production efficiency evaluation of energy companies based on the improved super-efficiency data...

Mathematical and Computer Modelling 58 (2013) 1057–1067

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Mathematical and Computer Modelling

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Production efficiency evaluation of energy companies based on theimproved super-efficiency data envelopment analysis consideringundesirable outputsLei Li ∗, Mingyue Li, Chunlin WuSchool of Management and Economics, Tianjin University, Tianjin, China

a r t i c l e i n f o

Article history:Received 25 December 2011Received in revised form 13 June 2012Accepted 2 July 2012

Keywords:Super-efficiency DEABenchmark sorting DEAUndesirable outputsProduction efficiency of energy companies

a b s t r a c t

The introduction of a precise and effective production efficiency evaluative model hasvital theoretical importance. It can promote the improvement of production efficiencyin energy companies and the enhancement of China’s energy supply. Data envelopmentanalysis (DEA) is a nonparametricmethod to evaluate the relative effectiveness of decision-making units (DMU). While DEA has many theoretical advantages, it is also very sensitiveto the number of decision-making units being evaluated as well as the accuracy of thedata. Super-efficiency DEA can make up this limitation. However, this model has severalshortcomings, like the possible exaggeration of the efficiency value and the variety of theevaluating benchmarks. Integrating the measurement of undesirable outputs, this papercombined the traditional CCR model, super-efficiency DEA model and ideal-DMU-basedbenchmark sortingmodel to get an improved super-efficiencyDEAmodel. Then,we appliedthis method to 10 subsidiaries of a well-known domestic energy corporation to testify tothe feasibility of it.

© 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Energy sources occupy a decisive position in the development of the global economic. China shows its huge demandon energy as a developing country with a large population. In 2011, China consumed 470 million tons of oil, increasedby 4.1 times compared with that in 1990. With 253.78 million tons imported in the year 2011, China is going to be amajor oil-importing country gradually, with the contradiction between the supply and demand of oil being more and moresalient. As energy has come to be one of the main restraints as a bottleneck on socioeconomic development in China, it isof great importance to improve the production efficiency of the domestic energy enterprises. Lots of problems still existin the system of product efficiency evaluation and budget management [1]. A set of accurate and effective methods toevaluate the production efficiency of energy companies is necessary in practice. For now, most energy enterprises adoptthe ‘‘indicator composite index method’’ to carry out efficiency evaluation, which has problems with the subjective factorsof the determination of weights, thus leading to controversial assessment results. In fact, an energy enterprise is a kind ofcomplex system with multiple inputs and outputs, it has lessa priori information. DEA is a more fully fledged method toevaluate the relative effectiveness of complex systems and does not require a priori information. This method is used in thispaper to evaluate the production efficiencies of energy enterprises.

The DEA method takes an economic system or a production process as an activity, where an entity (a unit) produces acertain amount of ‘‘productions’’ by investing a certain amount of elements within a limited range. These entities (units) are

∗ Corresponding author. Tel.: +86 13821260061; fax: +86 022 27401815.E-mail address: [email protected] (L. Li).

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1058 L. Li et al. / Mathematical and Computer Modelling 58 (2013) 1057–1067

called decision-making units (DMUs). Many DMUs constitute to be respective evaluation groups. The efficient productionfrontier is built on evaluating, with each input or output indicator’s weight as the variable under the analysis of input andoutput ratios. In the end, an efficient DMU or an inefficient DMU can be determined according to the distance between thisDMU and the efficient production frontier [2,3].We canmake clear the reasonwhy a DMU is non-DEA efficient or weak-DEAefficient. Also, the projectionmethod can give the improvement extent. DEA is a branch of production frontier theory whichmeasures DMU’s relative effectiveness, and belongs to the nonparametric methodological category. This method especiallyapplies to a production model with multiple inputs and outputs.

