An input relaxation model for evaluating congestion in fuzzy DEA

This paper develops a BCC input relaxation model for identifying input congestion as a severe form of inefficiency of decision-making units in fuzzy data envelopment analysis. The possibility approach is presented to obtain the models equivalent to fuzzy models. We use a one-model approach to determine input congestion based on the BCC input relaxation model. A numerical example is given to illustrate the proposed model and identify the congestion with precise and imprecise data. The proposed model is also used to determine the congestion in 16 hospitals using four fuzzy inputs and two fuzzy outputs with a symmetrical triangular membership function

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

Methodological Advances in Dea

We survey the methodological advances in DEA over the last 25 years and discuss the necessary conditions for a sound empirical application. We hope this survey will contribute to the further dissemination of DEA, the knowledge of its relative strengths and weaknesses, and the tools currently available for exploiting its full potential. Our main points are illustrated by the case of the DEA study used by the regulatory office of the Dutch electricity sector (Dienst Toezicht Elektriciteitswet; Dte) for setting price caps

Second-order conic programming for data envelopment analysis models

Data envelopment analysis (DEA) is a widely used benchmarking technique. Its strength stems from the fact that it can include several inputs and outputs of not necessarily the same type to evaluate efficiency scores. Indeed, the aforesaid method is based on mathematical optimization. This paper constructs a second-order conic optimization problem unifying several DEA models. Moreover, it presents an algorithm that solves the former problem, and provides a MATLAB function associated with it. As far as known, no MATLAB function solves DEA models. Among different types of DEA, this function can handle deterministic, Malmquist index, and stochastic models. In fact, DEA is involved in various practical applications, thus, this work will provide some possible future extensions, not only for MATLAB but also for any programming software in applications of decision science and efficiency analysis

Stochastic cost efficiency evaluation of a supply chain

The main goal of the paper is a consideration of cost efficiency evaluation models related to some supply chain when dealing with imprecise data. Data envelopment analysis (DEA) method is a non-parametric mathematical programming approach to assess the performance. This method is proposed for deterministic data and it can be generalized to inaccurate data, while considering real world applications. Here we consider data as random variables and after reviewing and introducing new models to evaluate cost efficiencies related to the special circumstances of the supply chain using DEA, these models are developed to probabilistic form. Also, deterministic and linear equivalents are proposed using the symmetric error structure of normal distributions. At final, by a numerical example, the proposed models are examined to show relationships of results.Publisher's Versio

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

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkData 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

Efficiency analysis of dairy farms in the Northern Great Plain Region using deterministic and stochastic DEA models

Running any dairy enterprise is a risky activity: the profitability of the enterprise is affected by the price fluctuation of feed and animal health products from inputs, as well as by the fluctuation of end-product prices. Under these circumstances, it is essential for the cattle breeders, in order to survive, to harness the reserves in management as effectively as possible. In this research the efficiency and risk of 32 sample dairy farms were analysed in the Northern Great Plain Region from the Farm Accountancy Data Network (FADN) by applying classical Data Envelopment Analysis (DEA) and stochastic DEA models. The choice of this method is justified by the fact that there was not such an available reliable database by which production functions could have been defined, and DEA makes possible to manage simultaneously some inputs and outputs, i.e. complex decision problems. By using DEA, the sources that cause shortfall on inefficient farms can be identified, analysed and quantified, so corporate decision support can be reinforced successfully. A disadvantage of the classical DEA model is that the stochastic factors of farming cannot be treated either on the side of inputs or outputs; therefore, their results can be adopted with reservations, especially in agricultural models. This may have been because we could not discover that many agricultural applications. Considering the price of inputs and outputs as probability variables, 5000 simulation runs have been done in this research. As a result, it can be stated that at which intervals of the input and output factors can become competitive and the fluctuation of these factors can cause what level of risk at each farm

Value of the stochastic efficiency in data envelopment analysis

YesThis article examines the potential benefits of solving a stochastic DEA model over solving a deterministic DEA model. It demonstrates that wrong decisions could be made whenever a possible stochastic DEA problem is solved when the stochastic information is either unobserved or limited to a measure of central tendency. We propose two linear models: a semi-stochastic model where the inputs of the DMU of interest are treated as random while the inputs of the other DMUs are frozen at their expected values, and a stochastic model where the inputs of all of the DMUs are treated as random. These two models can be used with any empirical distribution in a Monte Carlo sampling approach. We also define the value of the stochastic efficiency (or semi-stochastic efficiency) and the expected value of the efficiency

Satisficing data envelopment analysis: a Bayesian approach for peer mining in the banking sector

YesOver the past few decades, the banking sectors in Latin America have undergone rapid structural changes to improve the efficiency and resilience of their financial systems. The up-to-date literature shows that all the research studies conducted to analyze the above-mentioned efficiency are based on a deterministic data envelopment analysis (DEA) model or econometric frontier approach. Nevertheless, the deterministic DEA model suffers from a possible lack of statistical power, especially in a small sample. As such, the current research paper develops the technique of satisficing DEA to examine the still less explored case of Peru. We propose a Satisficing DEA model applied to 14 banks operating in Peru to evaluate the bank-level efficiency under a stochastic environment, which is free from any theoretical distributional assumption. The proposed model does not only report the bank efficiency, but also proposes a new framework for peer mining based on the Bayesian analysis and potential improvements with the bias-corrected and accelerated confidence interval. Our study is the first of its kind in the literature to perform a peer analysis based on a probabilistic approach

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented