Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China

Socio-Economic Planning Sciences xxx (2017) 1e10

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Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China Wanghong Li a, Zhepeng Li a, Liang Liang b, Wade D. Cook a, * a b

Schulich School of Business, York University, Toronto, M3J1P3, Canada He Fei University of Technology, He Fei, An Hui Province, People’s Republic of China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 September 2016 Received in revised form 11 January 2017 Accepted 7 March 2017 Available online xxx

A balance between environmental regulation and economic prosperity has become a major issue of concern to attain a sustainable society in China. This study proposes the application of Data Envelopment Analysis (DEA) for measuring the efficiencies of the ecological systems in various regions of that country. The proposed approach differs from most of the previous ecological systems models in that we view it in a two stage setting; the first stage models the ecological system itself, and from an economic perspective, while the second stage (decontamination system) models water recycling as a feedback process, and the treatment of other undesirable outputs coming from the first stage. There, we separate polluting gases and water into two parts; one part is treated, while the other is discharged. The model considers two major desirable outputs from the first stage, namely Population and Gross Region Product by expenditure (GRP), as well as undesirable variables in the form of consumed water, and certain pollutants, namely nitrogen oxide, sulfur dioxide and soot. At the same time, these undesirable outputs from the first stage are inputs to the second decontamination stage. As well, recycled water is fed back into stage 1. Thus, intermediate variables such as consumed water and waste gas emission simultaneously play dual roles of both outputs and inputs in the ecological system. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Two-stage DEA Environmental assessment Recycling undesirable outputs

1. Introduction With rapid industrial growth in China, environment problems are growing worse each year. The Chinese, especially the governors, researchers, and corporate leaders believe that it is critical to do more to prevent water and air pollution in the form of nitrogen oxide, sulfur dioxide, carbon dioxide and soot (dust), etc. Strategists have a variety of ideas between environmental protection and economic prosperity issues. Environment protection proponents are concerned about air and water pollution, while other, more business activists believe that regulation on water and gas pollution may damage economic prosperity. The two conflicting ideas lead to different business and policy implications. There would appear to be a growing desire for a National anti-pollution policy. There is a significant literature relating to the impact of economic development on the environment. One particular industry that has a major influence on energy consumption and the

* Corresponding author. E-mail addresses: [email protected] (W. Li), [email protected] (Z. Li), [email protected] (L. Liang), [email protected] (W.D. Cook).

environment is the iron and steel industry as discussed in Guo and Fu [15]. Those authors survey many of the key issues associated with the development in that industry, and some economic policy implications are suggested. One of the key features of economic development in China is the recycling of scarce resources such as iron, steel, copper, asphalt on roads, etc. See, for example, Mo et al. [29]. Those authors conduct a detailed survey in Suzhou city relating to the collection and recovery processes of recyclable resources, and the issues that impact recycling systems, and the main actors involved in each recycling system. A recent paper by Ma et al. [27] discusses China's growing circular economy, a concept based on the principles of reduce, reuse and recycle. In a resource-starved country like China, this closedloop concept has become critical to its growth. Many studies have shown that the development of a circular economy is important to mitigating undesirable environmental impacts at source. In this paper we apply Data Envelopment Analysis (DEA) models to measure the regional ecological efficiency of the full set of 31 administrative regions in China. Then, based on empirical results, concerning the environment, and human and economic sustainable development, we study the factors associated with improvement in

http://dx.doi.org/10.1016/j.seps.2017.03.002 0038-0121/© 2017 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002

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W. Li et al. / Socio-Economic Planning Sciences xxx (2017) 1e10

environmental performance in the different regions of China. There is a substantial amount of research on global environmental protection, as mentioned above. Charnes et al. [2,3] were the first to apply analytical approaches to study several global environmental protection issues. Cooper et al. [12] summarizes more than 100 papers that discuss most kinds of air pollution issues. Zhou et al. [35] provides a summary of more than 100 DEA studies on environment and energy policy. An important consideration when modeling environmental issues in a DEA setting is the presence of undesirable factors (e.g. air €re et al. [14] were the first to develop the concept of pollutants.) Fa undesirable and desirable outputs. Other studies have been conducted by Dodos and Vorosmarly [13]; Lim and Zhu [25]; Liu et al. [26]; Maghbouli et al. [28] and Zhou et al. [33,34,35]. Previous ecology-based research has tended to pay little attention to settings involving two-stage network structures with intermediate measures. In that regard, the current study proposes a model that views the regional ecological system as a two-stage network structure with feedback. The study concerns the treatment of both desirable and undesirable outputs that flow from the first stage, some of which represent inputs to the second stage of assessment. Recycled water, as one of the outputs from the second stage, is fed back to the first stage as one of that stage's inputs. Thus, these intermediate variables simultaneously play an important role of both output and input. Both intermediate variables and the feedback variables constitute what Cook et al. [8], Cook and Zhu [9] call dual-role variables. We use the DEA methodology in a two stage process to account for such treatment. Since pollution is such an important consideration in the sustainability of the Chinese economy, it is critical to explore the internal ecological process, human sustainable development, water recycling, and air cleaning. If water and air are polluted, that situation will not lead to sustainable development. Water is a core resource for human survival in any region. In recent years in China, continued news reports point to serious water shortages that continue to get worse every year. With water shortage, it becomes very difficult to support the population. Similarly, soot and other forms of air pollution seriously impact people's health. There is a growing concern about this situation, not only from an economic development perspective, but also from the viewpoint of human survival. One first impression of the approach in this paper might be that it is similar to other circular economy literature, such as that of Ma et al. [27]; it definitely subscribes to the principles “reduce, reuse, recycle”. Arguably, however, there are certain features that distinguish our problem setting and chosen methodology from that of earlier literature. First, our study is at a rather macro level, namely the entire economy in China, as opposed to those studies that examine a specific industry such as iron and steel. Second, given this macro thrust, our choice of decision making units, namely regions, cities or provinces in China would seem to be justified, as opposed to using say industry sectors or particular companies. Third, the predominant input variables used to support the analysis are water, land and investment. Fourth, a region's natural resources can help to feed people; hence population would appear to be an important consideration in the ecological system. In economic terms, it is a measure of the total consumption of goods and services created by the economic system. In short, it is a measure of the “structure” supported by the macro inputs to that system. At the same time, it is necessary to have a concrete measure of the total value of all generated goods and services; hence we have chosen Gross Region Product by expenditure (GRP) as a key regional desirable output. At the same time, consumed water and three polluting gases (nitrogen oxide, sulfur dioxide and soot) are undesirable outputs from the first stage. Treated waste water and treated polluting gases are desirable

