision making units (DMUs). Then, the common weights are found for all DMUs by utilizing the goal programming technique. To illustrate the performance of the proposed model, a numerical example is solved. Also, the proposed model of this paper is implemented by using some actual data from provincial gas companies in Iran.     

Fuzzy data envelopment analysis and its application to location problems

In this paper, fuzzy DEA (data envelopment analysis) models are proposed for evaluating the efficiencies of objects with fuzzy input and output data. The obtained efficiencies are also fuzzy numbers that reflect the inherent ambiguity in evaluation problems under uncertainty. An aggregation model for integrating fuzzy attribute values is provided in order to rank objects objectively. Using the proposed method, a case study involving a restaurant location problem is analyzed in detail. Rent of establishment, traffic amount, level of security, consumer consumption level and competition level are identified as the primary factors in determining an ideal location for a Japanese-style rotisserie restaurant. Based on field investigation, the uncertain information on primary factors is represented by fuzzy numbers. Using the fuzzy aggregation model, the best location of restaurant is determined. The case study shows that fuzzy DEA models can be quite useful for solving business problems under uncertainty.     

Cross efficiency evaluation method based on weight-balanced data envelopment analysis model

In this paper, the cross efficiency evaluation method, regarded as a DEA extension tool, is firstly reviewed for its utilization in identifying the Decision Making Unit (DMU) with the best practice and ranking the DMUs by their respective cross-efficiency scores. However, we then point out that the main drawback of the method lies in non-uniqueness of cross-efficiency scores resulted from the presence of alternate optima in traditional DEA models, obviously making it become less effective. Aiming at the research gap, a weight-balanced DEA model is proposed to lessen large differences in weighted data (weighted inputs and weighted outputs) and to effectively reduce the number of zero weights for inputs and outputs. Finally, we use two examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choosing of weights in cross-efficiency evaluations.     

Minimizing deviations of input and output weights from their means in data envelopment analysis

In this paper, we propose a model that minimizes deviations of input and output weights from their means for efficient decision-making units in data envelopment analysis. The mean of an input or output weight is defined as the average of the maximum and the minimum attainable values of the weight when the efficient decision making unit under evaluation remains efficient. Alternate optimal weights usually exist in the linear programming solutions of efficient decision-making units and the optimal weights obtained from most of the linear programming software are somewhat arbitrary. Our proposed model can yield more rational weights without a priori information about the weights. Input and output weights can be used to compute cross-efficiencies of decision-making units in peer evaluations or group decision-making units, which have similar production processes via cluster analysis. If decision makers want to avoid using weights with extreme or zero values to access performance of decision-making units, then choosing weights that are close to their means, may be a rational choice.     

Ranking alternatives in a preferential voting system using fuzzy concepts and data envelopment analysis

In this paper, a new method for aggregating the opinions of experts in a preferential voting system is proposed. The method, which uses fuzzy concept in handling crisp data, is computationally efficient and is able to completely rank the alternatives. Through this method, the number of votes for certain rank position that each alternative receives are first grouped together to form fuzzy numbers. The nearest point to a fuzzy number concept is then used to introduce an artificial ideal alternative. Data envelopment analysis is next used to find the efficiency scores of the alternatives in a pair-wise comparison with the artificial ideal alternative. Alternatives are rank based on these efficiency scores. If the alternatives are not completely ranked, a weight restriction method also based on fuzzy concept is used on the un-discriminated alternatives until they are completely ranked. Two examples are given for illustration of the method.     

An interactive application of data envelopment analysis in microcomputers

This article describes a general-purpose microcomputer code for data envelopment analysis (DEA) that incorporates four different DEA models in the form of a user-friendly, menu-driven structure.Research financially supported by Dean's Professorship, College of Business, the Ohio State University.     

Ranking discovered rules from data mining with multiple criteria by data envelopment analysis

In data mining applications, it is important to develop evaluation methods for selecting quality and profitable rules. This paper utilizes a non-parametric approach, Data Envelopment Analysis (DEA), to estimate and rank the efficiency of association rules with multiple criteria. The interestingness of association rules is conventionally measured based on support and confidence. For specific applications, domain knowledge can be further designed as measures to evaluate the discovered rules. For example, in market basket analysis, the product value and cross-selling profit associated with the association rule can serve as essential measures to rule interestingness. In this paper, these domain measures are also included in the rule ranking procedure for selecting valuable rules for implementation. An example of market basket analysis is applied to illustrate the DEA based methodology for measuring the efficiency of association rules with multiple criteria.     