Charnes et al. put forward the classical CCR model based on assuming the return to scale is constant [4]. The assumptiononly applies to the situation when all decision-making units are operated in the optimal scale of production points. It hasbeen improved by different kinds of models, such as the BCC model, super-efficiency model, two-stage model [5] andenvironment factors contained model [5,6]. These models make the original model more precise and effective in dealingwith practical problems. Banker et al. proposed the BCC model to explain the situation in which the scale is variable. Usingthe assumption of constant scale merit when the scale is variable will lead to a confusion of technical efficiency and scaleefficiency [7]. Therefore, the concept of efficiency splitting was raised in this period. Fare et al. put forward the method ofdetecting input congestion [8]. In the process of using the DEAmodel in projection improvement, the model of Phase I doesnot guarantee to identify all the relaxation. Ali and Seiford proposed to use two-stage linear programming to ensure theidentification of the efficient frontier point, displacing the projection point of phase I to the non-weak efficient point bymaximizing the relaxation [9]. The usual projection improvements are radial improvements against the origin. However,under the constraint of the current level of management or certain external conditions, some non-radical point of thefrontier should become the target of projection improvement. Therefore, a preference structure DEA model is necessaryto be created. Ray et al. carried out research on the relevant effectiveness of the state-owned iron and steel enterprises ofChina [10]. Wang and Lan applied the productivity analysis of the industrial economy of China by using both optimistic andpessimistic DEA [11]. In this paper, an improved super-efficiency model incorporating undesirable outputs is introduced toevaluate the production efficiencies of oil enterprises in this paper.

2. Methodology

2.1. The super-efficiency DEA model

In the application of DEA, if managers want to sort the DMUs by their efficiencies, the CCR efficiency could be adopted.That is feasible for the DEA inefficient DMUs. However, it is no longer feasible when it comes to the DEA efficient DMUswhose efficiency score is 1. This score means that the DEA efficient DMUs are all on the frontier. On the other hand, Coelliand Perelman pointed out that it would not result in a decline in the technical efficiency by adding an additional input oroutput, which means that the efficient DMUs are going to be more when there are more input or output indicators [12]. Inconsideration of that, Andersen and Petersen proposed using the super-efficiency DEA model to sort efficient DMUs [13].

Under the condition of variable returns to scale (VRS), the super-efficiencymodel to calculate the efficiency score of DMUnumbered J0 is described in Formula (1) as below. Assume there are n decision-making units, each decision-making unit hasm kinds of input and s kinds of outcome. xj = (x1j, x2j, . . . , xmj)

T > 0, j = 1, . . . , n, y = (y1j, y2j, . . . , ysj)T > 0, j = 1, . . . , nis the input and output vector of the jth decision-making unit. xij is the ith kind input of the jth decision-making unit. yrj isthe rth kind output of the jth decision-making unit. θ is a scalar whichmeets the condition θ ≤ 1. The result is the efficiencyvalue of the j0 decision-making unit. λj is the effective combination weight of decision-making units which is constructedby the j0 decision-making unit:

min θ super

s.t.

nj=1j=j0

λjxij ≤ θ superxio

nj=1j=j0

λjxij ≥ yro

j=j0

λj = 1

λj ≥ 0, j = o.

(1)

The main difference between the super-efficiency model and the basic DEA model is that the DMU to be evaluatedwill not appear in the reference set. In other words, the super-efficiency model is based on the reference set made up ofother DMUs [14]. The point of the super-efficiency model is that the efficiency remains unchanged when an efficient DMUincreases its inputs by a certain rate. Such a rate is the super-efficiency score, implying that the score of an efficient DMU isgreater than or equal to 1, while the score of an inefficient DMU remains the same with the CCR model [15].

L. Li et al. / Mathematical and Computer Modelling 58 (2013) 1057–1067 1059

Fig. 1. Computation of super-efficiency.

Fig. 2. Feasibility of computing super-efficiency score.

Greater capability of discernment is owned by the super-efficiency DEAmodel than the basic DEAmodel. However, therestill exist several problems using the super-efficiency model to sort out as follows.

(1) The score of the super-efficiency of a DMUmay be derived from a relatively weakly efficient DMU, meaning that thetrue score of the DMU has been exaggerated, as shown in Fig. 1.