outputs, while discharged waste water and discharged waste gases are undesirable outputs at the second stage. It is important to point out here what “efficiency” means in the two stage process discussed above. Stage 1 describes the process of converting macro inputs into desirable (and undesirable) outputs. The extent to which a region is more or less successful in doing this, as compared to other regions, is best captured by an efficiency measurement tool such as DEA. A region that supports a larger population, generates a higher GRP and creates less pollutants would be deemed more efficient than a region with less desirable outputs and/or more undesirable outputs. If no process were in place to address decontamination of consumed water and air pollutants, and if recycled water was not fed back into the input side of the first stage, a single stage model would suffice to describe the economic system. In the current setting, however, a concerted effort is in place to address the severe pollution issue, hence the need for a second stage decontamination process. Stage 2's efficiency refers to the conversion of contaminants (consumed water and waste gasses), and the use of a portion of the GRP to treat some of those contaminants. The greater the portion of the contaminants treated, the greater is the efficiency of that second stage process. In summary, this paper sets out to measure the regional economic and ecological efficiency of the 31 administrative regions in China. Specifically, we study the factors associated with economic development and improvement in environmental performance in those different regions. The remainder of this paper is organized as follows: Section 2 summarizes previous contributions on two-stage DEA approaches. In Section 3 we extend the models for environmental assessment, while taking account of the inherent two-stage structure. Section 4 discusses the DEA model used to measure the environmental efficiency of the set of 31 administrative regions in China. Concluding remarks appear in Section 5. 2. Modeling efficiency in two-stage processes: the literature The modeling of efficiency in two-stage processes has been the subject of numerous papers including Maghbouli et al. [28]; Liu et al. [26]; Chen et al. [6,7]; Kao and Hwang [20]; Kao [18,19]; Liang et al. [22,23,24]. A recent paper by Cook et al. [11] provides a comprehensive survey of developments in this area. A number of important recent articles on internal DEA structures and networks appear in Cook and Zhu [10]. As background for the development herein, we briefly review the methodology for one of the most common two-stage structures, namely the serial process. For discussion purposes, let fxij g and fzdj g denote the inputs and outputs respectively for stage 1, and fzdj g, and fyrj g the inputs to and outputs from stage 2. Their corresponding multipliers are denoted by vi ; hd ; ur , respectively. In a closed serial system, the variables fzdj g are referred to as intermediate variables. Fig. 1 is a pictorial representation of a conventional two stage closed serial process. To evaluate the overall efficiency of the set of decision make units (DMUs) considered herein, we choose to adopt an outputoriented (rather than input-oriented) model, since it is outcomes or outputs from the ecological system that we wish to enhance, as opposed to reducing resources (inputs) to that process. Furthermore, we propose to use the variable returns to scale (VRS) model of Banker et al. [1]; as opposed to the CRS model. There are at least two reasons for this choice. First, the choice is partially driven by the fact that the relative “sizes” of the DMUs (provinces or regions) range from what might be deemed very small (e.g. Tibet), to very large (such as Jiangsu.) This being the case, the CRS can often produce scores that exaggerate inefficiencies. The second reason for the VRS choice is that in a two stage setting the stages act as

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002

W. Li et al. / Socio-Economic Planning Sciences xxx (2017) 1e10

components of the “operation”, and as such management may wish to investigate possible returns to scale differences between those components. Specifically, the VRS technology has the added benefit that it can identify cases of increasing, constant, and decreasing returns to scale. In this setting one can represent the output-oriented VRS efficiency for stage 1 (for DMU jo denoted for convenience by “o”), as the solution to the radial projection model:

" 1 b e o ¼ min

X

#, vi xio þ v1

X

i

hd zdo

d

subject to #, " X P 1 vi xij þ v hd zdj  1; cj i

(2.1)

d

vi ; hd  0; v1 unrestricted in sign The stage 2 model is given by

" 2 b e o ¼ min

X

#,

hd zdo þ v2

X

ur yro

subject to #, " X P 2 hd zdj þ v ur yrj  1; cj d

one sets out to construct scores for the two stages separately, which are such that when put together yield the optimal overall score. One of the original models for two stage process that explicitly recognized the intermediate variables in their double role, was that put forward by Kao and Hwang [20]; and is a form of the cooperative or centralized approach. In their model, the overall efficiency is expressed as the product eo ¼ e1o e2o . It is important to point out that the Kao and Hwang [20] approach explicitly assumes that the values of multipliers assigned to intermediate variables are the same in both their role as outputs from stage 1 and inputs to stage 2. A limitation of the Kao et al. approach is that it is explicitly designed for those settings where the appropriate technology is CRS. To accommodate VRS situations, as is used in the application herein, Chen et al. [6] propose an additive or arithmetic mean approach for combining the two stages, as opposed to the geometric mean-style methodology suggested by Kao and Hwang [20]. Specifically, the proposal is to express the overall efficiency as a convex combination eo ¼ w1 e1o þ w2 e2o of the stage efficiencies, where w1 ; w2 are appropriate weights. Under the Chen et al. [6] approach, the objective function for the VRS setting then becomes

("

r

d

(2.2)

r

hd ; ur  0; v2 unrestricted in sign One of the first approaches to two stage processes was given by Seiford and Zhu [30]; and simply uses the standard DEA structure, applying the CRS model [5] separately to each of stages1 and 2. In that context, the role of the intermediate variables is essentially ignored. More explicitly, the weights assigned to the intermediate variables in their role as outputs from stage 1 would generally be unrelated to the weights assigned to those variables when they serve as inputs to stage 2. Thus, in the ecology setting this would mean that the multiplier assigned to contaminated water as it exits stage 1 would be unrelated to its importance as an input to the second (recycling) stage 2. To address the recognized deficiency of the Seiford and Zhu [30] approach, a number of methodologies have been suggested in the literature for deriving an overall efficiency score for the two stages combined, and from these, deriving scores for the individual stages. Two of the suggested methodologies are those based on game theoretic principles, namely the cooperative and non-cooperative game models [11]. The non-cooperative or non-centralized approach, views the two stages as players in a game and adopts a leader-follower methodology. This methodology, often referred to as a Stackelburg game, involves choosing one of the two stages as the leader, and then deriving multipliers for the inputs and outputs that yield the best possible score for that stage. The efficiency score for the other stage or player (the follower) is then derived by finding the best possible weights for its inputs and outputs, but with the restriction that the score of the leader is not compromised. The cooperative game (or centralized) methodology derives the best aggregate efficiency score for the two stages combined. Then,