A data envelopment analysis method for optimizing multi-response problem with censored data in the Taguchi method

Taguchi method is an efficient method used in off-line quality control in that the experimental design is combined with the quality loss. This method including three stages of systems design, parameter design, and tolerance design has been deeply discussed in Phadke [Quality engineering using robust design (1989)]. It is observable that most industrial applications solved by Taguchi method belong to single-response problems. However, in the real world more than one quality characteristic should be considered for most industrial products, i.e. most problems customers concern about are multi-response problems. As a result, Taguchi method is not appropriate to optimize a multi-response problem. At present, it is still necessary to rely on the engineering judgment to optimize the multi-response problem; therefore uncertainty will be increased during the decision-making process. On the other hand, due to some uncontrollable causes occurring, only a portion of experiment can be completed so that the censored data will be produced. Traditional approaches for analysis of censored data are computationally complicated. In order to overcome above two shortages, this article proposes an effective procedure on the basis of the neural network (NN) and the data envelopment analysis (DEA) to optimize the multi-response problems. A case study of improving the quality of hard disk driver in Su and Tong [ Total Quality Management 8 (1997) 409] is resolved by the proposed procedure. The result indicates that it yields a satisfactory solution.     

A unified model for detecting efficient and inefficient outliers in data envelopment analysis

Data envelopment analysis (DEA) uses extreme observations to identify superior performance, making it vulnerable to outliers. This paper develops a unified model to identify both efficient and inefficient outliers in DEA. Finding both types is important since many post analyses, after measuring efficiency, depend on the entire distribution of efficiency estimates. Thus, outliers that are distinguished by poor performance can significantly alter the results. Besides allowing the identification of outliers, the method described is consistent with a relaxed set of DEA axioms. Several examples demonstrate the need for identifying both efficient and inefficient outliers and the effectiveness of the proposed method. Applications of the model reveal that observations with low efficiency estimates are not necessarily outliers. In addition, a strategy to accelerate the computation is proposed that can apply to influential observation detection.     

The voting analytic hierarchy process method for discriminating among efficient decision making units in data envelopment analysis

Making optimal use of available resources has always been of interest to humankind, and different approaches have been used in an attempt to make maximum use of existing resources. Limitations of capital, manpower, energy, etc., have led managers to seek ways for optimally using such resources. In fact, being informed of the performance of the units under the supervision of a manager is the most important task with regard to making sensible decisions for managing them. Data envelopment analysis (DEA) suggests an appropriate method for evaluating the efficiency of homogeneous units with multiple inputs and multiple outputs. DEA models classify decision making units (DMUs) into efficient and inefficient ones. However, in most cases, managers and researchers are interested in ranking the units and selecting the best DMU. Various scientific models have been proposed by researchers for ranking DMUs. Each of these models has some weakness(es), which makes it difficult to select the appropriate ranking model. This paper presents a method for ranking efficient DMUs by the voting analytic hierarchy process (VAHP). The paper reviews some ranking models in DEA and discusses their strengths and weaknesses. Then, we provide the method for ranking efficient DMUs by VAHP. Finally we give an example to illustrate our approach and then the new method is employed to rank efficient units in a real world problem.     

In the determination of the most efficient decision making unit in data envelopment analysis

In recent years, several mixed integer linear programming (MILP) models have been proposed for determining the most efficient decision making unit (DMU) in data envelopment analysis. However, most of these models do not determine the most efficient DMU directly; instead, they make use of other less related objectives. This paper introduces a new MILP model that has an objective similar to that of the super-efficiency model. Unlike previous models, the new model’s objective is to directly discover the most efficient DMU. Similar to the super-efficiency model, the aim is to choose the most efficient DMU. However, unlike the super-efficiency model, which requires the solution of a linear programming problem for each DMU, the new model requires that only a single MILP problem be solved. Consequently, additional terms in the objective function and more constraints can be easily added to the new model. For example, decision makers can more easily incorporate a secondary objective such as adherence to a publicly stated preference or add assurance region constraints when determining the most efficient DMU. Furthermore, the proposed model is more accurate than two recently proposed models, as shown in two computational examples.     