Fig. 1 plots the inputs needed to produce per unit of output when the DMU consists of two kinds of inputs and oneoutput, assuming that production technology is of constant returns to scale (CRS). In Fig. 1, DMU1’s score of super-efficiencyis based on point C which is located in the production frontier (boundary), while point C is a point on the line along the yaxis of DMU2, and of weakly efficiency with larger slack variable in inputs. The score of DMU2 is based on the efficient pointon the connection line of DMU1 and DMU3. Nevertheless, the score of DMU1’s super-efficiency is exaggerated.

(2) Fig. 1 also shows that the benchmarks used to calculate each DMU’s super-efficiency score are different. That is tosay, the score of each DMU is based on all DMUs except itself.

(3) The super-efficiencymodel may be infeasible. Assuming that the production technology is of variable returns to scaleand each DMU consists of one input and one output. As shown in Fig. 2, the x axis represents inputs and the y axis representsoutputs; point A, point B and point C constitute the three DMUs on the production frontier.

The line AB in Fig. 2 is the segment of increasing returns to scale, and BC the segment of decreasing returns. B’s benchmarkis point B′′ on the line AB, while there is no benchmark for point C. That means that the model is infeasible in this case [16].

In view of these deficiencies above, the benchmark sorting DEA model is introduced to optimize the situation in thispaper.

2.2. Benchmark sorting DEA model

In the super-efficiency model, the benchmarks on which each DMU is based are different, while such a model may beinfeasible because managers may well specify one or several DMUs as the benchmarks. For this, one of the solutions is toadopt the benchmark sorting DEAmodel. Thismodel specifies several DMUs on the production frontier to evaluate the scoreof other DMUs, so as to ensure the consistency of the standards and meet the willingness of the managers.


To be simple, a multiplier form is used as the representation of the benchmark sorting DEA model in this paper. Definev = (v1, v2, . . . , vm)T as the weight vector of input and u = (u1, u2, . . . , us)

T as the weight vector of output. DMUnewrepresents the DMU to be evaluated, while E∗ stands for the set of DMU’s subscripts on the production frontier andB = {DMUj : j ∈ IB ⊂ E∗

} is the set of DMUs which make up the benchmark. θ∗ is the score of the efficiency. The model isshown as Formula (2):

θ∗= max

sr=1

urynewr

s.t.

sr=1

uryrj −mi=1

vixij = 0, j ∈ IB

sr=1

uryrj −mi=1

vixij ≤ 0, j ∈ IB

mi=1

vixnewi = 1

ur , vi ≥ 0.

(2)

Although the consistency of the standards is assured through the benchmark sorting model, there still exists a feasibilityproblem. When the number of DMUs in the set of B (the benchmark) is greater thanm+ s− 1, the model will be infeasible.Therefore an ‘‘ideal DMU’’ is described in this paper to solve infeasibility of the benchmark sorting model.

2.3. Ideal-DMU-based benchmark sorting model

If the manager does not specify the DMUs which constitute the benchmark, one of the ways to solve the infeasibility ofthe benchmark sorting model is to construct a dummy ideal DMU. The use of information of DMUs should be incorporated.It can satisfy that each input is smaller than any of the corresponding inputs and each output is greater than any of thecorresponding outputs of all the DMUs [17]. The scores of the DMUs would be calculated from the comparison with thedummy ideal DMU as the benchmark, thus sorting all the DMUs by their production efficiency.

The ideal DMU is defined to be: xideali = min{xij}, yidealr = max{yrj}. θ∗ is the score of the efficiency. Thus, the consistencyof the standards is assured by the ideal-DMU-based benchmark sorting model, with the problem of infeasibility solved atthe same time. Thus the ideal-DMU-based benchmark sorting model is shown as Formula (3):

θ∗= max

sr=1

urynewr + µ

s.t.

sr=1

uryidealr −

mi=1

vixideali = 0

mi=1

vixnewi = 0

ur , vi ≥ 0.