3

b e o ¼ minw1 $ (" þ w2 $

X

#, vi xio þ v1

i

X

#,

hd zdo þ v

2

X

)

hd zdo

d

X

)

(2.3)

ur yro

r

d

In the Chen et al. methodology, the intention is that the weights w1 ; w2 have the property that they sum to unity (convex combination of the efficiency scores of the two stages), and should be chosen such as to reflect the relative importance of the two stages. In regard to the latter property, since the output-oriented model is designed to determine the degree to which outputs need to be enhanced to reach the frontier, it appears reasonable to define w1 ; w2 as the proportions of the outputs generated by the respective stages. Specifically, define these weights as

w1 ¼

X

,"

hd zdo

d

w2 ¼

X

," ur yro

X

hd zdo þ

X

d

r

X

X

r

hd zdo þ

# ur yro ; #

(2.4)

ur yro ;

r

d

Under this definition, the efficiency measure (objective function) for the two-stages combined becomes:

" b e o ¼ min

X

1

vi xio þ v þ

i

X

#,"

hd zdo þ v

2

d

X

hd zdo þ

X

# ur yro

r

d

(2.5) Hence, the cooperative game model for deriving the overall efficiency for the two stages is given by:

" b e o ¼ min

X

vi xio þ v1 þ

i

X

#,"

hd zdo þ v2

d

X d

hd zdo þ

X

# ur yro

r

subject to #, " X P vi xij þ v1 hd zdj  1; cj " i #, d X P hd zdj þ v2 ur yrj  1; cj d

r

vi ; ur ; hd  0; v1 ; v2 unrestricted in sign (2.6) Fig. 1. A two stage serial process.

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It is important to make two observations regarding (2.6). First, the multipliers chosen should be such that when applied to the efficiency ratios for each of stages 1 and 2 (for each j), those ratios will behave as output oriented efficiency scores, and be appropriately at or above unity. We note that these conditions have been imposed. Second, constraints should be imposed as well, requiring that any multipliers chosen satisfy the condition that when applied to the aggregate scores for each of the DMUs j, the ratios for those DMUs will be at or above unity. However, in the presence of the constraints on the two stages, the aggregate ratio conditions are redundant, and therefore are automatically satisfied, hence are omitted. Having solved the overall efficiency problem (2.6) (or rather its linear equivalent to be discuss in section 3 below), and assuming that stage 1 or player 1 (in game theoretic terms), is chosen as the leader, we then solve (2.7), the modified player 1 problem:

" 1 b eo

¼ min

X

#, 1

vi xio þ v

i

X

hd zdo

d

subject to " #, X P 1 vi xij þ v hd zdj  1; cj d " i # " # X X X P 1 2 b vi xio þ v þ hd zdo þ v  e o hd zdo þ ur yro ¼ 0 i

d

vi ; hd  0; v1 unrestricted in sign

d

r

(2.7) This model derives the leader's optimal efficiency score, subject to the requirement that the combined score, representing the aggregate of the two stages, is at the level determined in (2.6). The stage 2 score, following the logic of (2.3), then becomes: 2 b eo ¼

1 b 1b b eo  w eo b2 w

(2.8)

If stage 2 is chosen as the leader, an analogous approach would be taken. 3. A two stage efficiency model for China's ecological system In this section, we present a particular two-stage model for measuring the regional ecological efficiency of 31 administrative regions in China. First, we discuss the economic factors on which we base our analysis. It is widely recognized that water is an important component in the ecological process, and possibly the dominant resource in ecosystems. Water is a basic necessity of life, but in some areas in China people lack easy access to this essential element for daily use. People can travel three or more hours each day to get clean water to drink and bath. Shortage of water impacts daily life and survival, and seriously hampers economic development. For this reason we have selected water consumption as a major study index and focus on water recycling. Despite the importance of water as an input to economic and ecological system, it cannot produce any output without other resources, such as investment and land [16].) Fig. 2 captures, in macro terms, an ecosystem with its relevant inputs and outputs. Based on the previous discussion, the first stage of the system portrays the use of fundamental resources, namely water, land, and investment as inputs to the system. On the output side, we argue that the major fundamental indexes of the economic and ecological system are GRP and population. As well, any ecological study must recognize the important role played by undesirable outputs, and without which the results of the measurement of ecological efficiency will be biased [35]. Hence, the second

