An improvement to the cost efficiency interval: A DEA-based approach
Introduction
Data envelopment analysis (DEA), introduced by Charnes et al. [2], presented a constant return to scale (CRS) model for evaluating the performance of a set of comparable decision making units (DMU). In DEA, each DMU is evaluated in terms of a set of outputs that represent accomplishment, and a set of inputs that represent the resources. In traditional the technical efficiency of a DMU is measured as the maximum ratio of weighted sum of outputs to the weighted sum of inputs and hence, this efficiency measure is calculated from the optimistic viewpoint. Another kind of relative efficiency in DEA literature is cost efficiency (or price efficiency) that measures the DMU’s success in choosing an optimal set of inputs with a given set of input price, this means that this efficiency is calculated from the optimistic viewpoint, too. In this paper, we first propose a DEA model to derive a cost efficiency measure from the pessimistic viewpoint. Then we propose the approaches to improve the cost efficiency intervals. The observed inputs and outputs of a DMU are adjusted so as to improve the efficiency interval, so that the lower bound of efficiency interval become as large as possible and the upper bound of efficiency interval become the maximum value one. The paper is structured as follows: the next section of the paper addresses an introduction to basic DEA model. The cost efficiency interval is introduced in Section 3. Section 4 extends the standard DEA model to improve the efficiency interval. An application on Iranian gas companies appears in Section 5 and conclusions appear in Section 6.
Section snippets
Preliminaries
In this section, we will briefly survey the basic DEA models. The data domain for a DEA study is the set A of n data points, a1, a2, … , an; one for each DMU. Each data point composed of two types of components, those pertaining to the m inputs, 0 ≠ xj ⩾ 0, and those corresponding to the s outputs, 0 ≠ yj ⩾ 0. We organize the data in the following way: A = [a1, a2, … , an] where , and A is the m + s by n matrix the columns of which are the data points. To estimate the DEA technical efficiency of
Cost efficiency interval
In this section, we introduce the efficiency interval. To derive the cost efficiency of the specific pth DMU, we solve the following linear programming problem:Here, ci, are the input prices. In this program we maximize the ratio of weighted sum of output to the weighted sum of inputs to that of maximum. This fractional programming problem can be easily converted to a linear format. Specifically, make the transformation and ,
Improving the efficiency interval
In this section DMUs are improved by adjusting their inputs and outputs. In order to improve a DMUp so as to be cost efficient, we use the following two steps procedure:
Step 1. In this step we introduce the ideal inputs and ideal outputs for DMUp. Consider the standard format of (6) as follows:Suppose (u∗, v∗, s∗, t∗) be the optimal solution to (11). Set, , Ep is the reference set for DMUp. The ith
Example
To illustrate the application of the interval efficiency model, we have utilized the data set for 14 Iranian gas companies. The data for this application are derived from operations during 2004. We use seven variables to form the data set as inputs and outputs. Inputs include number of staffs, amount of budget and the revenue of gas sold in 2003, and outputs include amount of piping, number of new customers, amount of branch-line and revenue of gas sold in 2004. The normal data are summarized
Conclusion
Model of DEA have been generalized here in both, to determine a cost efficiency interval and to improve the cost efficiency interval. In this paper, DMUs have been evaluated from two viewpoints so that the efficiency from optimistic viewpoint is the upper bound and the efficiency from pessimistic viewpoint is the lower bound of cost efficiency interval. The DMUs are improved by adjusting their observed inputs and outputs. The target point for the specific inefficient DMUp is located on
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Cited by (15)
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