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.     

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.     

Personnel selection using analytic network process and fuzzy data envelopment analysis approaches

This paper develops a decision support tool using an integrated analytic network process (ANP) and fuzzy data envelopment analysis (DEA) approach to effectively deal with the personnel selection problem drawn from an electric and machinery company in Taiwan. The current personnel selection procedure is a separate two-stage method. The administration practice shows that the separation between stages 1 and 2 reduces the administration quality and may incur both the top manager’s displeasure and the decision-makers’ depression. An illustrative example by a simulated application demonstrates the implementation of the proposed approach. This example demonstrates how this approach can avoid the main drawback of the current method, and more importantly, can deal with the personnel selection problem more convincingly and persuasively. This study supports the applications of ANP and fuzzy DEA as decision support tools in personnel selection.     

A method using weight restrictions in data envelopment analysis for ranking and validity issues in decision making

In this article we introduce a comprehensive yet efficient approach based on data envelopment analysis (DEA) with restricted multipliers for accountable and understandable multiple attribute decision making (MADM). Information system (IS) appraisals are motivated and used for illustrating the proposed methodology. Results show that the given DEA based approach can easily and significantly increase the information frame of the decision maker by identifying disparate rankings and by affirming the stability and validity of ranking outcomes. The given validity concept is contrary to the directions given in the main body of research and can also be used to question ranking outcomes of classic MADM methods.     

数据包络分析研究热点综述

数据包络分析是面向多输入多输出决策单元的有效性评估方法。在介绍数据包络分析的基本思想和模型基础之上,总结了近年来国内外的研究热点,包括两阶段DEA、效率排序DEA、随机DEA和相关扩展问题,旨在围绕以上研究热点,对DEA近年来的理论研究及其扩展模型进行梳理和分类。最后对数据包络分析进一步研究提出展望。     

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.     

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.     

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.     

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.     

A fuzzy group data envelopment analysis model for high-technology project selection: A case study at NASA

The assessment and selection of high-technology projects is a difficult decision making process at the National Aeronautic and Space Administration (NASA). This difficulty is due to the multiple and often conflicting objectives in addition to the inherent technical complexities and valuation uncertainties involved in the assessment process. As such, a systematic and transparent decision making process is needed to guide the assessment process, shape the decision outcomes and enable confident choices to be made. Various methods have been proposed to assess and select high-technology projects. However, applying these methods has become increasingly difficult in the space industry because there are many emerging risks implying that decisions are subject to significant uncertainty. The source of uncertainty can be vagueness or ambiguity. While vague data are uncertain because they lack detail or precision, ambiguous data are uncertain because they are subject to multiple interpretations. We propose a data envelopment analysis (DEA) model with ambiguity and vagueness. The vagueness of the objective functions is modeled by means of multi-objective fuzzy linear programming. The ambiguity of the input and output data is modeled with fuzzy sets and a new α-cut based method. The proposed models are linear, independent of α-cut variables, and capable of maximizing the satisfaction level of the fuzzy objectives and efficiency scores, simultaneously. Moreover, these models are capable of generating a common set of multipliers for all projects in a single run. A case study involving high-technology project selection at NASA is used to demonstrate the applicability of the proposed models and the efficacy of the procedures and algorithms.     

Evaluation and ranking DMUs in the presence of both undesirable and ordinal factors in data envelopment analysis

In the last decade,ranking units in data envelopment analysis(DEA) has become the interests of many DEA researchers and a variety of models were developed to rank units with multiple inputs and multiple outputs.These performance factors(inputs and outputs) are classified into two groups:desirable and undesirable.Obviously,undesirable factors in production process should be reduced to improve the performance.Also,some of these data may be known only in terms of ordinal relations.While the models developed in the past are interesting and meaningful,they didn t consider both undesirable and ordinal factors at the same time.In this research,we develop an evaluating model and a ranking model to overcome some deficiencies in the earlier models.This paper incorporates undesirable and ordinal data in DEA and discusses the efficiency evaluation and ranking of decision making units(DMUs) with undesirable and ordinal data.For this purpose,we transform the ordinal data into definite data,and then we consider each undesirable input and output as desirable output and input,respectively.Finally,an application that shows the capability of the proposed method is illustrated.     