stage involves the recycling of consumed water and decontamination of harmful gasses from stage 1. In more specific terms, fresh and treated waste water use (U) (unit: 100 million cu.m), regional cultivated land (E) (unit:10,000 ha), and capital investment (I) (unit:100 million Yuan) are inputs to the ecosystem. Here, we follow Lee [21] and Soytas and Sari [32]; replacing industrial capital stock with investment (I). The number of persons fed, or the population (H) (unit: 10,000 persons), in real terms for the year 2012, and GRP (unit:100 million Yuan), are outputs from the first stage. GRP is split into two sections; one (M1) goes toward the general economy, while the other (M2) is an environment investment as an input to the second stage. At the same time, consumed water (W) (unit: 100 million cu.m) and waste gas (S) (unit: ton) in the form of nitrogen oxides, sulfur dioxide and soot are undesirable outputs from stage 1. The intermediate product W flowing from stage 1 (the amount of water consumed or used), waste gasses and M2 are the inputs to stage 2. The (desirable) outputs from this stage are the treated water (W1) (unit: 100 million cu.m) and treated gases (S1) (unit: ton). Only treated water W1 is a feedback variable, and the undesirable output is the discarded (waste) water (W2) (unit: 100 million cu.m) and waste gasses (S2) (unit: ton) that are discharged into the atmosphere. What we wish to achieve in our analysis is a measure of efficiency, not only of the system, but as well the efficiency of the water recycling and waste gas treatment processes. We point out four important things: First, we recognize that nitrogen oxide, sulfur dioxide and soot are not intended to constitute the full range of atmosphere contaminants. For example, we have not included carbon dioxide emissions. We defend our choice, however, by the argument that the selected gasses hopefully constitute a reasonable cross-section of the set of all contaminants. As well, there is likely to be a high correlation between the selected and non-selected contaminants, meaning that regions high in one contaminant are likely to be high in others. Thus, the chosen for analysis contaminants serve as surrogates for the excluded ones. Second, we have chosen to lump together, as a single variable, the set of three (non-water) contaminants used, arguing that they are all in the same units, and should be treated as relatively equal in importance. Third, in regard to materials balance, we note, for example, that what is referred to as U (water available for use) does not balance out with W (water consumed) since not all available water is used. As well, W is not simply the sum of treated waste water (W1) and discharged water (W2). This is because a significant portion of W is used for bathing, laundering etc., hence goes back into the ground, never making it into the recycling system. Fourth, and finally, both the intermediate variable W and the feedback variable W1 constitute what Cook et al. [8]; Cook and Zhu [9] define as dual-role variables, in that they play roles of output and input simultaneously. The current study selects the 31 regions in China for analysis; Table 1 and Table 2 provide the data and the names of these regions (DMUs) from north to south in Chinese geography. The data cover the period 2007e2012. It is noted that the usual two-stage DEA models generally address settings where all outputs are of the desirable type. Treating undesirable factors within the DEA framework has been a subject of study over the past several years; a useful survey of methods are discussed by Hua et al. [17]; Seiford and Zhu [31] presented one of the first approaches for dealing with undesirable variables. Their approach involves the use of a linear monotone decreasing transformation of the undesirable variable bj , specifically replacing it by a (transformed) variable bj defined by bj ¼ bj þ v  0 where v is an appropriate translation vector that makes bj _0. This means we multiply each undesirable output by (1), and find a proper

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002

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5

Fig. 2. Two-stage network with feedback. Notation: E: Cultivated land; I: Investment; U: water available for use (fresh water and recycled water); H: Population; M1: Part of Gross Region Product by expenditure (GRP); M2: Part of GRP used as Decontamination system investment; W: Ecological system consumed water; S: nitrogen oxides, sulfur dioxide and soot (dust); W1: Treated waste water; W2: Discharged waste of water, S1: Treated nitrogen oxides, sulfur dioxide and soot (dust); S2: Discharged nitrogen oxides, sulfur dioxide and soot (dust) emission.

translation vector v to replace the resultant negative data bj by positive data bj . In selecting v, we might choose to think of it as the largest or worst value that this variable can assume, hence bj represents the amount of that undesirable factor not experienced. Thus,

The efficiency model for the stage 2 recycling process is given by (3.3), and the linear equivalent (3.4)

i.h i h 2 2 u11 Wo1 þu12 S1o þu21 W o þu22 So e2 ¼min h21 Mo2 þ h3 Wo þ h4 So þv2

while less of bj is desirable, more of bj is desirable, as is true of regular outputs. Here we defined v ¼ max (b)þ1. We point out that we have applied the undesirable output transformation only at the second stage on the discarded water and gas. An additional consideration, particularly regarding undesirable outputs such as sulfur dioxide, is the imposing of the weak disposability assumption. In the context of the output-oriented model this would generally mean that on the envelopment side P of the DEA model one would impose the condition lj yuj ¼ fyu0

subjectto i h i h 2 2 h21 Mj2 þ h3 Wj þ h4 Sj þv2  u11 Wj1 þu12 S1j þu21 W j þu22 Sj 0;cj

for an undesirable output yu0 . Using the multiplier model, we may invoke weak disposability of such a variable by allowing its multiplier to be unrestricted in sign. This has been done as shown in the models below. Focusing again on Fig. 2, and referring to the development in Section 2, the VRS output- oriented efficiency model for the ecological system (stage 1) of a particular DMUo is given by:

h

j

h21 ;u11 ;u12 ;u21 ;u22 0; h3 ; h4 ;v2 unrestrictedinsign (3.3) e2 ¼minp21 Mo2 þ p3 Wo þ p4 So þ y2 subject to 2

2

m11 Wo1 þ m12 S1o þ m21 W o þ m22 So ¼1

i h i 2 2 p21 Mj2 þ p3 Wj þ p4 Sj þ y2  m11 Wj1 þ m12 S1j þ m21 W j þ m22 Sj 0; cj

p21 ; m11 ; m12 ; m21 ; m22 0; p3 ; p4 ; y2 unrestrictedinsign (3.4)

i.h i h e1 ¼ min v1 Eo þ v2 Io þ v3 Uo þ v1 h11 Mo1 þ h21 Mo2 þ h2 Ho þ h3 Wo þ h4 So subject to i h i  v1 Ej þ v2 Ij þ v3 Uj þ v1  h11 Mj1 þ h2j Mj2 þ h2 Hj þ h3 Wj þ h4 Sj  0; cj

(3.1)

vi ; h11 ; h21 ; h2  0; h3 ; h4 ; v1 unrestricted in sign

Clearly, as mentioned earlier, (3.1) is a nonlinear programming problem, but can be converted to linear form via the Charnes and Cooper [4] transformation. Specifically, define a new variable t ¼ 1=ðh11 Mj1 þ h2j Mj2 þ h2 Ho þ h3 Wo þ h4 So Þ, multiply all numera-

Defining the aggregate efficiency score as a weighted average of the scores for the two stages, in a manner analogous to that given in

tors and denominators by this variable, and create new variables yi ¼ t ni ; p11 ¼ t h11 ; :::etc: Model (3.1) is then equivalent to model (3.2).

e1 ¼ miny1 Eo þ y2 Io þ y3 Uo þ y1 subject to p11 Mo1 þ p21 Mo2 þ p2 Ho þ p3 Wo þ p4 So ¼ 1 i h i  y1 Ej þ y2 Ij þ y3 Uj þ y1  p11 Mj1 þ p2j Mj2 þ p2 Hj þ p3 Wj þ p4 Sj  0; cj

(3.2)