(3)

2.4. Comprehensive evaluation of the relative efficiency of DMUs

The traditional CCR model can distinguish between the efficient and inefficient DMUs. However, the final result is thatmultiple DMUs are of DEA efficiency, thus the ‘‘all sorted’’ cannot be realized. As previously stated, the super-efficiencymodel can distinguish between the efficient and inefficient DMUs as well as realize the ‘‘all sorted’’ of the DMUs. Thismodel encounters a deficiency of infeasibility when it comes to the case that the benchmarks of evaluation are different. Theconsistency of standards and the feasibility can be achieved through the ideal-DMU-based benchmark sorting model, whileit cannot distinguish between the efficient and inefficient DMUs. It also cannot realize the ‘‘all sorted’’ effectively when thenumber of input and output indicators is a little small. In short, these three ways of sorting have their own advantages anddisadvantages. On the basis of the complementary advantages, this paper uses the solution as follows in order to make thefinal sorting result more complete and accurate.

The traditional CCR model is a basic model evaluating relative efficiency, whereas the super-efficiency model and theideal-DMU-based benchmark sorting model must fit with the CCR model. The fitness among these models requires that thenumbers and the distributions of efficient and inefficient DMUs discriminated by different models should be the same orsimilar. The results of the three models would be adopted if the fitness test is passed. The sorting process is described asfollows:


Fig. 3. Projection improvement of input oriented DEA.

(1) Sort the inefficient DMUs using the CCR model firstly;(2) Sort the efficient DMUs using the ideal-DMU-based benchmark sorting model. The sorting process will come to an

end when the ‘‘all sorted’’ is realized in this step. Otherwise, turn to the third step.(3) Sort the DMUs unsorted in the first two steps using the super-efficiency model. Though it may be infeasible for the

super-efficiency model, it is far less likely to occur in this case.The all sorted of DMUs’ efficiency can be achieved through the three steps above. If one of the models does not fit with

the others, the result of this model will not be taken into account in the comprehensive evaluation process. The final resultshall be evaluated with other models [18].

The non-argument Wilcoxon signed-rank test is used to make a fitting examination on the CCR model and the super-efficiency model. n is the number of right matching data:

µT = 0

σT =

n(n + 1)(2n + 1)

6.

(4)

The Spearman’s rank correlation coefficient shall be calculated and used to take a fitting examination on the super-efficiency and the ideal-DUM-based benchmark sorting model, n is the number of row rank, xi is the ith rank of the super-efficiency model, and yi is the ith rank of the benchmark arrangement model, di = xi − yi:

rs = 1 −6

d2in(n2 − 1)

. (5)

2.5. Undesirable variables

The comprehensive evaluation above refers to the handling of the ‘‘undesirable variables’’, which is introduced below.The DEA is not only a method evaluating relative efficiency of DMUs, but also a method giving guidance to weakly efficientand inefficient DMUs. What ‘‘weakly efficient’’ means is that the DMU is on the production frontier with an efficiency scoreof 1, while there exists input slack or output slack as the same time. The elementary principle under which DEA guidesimprovements is the projection improvement theory. This theory means that the projection on the production frontier ofan inefficient DMU is the objective the DMU should achieve. Thus, the projection provides some information on productionand management to the organization managers [19].

Taking the input orientated DEA model as an example, the traditional projection improvement seeks for reduction ofinputs in equal proportion, shown as Fig. 3.

In Fig. 3, SCDS′ is the production frontier; point B is an inefficient DMU, with B′ as its projection point in the traditionalprojection improvement. θ∗ is the efficiency score of the input orientated DEAmodel; s−i is the input slack and s+r the outputslack. The projection formula is as follows:

i. Superabundance of input:

1xo = (1 − θ∗)xio + s−i . (6)

ii. Lack of output:

1yo = s+r . (7)


Let x0 = x0 − 1x0, y0 = y0 + 1y0. (x0, y0) will be demonstrated to be an efficient DMU. However, an input variablemay be uncontrollable (at least in the short run), such as the number of buildings, the area of land and so on. Assuming thatx2 in Fig. 3 is an uncontrollable input factor, the objective point will have to be B′′ if the projection improvement takes theproduction frontier as the objective. Thus the formula in view of radial reduction does not apply any more. The DEA modelincluding undesirable variables is introduced in this paper.

