Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs

Data envelopment analysis (DEA) is a well-known non-parametric technique primarily used to estimate radial efficiency under a set of mild assumptions regarding the production possibility set and the production function. The technical efficiency measure can be complemented with a consistent radial metrics for cost, revenue and profit efficiency in DEA, but only for the setting with known input and output prices. In many real applications of performance measurement, such as the evaluation of utilities, banks and supply chain operations, the input and/or output data are often stochastic and linked to exogenous random variables. It is known from standard results in stochastic programming that rankings of stochastic functions are biased if expected values are used for key parameters. In this paper, we propose economic efficiency measures for stochastic data with known input and output prices. We transform the stochastic economic efficiency models into a deterministic equivalent non-linear form that can be simplified to a deterministic programming with quadratic constraints. An application for a cost minimizing planning problem of a state government in the US is presented to illustrate the applicability of the proposed framework

A fuzzy expected value approach under generalized data envelopment analysis

Fuzzy data envelopment analysis (DEA) models emerge as another class of DEA models to account for imprecise inputs and outputs for decision making units (DMUs). Although several approaches for solving fuzzy DEA models have been developed, there are some drawbacks, ranging from the inability to provide satisfactory discrimination power to simplistic numerical examples that handles only triangular fuzzy numbers or symmetrical fuzzy numbers. To address these drawbacks, this paper proposes using the concept of expected value in generalized DEA (GDEA) model. This allows the unification of three models - fuzzy expected CCR, fuzzy expected BCC, and fuzzy expected FDH models - and the ability of these models to handle both symmetrical and asymmetrical fuzzy numbers. We also explored the role of fuzzy GDEA model as a ranking method and compared it to existing super-efficiency evaluation models. Our proposed model is always feasible, while infeasibility problems remain in certain cases under existing super-efficiency models. In order to illustrate the performance of the proposed method, it is first tested using two established numerical examples and compared with the results obtained from alternative methods. A third example on energy dependency among 23 European Union (EU) member countries is further used to validate and describe the efficacy of our approach under asymmetric fuzzy numbers

Carbon efficiency evaluation:an analytical framework using fuzzy DEA

Data Envelopment Analysis (DEA) is a powerful analytical technique for measuring the relative efficiency of alternatives based on their inputs and outputs. The alternatives can be in the form of countries who attempt to enhance their productivity and environmental efficiencies concurrently. However, when desirable outputs such as productivity increases, undesirable outputs increase as well (e.g. carbon emissions), thus making the performance evaluation questionable. In addition, traditional environmental efficiency has been typically measured by crisp input and output (desirable and undesirable). However, the input and output data, such as CO2 emissions, in real-world evaluation problems are often imprecise or ambiguous. This paper proposes a DEA-based framework where the input and output data are characterized by symmetrical and asymmetrical fuzzy numbers. The proposed method allows the environmental evaluation to be assessed at different levels of certainty. The validity of the proposed model has been tested and its usefulness is illustrated using two numerical examples. An application of energy efficiency among 23 European Union (EU) member countries is further presented to show the applicability and efficacy of the proposed approach under asymmetric fuzzy numbers

Benchmarking with network dea in a fuzzy environment

Benchmarking is a powerful and thriving tool to enhance the performance and profitabilities of organizations in business engineering. Though performance benchmarking has been practically and theoretically developed in distinct fields such as banking, education, health, and so on, benchmarking of supply chains with multiple echelons that include certain characteristics such as intermediate measure differs from other practices. In spite of incremental benchmarking activities in practice, there is the dearth of a unified and effective guideline for benchmarking in organizations. Amongst the benchmarking tools, data envelopment analysis (DEA) as a non-parametric technique has been widely used to measure the relative efficiency of firms. However, the conventional DEA models that are bearing out precise input and output data turn out to be incapable of dealing with uncertainty, particularly when the gathered data encompasses natural language expressions and human judgements. In this paper, we present an imprecise network benchmarking for the purpose of reflecting the human judgments with the fuzzy values rather than precise numbers. In doing so, we propose the fuzzy network DEA models to compute the overall system scale and technical efficiency of those organizations whose internal structure is known. A classification scheme is presented based upon their fuzzy efficiencies with the aim of classifying the organizations. We finally provide a case study of the airport and travel sector to elucidate the details of the proposed method in this study