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W. Li et al. / Socio-Economic Planning Sciences xxx (2017) 1e10

the previous section, the resulting aggregate model is given by (3.5):

eo ¼ min h

We use the (*) in the objective function of (3.7) to signify that this stage 1 model has the additional restriction that any feasible

h i v1 Eo þ v2 Io þ v3 Uo þ v1 þ h21 Mo2 þ h3 Wo þ h4 So þ v2 2

2

h11 Mo1 þ h21 Mo2 þ h2 Ho þ h3 Wo þ h4 So þ u11 Wo1 þ u12 S1o þ u21 W o þ u22 So

i

subject to i h i  v1 Ej þ v2 Ij þ v3 Uj þ v1  h11 Mj1 þ h21 Mj2 þ h2 Hj þ h3 Wj þ h4 Sj  0; cj h i h i 2 2 h21 Mj2 þ h3 Wj þ h4 Sj þ v2  u11 Wj1 þ u12 S1j þ u21 W j þ u22 Sj  0; cj

(3.5)

vi ; h11 ; h21 ; h2 ; u11 ; u12 ; u21 ; u22  0; h3 ; h4 ; v1 ; v2 unrestricted in sign

solution must be such as to retain the optimal solution found in (3.6). Having solved for the optimal solution to the stage one model, the stage two optimal solution is given by:

and its linear equivalent is given by (3.6)

eo ¼ miny1 Eo þ y2 Io þ vy3 Uo þ y1 þ p21 Mo2 þ p3 Wo þ p4 So þ y2 subject to 2

2

p11 Mo1 þ p21 Mo2 þ p2 Ho þ p3 Wo þ p4 So þ u11 Wo1 þ u12 S1o þ u21 W o þ u22 So ¼ 1



i

h

i

y1 Ej þ y2 Ij þ y3 Uj þ y1  p11 Mj1 þ p2j Mj2 þ p2 Hj þ p3 Wj þ p4 Sj  0; cj

h

i

h

2

2

(3.6)

i

p21 Mj2 þ p3 Wj þ p4 Sj þ p2  m11 Wj1 þ m12 S1j þ m21 W j þ u22 Sj  0; cj

yi ; p11 ; p21 ; p2 ; m11 ; m12 ; m21 ; m22  0; p3 ; p4 ; y1 ; y2 unrestricted in sign

It is observed that any variable that plays the dual role of an output from stage 1 and input to stage 2, has the same multiplier. For example, M2 has the multiplier h21 in both the first set of constraints for stage 1 in model (3.5) (in its role of output from stage 1), and in the second set of constraints where it plays the role of input to stage 2. In the cooperative game approach, as discussed above, one first solves (3.6), and then assuming stage 1 is given first priority (is the leader), we solve (3.2), but with the added requirement that the optimality of (3.6) is not compromised. Model (3.7) serves this purpose.

i. h 2 o b e ¼ b e  w1 e1* w2

(3.8)

In the following section we evaluate the relative efficiencies of the 31 regions in China in terms of the performance of their ecological systems, as well as that of the associated water recycling and gas decontamination processes. We point out that in model (3.6) one has the option of imposing limits on the relative sizes of the weights w1 ; w2 . For example, a constraint restricting w1 to lie in the range (a,b) would take the form

e1* ¼ miny1 Eo þ y2 Io þ y3 Uo þ y1 subject to p11 Mo1 þ p21 Mo2 þ p2 Ho þ i p3hWo þ p4 So ¼ 1 i  y1 Ej þ y2 Ij þ y3 Uj þ y1  p11 Mj1 þ p2j Mj2 þ p2 Hj þ p3 Wj þ p4 Sj  0; cj

y1 Eohþ y2 Io þ vy3 Uo þ y1 þ p21 Mo2 þ p3 Wo þ p4 So þ y2 i 2 2 o b e p11 Mo1 þ p21 Mo2 þ p2 Ho þ p3 Wo þ p4 So þ u11 Wo1 þ u12 S1o þ u21 W o þ u22 So ¼ 0 yi ; p11 ; p21 ; p2 ; m11 ; m12 ; m21 ; m22  0; p3 ; p4 ; y1 ; y2 unrestricted in sign

(3.7)

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002

W. Li et al. / Socio-Economic Planning Sciences xxx (2017) 1e10

h ah

p11 Mo1 þ p21 Mo2 þ p2 Ho þ p3 Wo þ p4 So

i 2

2

p11 Mo1 þ p21 Mo2 þ p2 Ho þ p3 Wo þ p4 So þ u11 Wo1 þ u12 S1o þ u21 W o þ u22 So

Note that since the denominator of this ratio is equal to 1, we need only limit the numerator, specifically,

i h a  p11 Mo1 þ p21 Mo2 þ p2 Ho þ p3 Wo þ p4 So  b:

7

(3.9)

We impose such restrictions below.

4. Application In this section we examine the efficiencies of 31 regions in China. As portrayed in Fig. 2, we view the ecosystem as consisting of two distinct stages; stage 1 is the primary system, and stage 2 is decontamination. The input and output data for the two stages are displayed in Tables 1 and 2, respectively. We point out that we have combined the three waste gasses nitrogen oxide, sulfur dioxide and

ib

soot into a single factor namely S as shown in Table 1, and have separated it into treated gasses (S1) and discard or untreated (S2). In applying model (3.6), we derive the aggregate output efficiency scores b e o for the regions; these are presented in Table 3 in the form of output augmentation. For example, a score of 1.05 would mean that for this DMU an increase of 5% in each output would be required in order for it to reach the frontier. Using this aggregate score, and assuming stage 1 is the leader and stage 2 the follower, model (3.7) is solved, followed by (3.8); the results appear in columns (2) and (3), respectively. If stage 2 is chosen as the leader and stage 1 the follower, columns (4) and (5) result. For convenience, these results have been displayed in an alternative form in Table 4 (as reciprocals), since “efficiencies” are commonly taken as being  1. Shown as well are the weights w1 ; w2 . We point out that we have imposed the constraint that each weight must be at least 10%.