Now denote M as the set of subscripts of all input factors, and I as set of subscripts of ‘‘desirable variables’’ in M . Themodel is shown as Formula (6) under the condition of constant returns to scale:

min θ − ε

mi=1

s−i +

sr=1

s+r

s.t.

nj=1

λjxij + s−i = θxio, i ∈ I;

nj=1

λjxij + s−i = xio, i ∈ I;

nj=1

λjyrj − s+r = yro, r = 1, 2, . . . , s;

λj ≥ 0, j = 1, 2, . . . , n.

(8)

If the production technology is of variable returns to scale, there will be one more constraint:n

j=1 λj = 1. It can bedemonstrated that efficient DMUs are efficient containing undesirable variables in the traditional CCRmodel or BBCmodel. Italsoworks in reverse. In otherwords, the production frontiers of the twomodels are the same, but it is different regarding theimprovement objectives of inefficientDMUs. The superabundance of input in theDEAmodel containing ‘‘desirable variables’’is:

1xo = (1 − θ)xio + s−i , i ∈ I1xo = s−i , i ∈ I (9)

whereas the lack of output is:

1yo = s+r . (10)

It can be easily proved that, the DMU improved by the method above is at least weakly efficient.

3. Empirical study

The energy company selected for empirical study is the domestic dominant Oil andGas Company in China. Itsmain sourceof profit is the exploration and production departments. It consists of ten subordinate oilfield enterprises, marked as fromoilfield A through oilfield J.

Three input indicators and two output indicators are finally addressed after the preprocessing. The output indicators arethe production of oil and gas respectively whereas the input indicators are cost of main operation, operating expenses anddepreciation of fixed assets. For oilfield enterprises input, the main business indicators are labor costs, material costs andother associated costs in the process of exploration andproduction. Operating expenses are selling their exploitation of crudeoil andnatural gas costs. These two indicators have a greater relevance on the enterprisesmanagement level. The costs can bereduced by improving the oilfield enterprise business processes andmanagement systems. They are not undesirable inputs.The depreciation of fixed assets is depreciation extracted according to the fixed assets depreciation rate. The depreciation isto compensate for the loss of fixed assets within a certain period. The extraction of fixed assets depreciation is based on theoriginal value of the fixed assets of the oilfield enterprise, associated with the depreciation methods and the life span. In theshort run, the fixed assets of the oilfield enterprise are relatively stable. Thus, the indicator of depreciation of fixed assetsis used as an uncontrolled variable in this paper, denoted as an undesirable input indicator. In addition, taking into accountthe significant effect of macroeconomic factors on the production efficiency of oil companies, the absolute consumer priceis selected as an undesirable output indicator.

3.1. Preliminary effectiveness evaluation

According to the filtered results, the inputs and outputs of the oilfield enterprises are shown in Table 1.The efficiency of each oilfield enterprise and the slack variable for each indicator are shown in Table 2.We can concludes that the efficiencies of oilfield enterprises C, D, E, F, H and I are 1 and their slack variable for each

indicator is 0; thus these 6 enterprises are DEA efficient and the others are DEA inefficient.


Table 1Data of input and output indicators.

Indicator Oilfieldenter-priseA

Oilfieldenter-priseB

Oilfieldenter-priseC

Oilfieldenter-priseD

Oilfieldenter-priseE

Oilfieldenter-priseF

Oilfieldenter-priseG

Oilfieldenter-priseH

Oilfieldenter-priseI

Oilfieldenter-priseJ

Input indicator

Cost of main operation (mil $) 467.05 1307.23 74.89 522.53 486.21 779.49 1030.86 254.31 496.08 305.87Operation expenses (mil $) 4.68 4.61 0.8 0.87 0.51 3.13 3.82 3.67 5.72 10.8Depreciation of fixed assets (mil $) 278.33 655.63 34.76 280.56 227.19 297.72 456.65 102.52 243.76 143.62

Output indicator

Oil production (mil ton) 4.25 11.75 0.72 3.91 4.34 0.13 6.7 2.2 5.2 2.35Gas production (mil m3) 150 950 50 340 570 8600 4200 1300 1190 1210Absolute consumer price ($) 723 819 548 1244 548 451 404 460 514 514

Table 2Slack variables.