Stochastic simulation-based genetic algorithm for chance constraint programming problems with continuous random variables

In this article, we present a stochastic simulation-based genetic algorithm for solving chance constraint programming problems, where the random variables involved in the parameters follow any continuous distribution. Generally, deriving the deterministic equivalent of a chance constraint is very difficult due to complicated multivariate integration and is only possible if the random variables involved in the chance constraint follow some specific distribution such as normal, uniform, exponential and lognormal distribution. In the proposed method, the stochastic model is directly used. The feasibility of the chance constraints are checked using stochastic simulation, and the genetic algorithm is used to obtain the optimal solution. A numerical example is presented to prove the efficiency of the proposed method.     

Negative data in data envelopment analysis: Efficiency analysis and estimating returns to scale

The classic Data Envelopment Analysis (DEA) models developed with the assumption that all inputs and outputs are non-negative, whereas, we may face a case with negative data in the actual business world. So, the need to adapt the DEA models so that they are applicable to cases includes inputs and outputs which can take both negative and non-negative values has been an issue. It can be readily demonstrated that the assumption of constant returns to scale (CRS) is not possible in technologies under negative data. So, one of the interesting and challenge questions is how to determine the state of RTS in the presence of negative data under variable returns to scale (VRS) technology. Accordingly, in this contribution, we first address the efficiency measure and then suggest a method to discover the state of returns to scale (RTS) in the presence of negative input and output values which has not been discussed much enough so far in DEA literature. Finally, the main results are elaborated by some illustrative examples.     

Radial data envelopment analysis models with mixed orientation of input and output

This paper discusses parametric solutions and envelopment formulations of radial data envelopment analysis (DEA) models with mixed orientation of input and output. These solutions geometrically but not numerically lie between the two usual solutions from input and output orientations. The consequent results provide alternative optimal solutions between those from input‐ and output‐oriented CCR models for constant returns to scale DEA models and optimal scale efficiency in addition to technical efficient solutions from input‐ and output‐oriented BCC models for variable returns to scale DEA models.     

Optimal profit-maximizing system design data envelopment analysis models

This research introduces a new type of data envelopment analysis (DEA) model termed the optimal system design (OSD) DEA model. Conventional DEA models evaluate DMUs’ performances given their known input and output data. The OSD DEA models take this one step further. They optimally design a DMU’s resource allocation in terms of profit maximization given the DMU’s total available budget. The need to design optimal systems is quite common and is sometimes necessary in practice. In actual fact, this study demonstrates that through the OSD DEA models, we can provide DMUs with more information than optimal portfolios of resources such as optimal budgets and budget congestion, i.e., the more the budget is consumed, the less the maximal profit. The proposed OSD DEA models are linear programs, and thus can be solved by the standard LP solvers to obtain DMUs’ optimal designs. However, to derive the DMUs’ corresponding optimal budgets, and to verify if the DMUs provide evidence of budget congestion, we need to modify the solvers, which may not be trivial. Therefore, this study exploits the special structures of the models to develop a simple solution method that can directly not only derive both a DMU’s optimal design and optimal budget, but can also check for the existence of budget congestion.     

Robust data envelopment analysis approaches for evaluating algorithmic performance

Recent advances in state-of-the-art meta-heuristics feature the incorporation of probabilistic operators aiming to diversify search directions or to escape from being trapped in local optima. This feature would result in non-deterministic output in solutions that vary from one run to another of a meta-heuristic. Consequently, both the average and variation of outputs over multiple runs have to be considered in evaluating performances of different configurations of a meta-heuristic or distinct meta-heuristics. To this end, this work considers each algorithm as a decision-making unit (DMU) and develops robust data envelopment analysis (DEA) models taking into account not only average but also standard deviation of an algorithm’s output for evaluating relative efficiencies of a set of algorithms. The robust DEA models describe uncertain output using an uncertainty set, and aim to maximize a DMU’s worst-case relative efficiency with respect to that uncertainty set. The proposed models are employed to evaluate a set of distinct configurations of a genetic algorithm and a set of parameter settings of a simulated annealing heuristic. Evaluation results demonstrate that the robust DEA models are able to identify efficient algorithmic configurations. The proposed models contribute not only to the evaluation of meta-heuristics but also to the DEA methodology.