Table 1 Stage 1 data for the regional ecological system index in China. Variable

Unit Region Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Tibet Shanxi Gansu Qinghai Ningxia Xinjiang

Inputs

Desirable outputs

Cultivated Investment: Water land: E I available for use: U

Gross Regional Product Total investment in by Expenditure Treatment of Approach: M 1 Environmental Pollution: M2

Undesirable outputs Population: Consumption Total volume of Nitrogen oxides, H of water: W Sulfur dioxide, and Soot (Dust) emission: S

1000 ha

100 million Yuan

100 million 100 million Yuan cu.m

100 million Yuan

10,000 Persons

100 million cu.m

tons

231.7 441.1 6317.3 4055.8 7147.2

8870.8 8853.6 20,106 8311.7 12,174.6

35.9 23.1 195.3 73.4 184.4

17,536.8 12,736.4 26,088.9 11,784.6 15,435.5

342.6 157.5 486.1 328.2 445.1

2069 1413 7288 3611 2490

19.6 15.5 144 56 123.1

338,167 642,808 4,338,188 3,616,588 3,636,835

4085.3 5534.6 11,830.1 244 4763.8 1920.9 5730.2 1330.1 2827.1 7515.3 7926.4 4664.1 3789.4 2830.7 4217.5 727.5 2235.9 5947.4 4485.3 6072.1 361.6 4050.3 4658.8 542.7 1107.1 4124.6

24,225.6 9694.4 10,400.5 6961.2 36,552.9 19,243.6 16,587.8 13,850.7 12,103.1 33,538.2 21,710.1 16,884.5 15,898.5 22,005.9 10,506.8 2755.8 10,312 18,204 5949.1 8047.5 696.7 13,222.3 5365.8 1982.7 1998.3 6572.9

142.2 129.8 358.9 116 552.2 198.1 292.6 200.1 242.5 221.8 238.6 299.3 328.8 451.5 303 45.3 82.9 245.9 100.8 151.8 29.8 88 123.1 27.4 69.4 590.1

24,163 12,585 13,473.5 20,047.6 53,401.1 34,289.9 16,881.9 19,479.3 12,632.8 49,274.1 29,389.8 22,373.9 21,963.9 56,807.7 12,844.6 2810.8 11,222.7 23,694.5 6783.3 10,177.1 697 14,273.1 5528.8 1869.4 2285.6 7250.2

683.4 103.4 218.1 134.1 657.1 375.4 330.2 222.5 316.1 739.1 209.5 285.5 190.3 260.2 190.5 44.7 186.9 178.3 68.9 132.4 4 180.6 121.4 24.1 55.7 255.1

4389 2750 3834 2380 7920 5477 5988 3748 4504 9685 9406 5779 6639 10,594 4862 887 2945 8076 3484 4659 308 3753 2578 573 647 2233

91.1 67.1 204.7 20 281.9 109.7 148.2 90.6 107.8 143.9 134.5 132.6 136.5 172.8 129.9 20.7 41.5 120.8 46.6 84.9 24.3 51.4 80.5 17.2 31.3 396.1

2,821,292 1,244,090 1,994,186 716,984 2,914,784 1,688,645 1,907,916 1,091,097 1,502,155 4,183,047 3,501,630 1,612,032 1,592,897 2,430,904 1,302,102 154,135 1,129,714 1,819,281 1,899,123 1,607,208 55,088 2,113,935 1,253,438 436,305 1,060,375 2,311,731

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002

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W. Li et al. / Socio-Economic Planning Sciences xxx (2017) 1e10

Table 2 Stage 2 data for the regional ecological system index in China. Variable

Inputs

Desirable outputs

Undesirable outputs

M2

W

S

W1

S1

W2

S2

Unit

100 million Yuan

100 million cu.m

ton

100 million cu.m

ton

100 million cu.m

ton

Region Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Tibet Shanxi Gansu Qinghai Ningxia Xinjiang

342.6 157.5 486.1 328.2 445.1 683.4 103.4 218.1 134.1 657.1 375.4 330.2 222.5 316.1 739.1 209.5 285.5 190.3 260.2 190.5 44.7 186.9 178.3 68.9 132.4 4 180.6 121.4 24.1 55.7 255.1

19.6 15.5 144 56 123.1 91.1 67.1 204.7 20 281.9 109.7 148.2 90.6 107.8 143.9 134.5 132.6 136.5 172.8 129.9 20.7 41.5 120.8 46.6 84.9 24.3 51.4 80.5 17.2 31.3 396.1

338,167 642,808 4,338,188 3,616,588 3,636,835 2,821,292 1,244,090 1,994,186 716,984 2,914,784 1,688,645 1,907,916 1,091,097 1,502,155 4,183,047 3,501,630 1,612,032 1,592,897 2,430,904 1,302,102 154,135 1,129,714 1,819,281 1,899,123 1,607,208 55,088 2,113,935 1,253,438 436,305 1,060,375 2,311,731

0.0099 0.0046 0.0085 0.0029 0.002 0.0106 0.0061 0.0021 0.0355 0.0282 0.0495 0.0174 0.0264 0.026 0.0331 0.0142 0.0254 0.0402 0.0542 0.0121 0.0052 0.0142 0.023 0.0052 0.0111 0.0002 0.0086 0.0036 0.0007 0.0011 0.0041

399 292 212 118 16 126 36 16 348 964 675 999 60 34 436 118 173 64 1760 153 134 28 693 6 35 4 19 230 3 6 47

14.0175 8.2767 30.5688 13.4269 10.2404 23.8663 11.9448 16.2568 21.8889 59.7929 42.0466 25.4155 25.5999 1.9859 47.8769 40.3526 28.9946 30.3812 83.8009 24.5457 3.7051 13.2288 28.3427 9.1403 15.3899 0.4681 12.8663 6.2777 2.1987 3.8937 9.3769

337,768 642,516 4,337,976 3,616,470 3,636,819 2,821,166 1,244,054 1,994,170 716,636 2,913,820 1,687,970 1,906,917 1,091,037 1,502,121 4,182,611 3,501,512 1,611,859 1,592,833 2,429,144 1,301,949 154,001 1,129,686 1,818,588 1,899,117 1,607,173 55,084 2,113,916 1,253,208 436,302 1,060,369 2,311,684

Table 3 Two stage output oriented efficiency scores.

Table 4 Two stage input oriented efficiency scores.