DMU Efficiency Cost of mainoperation

Operatingexpenses

Depreciation of fixedassets

Oilproduction

Gasproduction

Absoluteconsumer price

Oilfield A 0.894088126 0.0000 0.0000 7574.0827 0.0000 7.0383 0.0000Oilfield B 0.967040852 0.0000 0.0000 5772.5010 0.0000 8.9934 578.4206Oilfield C 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Oilfield D 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Oilfield E 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Oilfield F 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Oilfield G 0.97001501 0.0000 0.0000 1992.4584 0.0000 0.0000 683.3035Oilfield H 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Oilfield I 1 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000Oilfield J 0.861767507 0.0000 564.2634 3383.3479 0.0000 0.0000 0.0000

Table 3Evaluation result of the basic DEA model.

DMU Technical (CRS) efficiency value CRS efficiency value Scale efficiency value Returns to scale

Oilfield A 0.959775646 0.894088126 0.931559505 DecreasingOilfield B 1 0.967040852 0.967040852 DecreasingOilfield C 1 1 1 ConstantOilfield D 1 1 1 ConstantOilfield E 1 1 1 ConstantOilfield F 1 1 1 ConstantOilfield G 1 0.97001501 0.97001501 DecreasingOilfield H 1 1 1 ConstantOilfield I 1 1 1 ConstantOilfield J 0.894968284 0.861767507 0.962902846 Decreasing

The BCC efficiency scores are calculated from the technical efficiency value. The formula SE = TE(CRS)/TE(VRS) meansthat the scale efficiency is equal to the ratio of the CRS efficiency value to the VRS efficiency value. The scale efficiency valueand the changes of economies of scale according to the formula are shown in Table 3.

As can be seen in Table 3, the scale inefficient oilfield enterprises all experience decreasing returns to scale. Thus, it isnecessary for these enterprises to take some measures to reduce their size in order to be scale efficient.

3.2. Efficiency evaluation with the super-efficiency model

The efficiency values are shown in Table 4. They are calculated by using the super-efficiency model consisting of theundesirable indicators adjusted for the environment variables.

3.3. Efficiency evaluation based on the ideal-DMU-based benchmark sorting model

Firstly, an ‘‘ideal oilfield’’ is constructed according to the data of inputs and outputs of the ten oilfield enterprises, withits inputs the smallest and its outputs the largest among all the enterprises. The data of the ideal oilfield is shown in Table 5.

Without the consideration of the environment factors, the efficiency value of each oilfield calculated by using the ideal-DMU-based benchmark sorting model is shown in Table 6.


Table 4Super-efficiency value.

DMU Super-efficiency score

Oilfield A 0.894088126Oilfield B 0.967040852Oilfield C 3.537010529Oilfield D 1.55856634Oilfield E 2.04468624Oilfield F 3.050343353Oilfield G 0.97001501Oilfield H 1.29038413Oilfield I 1.130033727Oilfield J 0.861767507

Table 5The ideal oilfield.

Cost of main operation Operation expenses Depreciation of fixed assets Oil production Gas production

The ideal oilfield 47178 320 21900 1175 86

Table 6Efficiency score with ideal-DMU-based benchmark sorting model.

DMU Score of efficiency


Table 7Adjusted efficiency scores.

DMU Adjusted efficiency score


Then the Tobit regression analysis is carried out for each DMU, and with the adjustment based on the regressioncoefficients to the score, all oilfield’s scores are on the best environmental level, calculated as:

θ ′= θ −

ni=1

βi × (xi − ximin). (11)

The θ ′ is the adjusted efficiency score; θ is the original efficiency score; n stands for the number of environmental factorsthat have significant impact on the efficiency score; β is the regression coefficient; x means the environmental factors thathave significant impact on the efficiency score, and xmin is the least environmental level. The adjusted efficiency scores areshown in Table 7.

3.4. Comprehensive effectiveness evaluation

To take into consideration the technical efficiency and scale efficiency of each oilfield enterprise, the comprehensiveresult from the CCR model, the super-efficiency model and the ideal-DMU-based benchmark sorting model combined isadopted to evaluate the sufficiency. The fitting examination is taken on the results above.


