Dealing with Interval Scale Data in Data Envelopment Analysis

This papaer considers the problem of interval scale data in the most widely used models of Data Envelopment Analysis (DEA), the CCR, and the BCC models. Radial models require inputs and outputs measured on the ratio scale. Our focus is on how to deal with interval scale variables especially when the interval scale variable is a difference of two ratio scale variables like profit or the decrease/increase in bank accounts. Using these ratio scale variables as variables in the DEA model we suggest radial models. An approach to how to deal with interval scale variables when we relax the radiality assumption is also discussed

A Quasi-Malmquist Index

Abstract The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of "one-sided" efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking

A quasi-malmquist productivity index

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of "one-sided" efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking

Coupling distinct MOLP interactive approaches with a novel DEA hybrid model

We propose a modelling framework which allows considering different priorities and individual expansion and contraction scales for distinct types of inputs and outputs, through the Weighted Russell Directional Dis- tance Model (WRDDM). An equivalence model between the WRDDM and the super-ideal point model has also been established, which is then incorporated into several interactive Multiobjective Linear Programming (MOLP) approaches. The use of these diverse interactive methodologies allows obtaining the benchmark Decision Making Units (DMUs) which best suit the decision maker’s (DM) preferences. This feature can be useful since traditional Data Envelopment Analysis (DEA) models tend to completely neglect the DM’s preferences and value judgements in the computation of the DMUs used as a reference of best practices. Therefore, with this tool the DMs have the possibility of translating into the decision-making process man- agement constraints (namely, budgetary) and aspiration levels regarding the inputs and outputs, providing much more realistic support for actual decision-making.This research was partly supported by the Spanish Ministry of Economy and Competitiveness (project ECO2017-88883-R) and by the Fundação para a Ciência e a Tecnologia (FCT) un- der project grant UID/Multi/00308/2020 and the European Regional Development Fund in the framework of COMPETE 2020 Programme within project T4ENERTEC (POCI-01-0145- FEDER-029820). This work has also been partly supported by the Andalusian Regional Min- istry of Economy, Knowledge, Business and University (PAIDI group SEJ-532 and UMA18- FEDERJA-024 also supported by FEDER funding). Carla Oliveira Henriques also acknowledges the training received from the University of Malaga PhD Programme in Economics and Business (Programa de Doctorado en Economía y Empresa de la Universidad de Malaga)

Value efficiency in data envelopment analysis: Weighted global measure

Master'sMASTER OF ENGINEERIN

Measurement of dynamic efficiency, a directional distance function parametric approach

This research proposes a parametric estimation of the structural dynamic efficiency measures proposed by Silva and Oude Lansink (2009). Overall, technical and allocative efficiency measurements are derived based on a directional distance function and the duality between this function and the optimal value function. The applicability of the parametric proposal is illustrated by assessing dynamic efficiency ratings for a sample of Dutch dairy farms observed from 1995 to 2005.structural dynamic efficiency, dairy farms, parametric approach, Agricultural and Food Policy, Farm Management, Land Economics/Use, D21, D24, D61, D92,

Using Enhanced Russell Model to Solve Inverse Data Envelopment Analysis Problems

This paper studies the inverse data envelopment analysis using the nonradial enhanced Russell model. Necessary and sufficient conditions for inputs/outputs determination are introduced based on Pareto solutions of multiple-objective linear programming. In addition, an approach is investigated to identify extra input/lack output in each of input/output components (maximum/minimum reduction/increase amounts in each a of input/output components). In addition, the following question is addressed: if among a group of DMUs, it is required to increase inputs and outputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other DMUs, how much should the inputs and outputs of the DMU increase? This question is discussed as inverse data envelopment analysis problems, and a technique is suggested to answer this question. Necessary and sufficient conditions are established by employing Pareto solutions of multiple-objective linear programming as well

Finding closest targets in non-oriented DEA models: the case of convex and non-convex technologies

This paper draws attention for the fact that traditional Data Envelopment Analysis (DEA) models do not provide the closest possible targets (or peers) to inefficient units, and presents a procedure to obtain such targets. It focuses on non-oriented efficiency measures (which assume that production units are able to control, and thus change, inputs and outputs simultaneously) both measured in relation to a Free Disposal Hull (FDH) technology and in relation to a convex technology. The approaches developed for finding close targets are applied to a sample of Portuguese bank branches