Developing Common Set of Weights with Considering Nondiscretionary Inputs and Using Ideal Point Method

Reza Kiani Mavi,Sajad Kazemi,Jay M Jahangiri

doi:10.1155/2013/906743

Reza Kiani Mavi, Sajad Kazemi + Show 1 more

Open Access

https://doi.org/10.1155/2013/906743

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Abstract

Data envelopment analysis (DEA) is used to evaluate the performance of decision making units (DMUs) with multiple inputs and outputs in a homogeneous group. In this way, the acquired relative efficiency score for each decision making unit lies between zero and one where a number of them may have an equal efficiency score of one. DEA successfully divides them into two categories of efficient DMUs and inefficient DMUs. A ranking for inefficient DMUs is given but DEA does not provide further information about the efficient DMUs. One of the popular methods for evaluating and ranking DMUs is the common set of weights (CSW) method. We generate a CSW model with considering nondiscretionary inputs that are beyond the control of DMUs and using ideal point method. The main idea of this approach is to minimize the distance between the evaluated decision making unit and the ideal decision making unit (ideal point). Using an empirical example we put our proposed model to test by applying it to the data of some 20 bank branches and rank their efficient units.

Highlights

Data envelopment analysis (DEA) which was first proposed by Charnes et al [1] and developed by Banker et al [2] is a nonparametric technique for measuring the efficiency of a homogeneous group of decision making units (DMUs) on the basis of multiple inputs and outputs based on observed data [3,4,5,6,7]
For any evaluated DMUj, the efficiency score H can be calculated by the following CCR model according to following hypotheses: j is the number of decision making units (DMUs) being compared in the DEA analysis, DMUj the jth decision making unit, θ the efficiency rating of the decision making unit being evaluated by DEA, yrj the amount of output r used by decision making unit j, xij the amount of input i used by decision making unit j, i the number of inputs used by the DMUs, r the number of outputs generated by the DMUs, ur the coefficient or weight assigned to output r by DEA, and Vi the coefficient or weight assigned to input i by DEA
Based on multiple objective nonlinear programming and by using compromise solution approach, proposed a method to generate a common set of weights for all DMUs which are able to produce a vector of efficiency scores closest to the efficiency scores calculated from the standard DEA model

Summary

Introduction

Data envelopment analysis (DEA) which was first proposed by Charnes et al [1] and developed by Banker et al [2] is a nonparametric technique for measuring the efficiency of a homogeneous group of decision making units (DMUs) on the basis of multiple inputs and outputs based on observed data [3,4,5,6,7]. DEA provides weights that are DMU-specific and permits individual circumstances of operation of the DMUs and for each DMU, it provides efficiency scores in the form of a ratio of a weighted sum of the outputs to a weighted sum of the inputs [8] This method was applied to evaluate productivity and performance of airports, efficiency of air force maintenance units, hospitals, university departments, schools, industries, banks, products and services, strategic decision making, and technologies [9]. Fundamental assumptions of the original DEA models [12] are that inputs and outputs are measured by exact values or are factual and definite factors [4] and assume that the assessed units (DMUs) are homogeneous.

CCR Model

Common Set of Weights

Nondiscretionary Model

Proposed Model

Numerical Examples

Conclusions and Future Research