Region

* b e0

e*1

e2

e*2

e1

u1

u2

Region

1=b e0

1=e*1

1=e2

1=e*2

1=e1

u1

u2

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Tibet Shanxi Gansu Qinghai Ningxia Xinjiang

1.0000 1.0000 1.1195 1.0136 1.1691 1.3158 1.1735 1.2441 1.0000 1.0833 1.0000 1.0126 1.1637 1.0037 1.0346 1.0696 1.2585 1.0320 1.0000 1.1502 1.0177 1.1182 1.0199 1.0108 1.0178 1.0000 1.1253 1.0182 1.0000 1.0737 1.1292

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.2678 1.1274 1.0000 1.0000 1.0000 1.1257 1.0773 1.0371 1.0000 1.0000 1.2307 1.1230 1.0000 1.0599 1.1766 1.1913 1.0164 1.0000 1.0000 1.0000 1.1212 1.0102 1.0000 1.0000 1.0000

1.0000 1.0000 2.1952 1.1362 1.1879 1.3509 1.1630 1.2571 1.0000 1.8335 1.0000 1.0000 1.1733 1.0000 1.3460 1.6956 1.2615 1.0219 1.0000 1.9628 1.0000 1.0942 1.0515 1.1082 1.1783 1.0000 1.1621 1.0191 1.0000 1.0819 1.1436

1.0000 1.0000 1.4155 1.1362 1.1258 1.3131 1.1425 1.2239 1.0000 1.3159 1.0000 1.0000 1.1324 1.0000 1.3460 1.6956 1.2466 1.0000 1.0000 1.2674 1.0000 1.0941 1.0136 1.1082 1.1783 1.0000 1.1553 1.0019 1.0000 1.0413 1.1013

1.0000 1.0000 1.0866 1.0000 1.5591 1.3407 1.4517 1.4264 1.0000 1.0575 1.0000 1.1257 1.4449 1.0371 1.0000 1.0000 1.3653 1.3197 1.0000 1.1371 1.1766 1.1918 1.0206 1.0000 1.0000 1.0000 1.1219 1.1647 1.0000 1.3649 1.3802

0.7468 0.8635 0.9000 0.9000 0.1000 0.1000 0.1000 0.1000 0.7313 0.9000 0.4400 0.1000 0.1000 0.1000 0.9000 0.9000 0.1000 0.1000 0.4641 0.9000 0.1000 0.2469 0.9000 0.9000 0.9000 0.8816 0.9000 0.1000 0.8706 0.1000 0.1000

0.2532 0.1365 0.1000 0.1000 0.9000 0.9000 0.9000 0.9000 0.2687 0.1000 0.5600 0.9000 0.9000 0.9000 0.1000 0.1000 0.9000 0.9000 0.5359 0.1000 0.9000 0.7531 0.1000 0.1000 0.1000 0.1184 0.1000 0.9000 0.1294 0.9000 0.9000

Beijing Tianjin Hebei Shanxi Inner Mongolia Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Hainan Chongqing Sichuan Guizhou Yunnan Tibet Shanxi Gansu Qinghai Ningxia Xinjiang

1.0000 1.0000 0.8932 0.9866 0.8554 0.7600 0.8522 0.8038 1.0000 0.9231 1.0000 0.9876 0.8594 0.9963 0.9666 0.9350 0.7946 0.9690 1.0000 0.8694 0.9826 0.8943 0.9805 0.9893 0.9825 1.0000 0.8887 0.9821 1.0000 0.9314 0.8856

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.7888 0.8870 1.0000 1.0000 1.0000 0.8883 0.9283 0.9642 1.0000 1.0000 0.8125 0.8905 1.0000 0.9435 0.8499 0.8394 0.9839 1.0000 1.0000 1.0000 0.8919 0.9899 1.0000 1.0000 1.0000

1.0000 1.0000 0.4555 0.8801 0.8418 0.7402 0.8599 0.7955 1.0000 0.5454 1.0000 1.0000 0.8523 1.0000 0.7429 0.5898 0.7927 0.9786 1.0000 0.5095 1.0000 0.9139 0.9511 0.9023 0.8487 1.0000 0.8605 0.9813 1.0000 0.9243 0.8745

1.0000 1.0000 0.7064 0.8801 0.8883 0.7616 0.8752 0.8171 1.0000 0.7599 1.0000 1.0000 0.8831 1.0000 0.7429 0.5898 0.8022 1.0000 1.0000 0.7890 1.0000 0.9140 0.9866 0.9023 0.8487 1.0000 0.8656 0.9981 1.0000 0.9603 0.9080

1.0000 1.0000 0.9203 1.0000 0.6414 0.7459 0.6889 0.7011 1.0000 0.9456 1.0000 0.8883 0.6921 0.9642 1.0000 1.0000 0.7325 0.7577 1.0000 0.8794 0.8499 0.8390 0.9798 1.0000 1.0000 1.0000 0.8913 0.8586 1.0000 0.7327 0.7245

0.7468 0.8635 0.9000 0.9000 0.1000 0.1000 0.1000 0.1000 0.7313 0.9000 0.4400 0.1000 0.1000 0.1000 0.9000 0.9000 0.1000 0.1000 0.4641 0.9000 0.1000 0.2469 0.9000 0.9000 0.9000 0.8816 0.9000 0.1000 0.8706 0.1000 0.1000

0.2532 0.1365 0.1000 0.1000 0.9000 0.9000 0.9000 0.9000 0.2687 0.1000 0.5600 0.9000 0.9000 0.9000 0.1000 0.1000 0.9000 0.9000 0.5359 0.1000 0.9000 0.7531 0.1000 0.1000 0.1000 0.1184 0.1000 0.9000 0.1294 0.9000 0.9000