Table 8Fitting examination.

DMU CCR model Super-efficiency model Absolute difference

Oilfield A 0 0 0Oilfield B 0 0 0Oilfield C 1 1 0Oilfield D 1 1 0Oilfield E 1 1 0Oilfield F 1 1 0Oilfield G 0 0 0Oilfield H 1 1 0Oilfield I 1 1 0Oilfield J 0 0 0

Table 9Rank of the two models.

DMU Rank of the super-efficiency model Rank of the benchmark sorting model

Oilfield A 9 5Oilfield B 8 3Oilfield C 1 6Oilfield D 4 2Oilfield E 3 1Oilfield F 2 4Oilfield G 7 8Oilfield H 5 9Oilfield I 6 7Oilfield J 10 10

3.4.1. Fitting examination on the CCR model and the super-efficiency modelThe non-argumentWilcoxon signed-rank test is used to take the fitting examination on the model. After the preprocess-

ing of data, the efficient oilfield is marked as 1 and the inefficient 0, as shown in Table 8.The given statistical hypothesis is that:H0: the two models do fit; H1: the two models don’t fit.The sum of the Wilcoxon signed-ranks is 0 and the P value is 1. Thus, the null hypothesis cannot be rejected, meaning

that the two models are fitted.

3.4.2. Fitting examination on the super-efficiency and the ideal-DUM-based benchmark sorting modelAccording to the efficiency evaluation results of the two models, the sorting rank is calculated as shown in Table 9.The Spearman’s rank correlation coefficient shall be calculated using Formula (5):The result is rs = 0.903. Giving the statistical hypothesis that:

H0: ρs = 0 (the two models do not fit).H1: ρs = 0 (the two models fit).

Under the condition of the null hypothesis that there is no rank correlation, the sorting process is independent. The

distribution of rs is: mean: µrs = 0, standard deviation: σrs =

1

n−1 , and it approximates the normal distribution whenn ≥ 10.

z =rs−µrs

σrs=

0.903−00.333 = 2.709, and the p-value is 0.0067 < 0.05. Thus, H0 shall be rejected under the 0.05 significance

level, meaning that the two models fit. According to the transitive property of fitting, the results of the three models arefitting.

According to the comprehensive evaluation process in Section 2, the final sorting result is shown in Table 10.Taking into consideration the analysis above, the final result of efficiency evaluation in this paper is concluded as shown

in Table 11.It can be thought that the geological exploration costs, gross domestic product and absolute consumer price had a

significant impact if using a 0.05 level of significance. This paper uses a 0.01 level. Only the absolute consumer price asan undesirable output indicator has a pronounced impact on the efficiency of the oilfield enterprise under this condition.

3.5. Analysis of results

3.5.1. Analysis of the overall efficiencyIn the CCR model, the oilfields whose efficiency is 1 make up the production frontier, compared to those oilfields

whose efficiency is less than 1 which are DEA inefficient. Ten oilfield enterprises of a well-known oil company in the


Table 10Comprehensive evaluation result of the three DEA models.

DMU Efficiency score of CCR model Efficiency score of benchmark sorting model Efficiency score of super-efficiency model Rank

Oilfield E 1 0.392684902 2.04468624 1Oilfield D 1 0.330039684 1.55856634 2Oilfield F 1 0.169779605 3.050343353 3Oilfield C 1 0.084599796 3.537010529 4Oilfield I 1 0.084581437 1.130033727 5Oilfield H 1 0.072440438 1.29038413 6Oilfield G 0.97001501 0.075744328 0.97001501 7Oilfield B 0.967040852 0.177480799 0.967040852 8Oilfield A 0.894088126 0.109826779 0.894088126 9Oilfield J 0.861767507 0.066742193 0.861767507 10

Table 11Final table of sufficiency evaluation.

