A cost Malmquist productivity index capturing group performance

This paper develops an index for comparing the productivity of groups of operating units in cost terms when input prices are available. In that sense it represents an extension of a similar index available in the literature for comparing groups of units in terms of technical productivity in the absence of input prices. The index is decomposed to reveal the origins of differences in performance of the groups of units both in terms of technical and cost productivity. The index and its decomposition are of value in contexts where the need arises to compare units which perform the same function but they can be grouped by virtue of the fact that they operate in different contexts as might for example arise in comparisons of water or gas transmission companies operating in different countries

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 Redundancy Detection Algorithm for Fuzzy Stochastic Multi-Objective Linear Fractional Programming Problems

The computational complexity of linear and nonlinear programming problems depends on the number of objective functions and constraints involved and solving a large problem often becomes a difficult task. Redundancy detection and elimination provides a suitable tool for reducing this complexity and simplifying a linear or nonlinear programming problem while maintaining the essential properties of the original system. Although a large number of redundancy detection methods have been proposed to simplify linear and nonlinear stochastic programming problems, very little research has been developed for fuzzy stochastic (FS) fractional programming problems. We propose an algorithm that allows to simultaneously detect both redundant objective function(s) and redundant constraint(s) in FS multi-objective linear fractional programming problems. More precisely, our algorithm reduces the number of linear fuzzy fractional objective functions by transforming them in probabilistic-possibilistic constraints characterized by predetermined confidence levels. We present two numerical examples to demonstrate the applicability of the proposed algorithm and exhibit its efficacy

A NOTE ON AN EXTENDED NUMERATION METHOD FOR SOLVING FREE DISPOSAL HULL MODELS IN DEA

This note identifies and corrects an error in Keshvari, A and N Dehghan Hardoroudi (2008). Asia-Pacific Journal of Operational Research, 25, 689–696.Data envelopment analysis, free disposal hull (FDH), dominant units, efficiency

A joint chance-constrained data envelopment analysis model with random output data

Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the technical efficiency performances of a set of comparable decision-making units that transform multiple inputs into multiple outputs. The conventional DEA models are based on crisp input and output data, but real-world problems often involve random output data. The main purpose of the paper is to propose a joint chance-constrained DEA model for analyzing a real-world situation characterized by random outputs and crisp inputs. After developing the model, we carry out the following: First, we obtain an upper bound of this stochastic non-linear model deterministically by applying a piecewise linear approximation algorithm based on second-order cone programming; Second, we obtain a lower bound with use of a piecewise tangent approximation algorithm, which is also based on second-order cone programming; and then we use a numerical example to demonstrate the applicability of the proposed joint chance-constrained DEA framework

Convex and non-convex approaches for cost efficiency models with fuzzy data

Classical cost efficiency (CE) measurement models require exact and accurate knowledge of the input and output values for each decision making unit (DMU). However, the observed values of the input and output data in real-world problems are often imprecise or vague. In recent years, fuzzy data envelopment analysis (DEA) has been successfully used to deal with imprecise or vague data in efficiency measurement. In this paper, we incorporate fuzzy set theory into the traditional CE measurement. We propose two approaches based on the convex DEA and non-convex free disposable hull (FDH) approach with fuzzy variables. The purpose of this paper is two-fold: 1) we develop a CE analysis for non-parametric convex methods based on fuzzy set theory; 2) we further develop a non-convex CE analysis model where the non-convexity is formulated based on the FDH approach. We also present a numerical example to demonstrate the applicability of the proposed models and exhibit the efficacy of the procedures and algorithms

A cost Malmquist productivity index capturing group performance

This paper develops an index for comparing the productivity of groups of operating units in cost terms when input prices are available. In that sense it represents an extension of a similar index available in the literature for comparing groups of units in terms of technical productivity in the absence of input prices. The index is decomposed to reveal the origins of differences in performance of the groups of units both in terms of technical and cost productivity. The index and its decomposition are of value in contexts where the need arises to compare units which perform the same function but they can be grouped by virtue of the fact that they operate in different contexts as might for example arise in comparisons of water or gas transmission companies operating in different countries. (C) 2014 Elsevier B.V. All rights reserved

Fuzzy free disposal hull models under possibility and credibility measures

The free disposal hull (FDH) models are used as an alternative to data envelopment analysis (DEA) models for performance measurement and efficiency assessment. The conventional FDH models are used to evaluate the performance of a set of firms or decision-making units (DMUs) using deterministic input and output data. However, the input and output data in the real-life performance evaluation problems are often imprecise and ambiguous. The impreciseness and ambiguity associated with the input and output data in FDH can be represented with fuzzy variables. In this paper, the concept of chance-constrained programming is used to develop FDH models with various returns to scale assumptions, including variable returns to scale (VRS), variable non-increasing returns to scale (NIRS), variable non-decreasing returns to scale (NDRS), and constant returns to scale (CRS), for efficient DMUs with fuzzy data. We propose two fuzzy FDH models with respect to possibility and expected value (credibility approach) constraints. Finally, a numerical example is presented to demonstrate the efficacy of the proposed procedures and algorithms

A random-fuzzy portfolio selection DEA model using value-at-risk and conditional value-at-risk

The complexity involved in portfolio selection has resulted in the development of a large number of methods to support ambiguous financial decision making. We consider portfolio selection problems where returns from investment securities are random variables with fuzzy information and propose a data envelopment analysis model for portfolio selection with downside risk criteria associated with value-at-risk (V@R) and conditional value-at-risk (CV@R). Both V@R and CV@R criteria are used to define possibility, necessity, and credibility measures, which are formulated as stochastic nonlinear programming programs with random-fuzzy variables. Our constructed stochastic nonlinear programs for analyzing portfolio selection are transformed into deterministic nonlinear programs. Moreover, we show an enumeration algorithm can solve the model without any mathematical programs. Finally, we demonstrate the applicability of the proposed framework and the efficacy of the procedures with a numerical example