An application of DEA method for ranking different Tehran municipality branches

Article history: Received 5 January 2014 Received in revised format 8 March 2014 Accepted 16 March 2014 Available online 18 March 2014 Measuring the performance of governmental organizations plays essential role on making strategic decisions. In this paper, we present an empirical investigation to measure the performance of 22 different branches of municipalities in city of Tehran, Iran. The proposed study uses data envelopment analysis (DEA) for measuring the relative efficiencies of various units. The proposed DEA uses fixed assets, employee expenses and total income as input and Green Space Development, Resumption and Waste, Development of Cultural Spaces as well as Improvement of Passages and highways are considered as the output of the model. The results indicate that 9 regions were operating efficiently and 14 regions were inefficient. © 2014 Growing Science Ltd. All rights reserved.


Introduction
For years, there have been outstanding attempts on applying various techniques for computing the relative efficiency of similar business units (Kuah et al., 2010;Cooper et al., 2011).Data envelopment analysis (DEA) is one of the most popular methods for measuring non-financial units (Charnes, 1978) and it has been successfully applied for measuring the performance of various technologies (Khouja, 1995), in airport industry (Roghanian & Foroughi, 2010), supplier selection (Levary, 2008;Azar et al., 2011;Nourbakhsh et al., 2013) and heath care (Ghotbuee et al., 2012;Khani et al., 2012).Charnes et al. (1978Charnes et al. ( , 1985Charnes et al. ( , 1990) ) are named as the first who introduced the idea of comparing non-financial units based on different inputs/outputs.There are various kinds of DEA methods including constant return to scale, variable return to scale, input/output oriented, etc. DEA has been extensively implemented in rural industry for several years (Minciardi et al., 2008).Rogge and De Jaeger (2012) proposed an adjusted "shared-input" model of DEA, which helps evaluating municipality waste collection and processing performances in settings in which one waste costs are shared among treatment efforts of multiple municipal solid waste fractions.The proposed DEA not only provides an estimate of the municipalities overall cost efficiency but also provides forecasts on the municipalities' cost efficiency in the treatment of the various fractions of municipal solid waste.
lo Storto, C. (2013) presented findings of an exploratory study aimed at evaluating expenditure efficiency of 103 Italian major municipalities.The study applied DEA to calculate an efficiency score and investigated economies of scale.Their findings disclosed that there were some scale inefficiencies in a number of municipalities that need an in depth investigation.Rogge and De Jaeger (2013) proposed an adjusted version of the popular efficiency measurement DEA, which makes it possible to evaluate the cost efficiency of municipalities in the collection and processing of multiple household waste fractions.The method is also capable of robustifying the cost efficiency evaluations for the effect of measurement errors in the data or municipalities with outlying and atypical performances.The method also corrected the evaluations for differences in the operating environments of municipalities such as demography and median income of the municipality population.

The proposed study
In this paper, we present an empirical investigation to measure the relative efficiency of various units using data envelopment analysis (DEA).

The DEA method
There are literally various DEA methods and the constant return to scale DEA (CCR) introduced by Charnes, et al. (1978Charnes, et al. ( , 1985Charnes, et al. ( , 1994) is explained in this paper for measuring the relative efficiency of various decision making units (DMU).In this method we form a set of production feasibility, which constituts of various principles such as fixed-scale efficiency, convexity and feasibility as follows, where X and Y state the input and output vectors, respectively.The CCR production feasibility set border provides the relative efficiency where any off-border DMU is stated as inefficient.The CCR model can be measured in two types of either input or output oriented.The input CCR tries to decrease the maximum input level with a ratio of  so that, at least, the same output is produced, i.e.: 2) is an envelopment form of input CCR where  is the relative efficiency of the DMU and it is possible to demonstrate that the optimal value of  ,  * , is located between zero and one.In an input oriented DEA model, once the efficiency of a DMU unit, p DMU , lies in case of inefficiency, one may directs it towards the border to change it efficient.

Input/output
The proposed study of this paper uses three inputs and four outputs for measuring the relative efficiencies of various units.Fig. 1 shows details of the propsoed study.

The results
We first present the optimal weights of input/output parameters computed by input oriented DEA method.Table 1 shows details of our results.

Table 1
The optimal weights of input/output In addition, Table 2 demonstrates the summary of relative efficiencies of 22 units along with the values of dual variables associated with input/output.

Table 2
The results of DEA implementation According to the results of Table 1, 9 units are detected as efficient units and 14 units are found inefficient.The average efficiency of these 14 inefficient units is equal to 0.93, which means they have to reduce approximately 7% of their inputs.Based on the optimal weights computed for inefficient units, we may find efficient amount of inputs for the 14 inefficient units.For instance for unit 3, we have As we can observe, unit 3 has to reduce its fixed assets, employee expenses and total income from 12. 939, 12.460 and 11.035 to 10.8, 10.42 and 9.3, respectively.Similarly, we can compute the efficient numbers for other units and Table 2 summarizes the results of our survey.Next, we present details of our findings on present and optimal values of inefficient units in Table 3 as follows,

Fig. 1 .
Fig. 1.The structure of the proposed study Next, we present details of the DEA implementation based on model (2).

Table 3
The summary of efficient weights of input projection points