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.     

Modeling data envelopment analysis by chance method in hybrid uncertain environments

This article first presents several formulas of chance distributions for trapezoidal fuzzy random variables and their functions, then develops a new class of chance model (C-model for short) about data envelopment analysis (DEA) in fuzzy random environments, in which the inputs and outputs are assumed to be characterized by fuzzy random variables with known possibility and probability distributions. Since the objective and constraint functions contain the chance of fuzzy random events, for general fuzzy random inputs and outputs, we suggest an approximation method to compute the chance. When the inputs and outputs are mutually independent trapezoidal fuzzy random variables, we can turn the chance constraints and the chance objective into their equivalent stochastic ones by applying the established formulas for the chance distributions. In the case when the inputs and the outputs are mutually independent trapezoidal fuzzy random vectors, the proposed C-model can be transformed to its equivalent stochastic programming one, in which the objective and the constraint functions include a number of standard normal distribution functions. To solve such an equivalent stochastic programming, we design a hybrid algorithm by integrating Monte Carlo (MC) simulation and genetic algorithm (GA), in which MC simulation is used to calculate standard normal distribution functions, and GA is used to solve the optimization problems. Finally, one numerical example is presented to demonstrate the proposed modeling idea and the efficiency in the proposed model.     

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.     

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.     

Multiobjective target setting in data envelopment analysis using AHP

In this paper two new target setting DEA approaches are proposed. The first one is an interactive multiobjective method that at each step of the process asks the decision maker (DM) which inputs and outputs he wishes to improve, which ones are allowed to worsen and which ones should stay at their current level. The local relative priorities of these inputs and outputs changes are computed using the analytic hierarchy process (AHP). After obtaining the candidate target, the DM can update his preferences for improving, worsening or maintaining current inputs and outputs levels and obtain a new candidate target. Thus continuing, until a satisfactory operating point is computed. The second method proposed uses a lexicographic multiobjective approach in which the DM specifies a priori a set of priority levels and, using AHP, the relative importance given to the improvements of the inputs and outputs at each priority level. This second approach requires solving a series of models in order, one model for each priority level. The models do not allow for worsening of neither inputs nor outputs. After the lowest priority model has been solved the corresponding target operating point is obtained. The application of the proposed approach to a port logistics problem is presented.     

Online banking performance evaluation using data envelopment analysis and principal component analysis

This paper presents a hybrid approach to conducting performance measurements for Internet banking by using data envelopment analysis (DEA) and principal components analysis (PCA). For each bank, DEA is applied to compute an aggregated efficiency score based on outputs, such as web metrics and revenue; and inputs, such as equipment, operation cost and employees. The 45 combinations of DEA efficiencies of the studied banks are calculated, and used as a ranking mechanism. PCA is used to apply relative efficiencies among the banks, and to classify them into different groups in terms of operational orientations, i.e., Internet banking and cost efficiency focused orientations. Identification of operational fitness and business orientation of each firm, in this way, will yield insights into understanding the weaknesses and strengths of banks, which are considering moving into Internet banking.     

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.     

Data envelopment analysis of reservoir system performance

In long-term performance analyses of water systems with surface reservoirs for different operating scenarios, the analyst (or decision maker) is faced with two connected problems: (1) how to handle the extensive output of the simulation model and derive information on the scenarios scores for a prescribed set of performance criteria, and (2) how to compare scenarios in a multi-criterial sense while identifying the most desired. The data sets may overburden the analyst, while an evaluating procedure may be subjective due to personal preferences, attitudes, knowledge and miscellaneous factors. The data envelopment analysis (DEA) approach proposed here seems to be reliable in treating these situations, and sufficiently objective in evaluating and ranking the scenarios. Certain performance indices are defined as evaluating criteria in a standard multi-criterial sense, and then virtually divided into scenarios' output and input measures. By considering scenarios as product units, the DEA optimizes the weights of inputs and outputs, computes productivity efficiency for each unit, and rank them appropriately. Omitting the analyst's personal judgment on the technical parameters that describe system's performance restricts, in this way, the influence of the decision maker. A case study application on the reservoir system in Brazil proved that a methodological connection for solving decision problems with discrete alternatives really exists between the DEA and standard multi-criteria methods.