Three aspects on complex performance analysis under uncertainty

Data envelopment analysis (DEA) is a widely used non-parametric method for estimating the relative input-output efficiency for a set of homogenous decision making units (DMUs). Due to its solid underlying mathematical basis and wide applications to real-world problems, much effort has been devoted to DEA models. Though DEA as a well-known methodology provides many advantages relative to other approaches, there are some limitations, complexities and challenges that need to be addressed. It is therefore important to extend the DEA models to fit the real characteristics involving (i) the data generating process (DGP), (ii) the production process, and (iii) the evaluation need. Conventional DEA methods require accurate measurement of both input and output data. However, the observed values of the inputs and outputs in real-world problems are sometimes ambiguous, uncertain and imprecise. In the first aspect of this thesis, we deal with such imperfect data in measuring the managerial and operational efficiency of firms along with providing a robust ranking order when both input and output data are imprecise. In the second aspect, we show how to apply DEA methods in multilevel structures such as supply chains, also in the presence of uncertainty. In the third aspect, we develop a fuzzy DEA model with imprecise and ambiguous data in order to evolve the scope of application to a larger set of real-life problems. Finally, we propose a two-stage algorithm to extend the DEA model using a common set of input and output weights (CSW).(IAG 3) -- UCL, 201

2012/8 Frontier-Based Performance Analysis Models for Supply Chain Management; State of the Art and Research Directions Per AGRELL

Frontier-based performance analysis models for supply chain management: state of the art and research direction

An extension of the Electre I method for group decision-making under a fuzzy environment

Many real-world decision problems involve conflicting systems of criteria, uncertainty and imprecise information. Some also involve a group of decision makers (DMs) where a reduction of different individual preferences on a given set to a single collective preference is required. Multi-criteria decision analysis (MCDA) is a widely used decision methodology that can improve the quality of group multiple criteria decisions by making the process more explicit, rational and efficient. One family of MCDA models uses what is known as "outranking relations" to rank a set of actions. The Electre method and its derivatives are prominent outranking methods in MCDA. In this study, we propose an alternative fuzzy outranking method by extending the Electre I method to take into account the uncertain, imprecise and linguistic assessments provided by a group of DMs. The contribution of this paper is fivefold: (1) we address the gap in the Electre literature for problems involving conflicting systems of criteria, uncertainty and imprecise information; (2) we extend the Electre I method to take into account the uncertain, imprecise and linguistic assessments; (3) we define outranking relations by pairwise comparisons and use decision graphs to determine which action is preferable, incomparable or indifferent in the fuzzy environment; (4) we show that contrary to the TOPSIS rankings, the Electre approach reveals more useful information including the incomparability among the actions; and (5) we provide a numerical example to elucidate the details of the proposed method.Multi-criteria decision-making Electre I Fuzzy preference modeling Ranking problem

Ef?ciency analysis in two-stage structures using fuzzy data envelopment analysis

Abstract Two-stagedataenvelopmentanalysis(TsDEA)modelsevaluatetheperformance of a set of production systems in which each system includes two operational stages. Taking into account the internal structures is commonly found in many situations such as seller-buyer supply chain, health care provision and environmental management.ContrarytoconventionalDEAmodelsasablack-boxstructure,TsDEA providesfurtherinsightintosourcesofinef?cienciesandamoreinformativebasisfor performance evaluation. Inaddition, ignoring the qualitative and imprecise data leads to distorted evaluations, both for the subunits and the system ef?ciency. We present the fuzzy input and output-oriented TsDEA models to calculate the global and pure technicalef?cienciesofasystemandsub-processeswhensomedataarefuzzy.Tothis end,weproposeapossibilisticprogrammingproblemandthenconvertitintoadeterministicintervalprogrammingproblemusingthe?-levelbasedmethod.Theproposed methodpreservesthelinkbetweentwostagesinthesensethatthetotalef?ciencyofthe system is equal to the product of the ef?ciencies derived from two stages. In addition to the study of technical ef?ciency, this research includes two further contribution

The state of the art in fuzzy data envelopment analysis

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. This chapter provides a taxonomy and review of the fuzzy DEA (FDEA) methods. We present a classification scheme with six categories, namely, the tolerance approach, the alpha-level based approach, the fuzzy ranking approach, the possibility approach, the fuzzy arithmetic, and the fuzzy random/type-2 fuzzy set. We discuss each classification scheme and group the FDEA papers published in the literature over the past 30 years