DMU Efficiency of CCR model Efficiency of BCC model Scale efficiency Returns to scale Rank

Oilfield E 1 1 1 Constant 1Oilfield D 1 1 1 Constant 2Oilfield F 1 1 1 Constant 3Oilfield C 1 1 1 Constant 4Oilfield I 1 1 1 Constant 5Oilfield H 1 1 1 Constant 6Oilfield G 0.97001501 1 0.97001501 Decreasing 7Oilfield B 0.967040852 1 0.967040852 Decreasing 8Oilfield A 0.894088126 0.959775646 0.931559505 Decreasing 9Oilfield J 0.861767507 0.894968284 0.962902846 Decreasing 10

Mean 0.96929115 0.985474393 0.983151821 – –

domestic market are selected to be evaluated, with the overall efficiency value 0.92, which means that there is 3% roomfor improvement. Among the ten oilfields, the oilfields E, D, F, C, I, and H are DEA efficient with the rank from first throughsixth respectively. The oilfield J has the worst efficiency of 0.86, owning the largest room for improvement up to 14% amongthe ten. The oilfields B, G, and A own 3.3%, 3% and 11% room for improvement respectively.

3.5.2. Analysis of technical efficiencyWhat the BBC model evaluates is the pure technical efficiency value [20]. The mean technical efficiency value of the ten

oilfields is about 0.985, with 1.5% room for improvement. The technical efficiency value of oilfield J is only 0.89; therefore itshould draw on the experience of other oilfields in the future, improve the technical level of production and reduce wastageof inputs under the premise of maintaining outputs. The technical efficiency value of oilfield A is about 0.96, with 4% roomfor improvement.

3.5.3. Analysis of scale efficiencyThe mean scale efficiency value of the ten oilfields is about 0.98, meaning that there exists 2% of scale inefficiency.

Among them, the oilfields B, G, A, and J are scale inefficient and in the stage of decreasing returns to scale, meaning thatthe marginal revenue is less than the marginal cost. The main reason is that wrong decisions and bad management of themanagement of the oil enterprise, and the blind expansion of inputs did not gain the expected oil or gas production, leadingto the wastage of the resource of input. The six oilfields left are producing under the most appropriate scale. At the sametime, the DEA inefficiencies of oilfields B and G are caused by the scale inefficiency, whereas the DEA inefficiencies of A andJ come from pure technical aspects as well as scale. There should be attached great importance and in-depth investigationin the management processes. Disposal of low utilization fixed assets or for other purposes can reduce the input waste.

4. Conclusions

When using the CCR model of traditional DEA, if the number of DMUs is not relative enough to the number of indicators(the number of DMUs is less than twice the number of indicators), there will be more DEA efficient DMUs. This situationleads to a low capability of discernment. The DEA super-efficiency model can compensate for this shortcoming, while ithas the deficiency itself of the benchmark for evaluation and feasibility. This paper has documented an ideal-DMU-basedbenchmark sorting model to improve the super-efficiency model. The non-argument Wilcoxon signed-rank test is used totake a fitting examination on the CCR model and the super-efficiency model. The Spearman’s rank correlation coefficient isused to take a fitting examination on the super-efficiency and the ideal-DUM-based benchmark sorting model. Indeed, itis a comprehensive application of the CCR model, the super-efficiency model and the benchmark sorting model. In usingDEA methods to improve and guide the projection process, only the invalid or weak and effective DMU can guide the


improvement of the advice. However, the DEA method cannot give guidance to effective decision-making units. EffectiveDMUs are not perfect in technology and management processes, they are only relatively better. This is a future researchquestion. With ten oilfield enterprises of a famous energy company as the empirical objects, the applicability of the setof comprehensive methods is tested. The study realizes the all sorted of the ten DMUs, which cannot be reached with thetraditional CCRmodel or the super-efficiencymodel. This paper conducts a detailed analysis on the ten DMUs from the threeaspects of overall efficiency, scale efficiency and technical efficiency. We give some theoretical suggestions to the energycompany to improve its production efficiency. Some oilfield enterprises of the energy company should reduce the mainbusiness and operating expenses costs, excessive investment in fixed assets for disposal or for other purposes, and improvethe overall level of technology in various oilfield enterprises.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant No. 70871085, and71111120059); the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20100032120031);and the China Postdoctoral Science Foundation (Grant No. 20100480650). The authors are grateful for this support.

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