*

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002

W. Li et al. / Socio-Economic Planning Sciences xxx (2017) 1e10

It is acknowledged that this is a rather arbitrary choice to prevent some regions from unfairly enhancing their aggregate scores, by allowing one or the other of their stage scores to approach 0. From Tables 3 and 4, it is apparent that Beijing, Tianjing, Shanghai, Zhejiang, Guangdong, Tibet and Qinhai Province are efficient overall, as well as in each stage. We point out again that overall or aggregate efficiency is possible only in the situation where both stages are efficient as well. While Beijing, Tianjing and Shanghai are the economic and political centers of China, Zhejiang and Guangdong are the leading provinces in terms of economic development. Tibet and Qinhai provinces, having less industry, are seen as leaders in an environmental sense in China. The remaining 24 regions exhibit varying degrees of inefficiency. For example, Shanxi, Inner Mongolia, Liaoning, Jiangshu, Shandong, Henan, Gueizhou, Yunnan, Qinghai, Ningxia and Xinjiang are efficient in the first stage, but they are inefficient in the second stage, meaning that overall they are inefficient. In all cases, when the first stage is dominant, the efficiency of that stage is higher than when the second stage is dominant. It is worth noting that Hebei province is inefficient. One reason for this is that it has more waste water, waste gasses and more total investment in treatment of environmental pollution. This is partially due to its proximity to the capital, Beijing, in that some of produced pollution moves from Beijing to Hebei province. As well, some of the waste water from the capital is processed in Hebei. Our two-stage approach is able to uncover the fact that in certain regions, specifically Tibet and Qinghai, the overall efficiencies and the individual stage efficiencies are very high, being at or near the 100% efficient levels. These efficiency scores reflect the fact that the ecological systems in those regions are superior to the systems in other locations. In China, as mentioned above, those particular regions have the best environmental reputation as compared to other regions. Potential for Policy Formulation: It is well know that during the past two decades, China's government has made efforts to reduce emission of air pollutants and reduce polluted water. They would be interested to know the factors associated with improvement in environment performance in the different regions in different processes. Our developed model aids in understanding the extent of waste water and waste gas treatment in different regions. These are the main factors influencing environment quality. As well, government authorities would find it useful to see the extent to which particular regions are succeeding at reducing pollution in a meaningful way, and which regions represent the benchmarks in environment protection. China has a severe lack of fresh water resources, meaning that some regions have to depend on diverting water from other locations, such as the famous water project in China: this diverts water from the south to the north. In a recent declaration of the state council of China (April 16, 2015), the water pollution prevention plan calls for four expected results: (1) optimize economic development; (2) strengthen the environmental protection industry; (3) put in place a systematic process for managing water quality; and (4) improve people's livelihood. Regional ecological systems should be managed from a network perspective. China has a severe haze (soot) problem that is having a damaging influence on people's health; some of the larger cities now have a very unfavorable reputation in terms of air pollution. In the absence of an effective approach to stop the growing damage to air quality, the entire ecological system in China can only become worse, especially in large cities such as Beijing, Shanghai, etc. Policy makers require a formalized methodology to be able to identify where inefficiencies exist, and be in a position to address those inefficiencies. The two stage methodology presented here has the advantage of being able to monitor the economic efficiency in

9

terms of GRP and the feeding population (stage 1), while at the same time being able to evaluate the waste water recycling and waste gas treatment capability (stage 2). Our two-stage DEA methodology can be used not only to evaluate overall ecological efficiency and waste water and waste gas decontamination, but also to evaluate other network-based processes. 5. Conclusions and future developments This paper develops an optimization model for evaluating the relative overall efficiency of the ecological system of each of a set of 31 regions in China. The proposed approach differs from most of the previous (single stage) ecological systems models, in that we view it from the perspective of economic prosperity, as well as focusing on the ecological concern of waste water recycling (and reuse as a feedback process), and waste gas treatment processes. The mathematical model uses Data Envelopment Analysis as a framework within which to address these two principal concerns. The model considers both desirable outputs (the gross regional product and population of the region), and undesirable outputs in the form of waste gas and waste water, and their treatment processes. Ecological efficiency measurement is an important issue in developing countries such as China. Rapid development of the economy is definitely a priority, but at the same time there is a need for fresh water and clean air. The present paper addresses the fact that waste water, when recycled, is then fed back into the system as a desirable input to the economic process. The presence of such feedback variables renders the conventional approaches of the CCR and BCC models inappropriate for measuring efficiency here. This being the case, the current paper adopts the view that ecological efficiency needs to be viewed from a two-stage perspective: efficiency of the region from the standpoint of economic prosperity (stage 1); and efficiency of the environmental or ecological preservation process, mainly waste water and waste gas decontamination (stage 2). The advantage of this network structure lies in the fact that we can separate the two concepts (economic efficiency and ecological preservation efficiency), obtaining a measure for each, while at the same time providing a mechanism for combining the two measures to create an overall efficiency score. The network structure can be an important policy-setting tool. Individual stage efficiency scores can provide policy makers with detailed information that can aid in identifying specific problem areas, leading to the ultimate goal of overall system optimization. Further research is being conducted in this area. An important follow up study might examine impacts of pollutants on the population as opposed to quantities of the pollutant themselves. Specifically data on mortality rates/lifespans in the various regions would provide a possibly provide more stark contrast between regions. Later work will examine this area. Acknowledgments Wade Cook and Wanghong Li acknowledge support from the Natural Sciences and Engineering Council of Canada under grant number A8966. References [1] Banker RD, Charnes A, Cooper WW. Some models for estimating technical and scale inefficiencies in data envelopment analysis. Man Sci 1984;30:1078e92. [2] Charnes A, Cooper WW, Mellon B. Blending aviation gasolineea study in programming interdependent activities in an integrated oil company. Econometrica 1952;20:135e59. [3] Charnes A, Cooper WW, Symonds GH. Cost horizon and certainty equivalents: an approach to stochastic programming of heating oil by the horizon method. Man Sci 1958;4:235e63. [4] Charnes A, Cooper WW. Programming with linear fractional functionals. Nav

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Wade D. Cook is the Gordon Charlton Shaw Professor of Management Science, and holds the title University Professor at the Schulich School of Business, York University, Toronto. His publications appear in a wide range of journals including Management Science, Operations Research, EJOR, JORS, IIE Transactions, etc. He is the author of several books on Data Envelopment Analysis.

Wanghong Li recently received her PhD from the University of Science and Technology of China, and is currently a Post-Doctoral Fellow at the Schulich School of Business, York University in Toronto. Her recent publications in the area of Data Envelopment Analysis have appeared in ANOR, EJOR and OMEGA.

Liang Liang recently held the position of Professor and Dean in the School of Management, University of Science and Technology of China. He is now President of the He Fei University of Technology, China. He has published research in the area of DEA in a wide range of journals including Operations research, OMEGA, IIE Transactions, EJOR, etc.

Zhepeng Li is an Assistant Professor in the Schulich School of Business, York University, Toronto. His area of research interest is machine learning and organizational performance. His publications appear in a number of journals including Management Science.

Please cite this article in press as: Li W, et al., Evaluation of ecological systems and the recycling of undesirable outputs: An efficiency study of regions in China, Socio-Economic Planning Sciences (2017), http://dx.doi.org/10.1016/j.seps.2017.03.002