A DEA-based improvement of China's green development from the perspective of resource reallocation

Journal Pre-proof A DEA-based improvement of China's green development from the perspective of resource reallocation

Jie Wu, Wei Lu, Mingjun Li PII:

S0048-9697(20)30616-1

DOI:

https://doi.org/10.1016/j.scitotenv.2020.137106

Reference:

STOTEN 137106

To appear in:

Science of the Total Environment

Received date:

6 November 2019

Revised date:

2 February 2020

Accepted date:

2 February 2020

Please cite this article as: J. Wu, W. Lu and M. Li, A DEA-based improvement of China's green development from the perspective of resource reallocation, Science of the Total Environment (2018), https://doi.org/10.1016/j.scitotenv.2020.137106

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© 2018 Published by Elsevier.

Journal Pre-proof

A DEA-based improvement of China’s green development from the perspective of resource reallocation Jie Wua, Wei Lua, Mingjun Lia,* a

School of Management, University of Science and Technology of China

Abstract As the current important environmental management method in China, the green development

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concept aims to improve the environmental development status of the region from the perspectives

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of energy conservation, emission reduction, and pollutant control. Based on the concept of green development, we mainly consider the allocation of resources and the distribution of emission

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rights from the perspective of resource allocation and improve the efficiency of green

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development. We analyze how to allocate the additional fixed assets investment and emission rights to each province. We determine that the government should prioritize the faster economic

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growth areas when there is enough additional investment. Some coastal areas are not priority allocation regions, indicating that their development has basically reached saturation. We also

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investigated the emission rights of “three wastes” of 30 provinces in China. The result shows that only Shanghai, Sichuan, Guangxi, and Gansu are affected by three wastes emissions after the

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allocation of additional resources, and their emissions of those three wastes are all reduced. Finally, we dynamically analyze the amount of resource reallocation between different regions

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under different growth (reduction) rates of fixed resources and emission rights while ensuring maximum overall efficiency. Eventually, we obtained the optimal investment increase and emission reduction by the algorithm. Keywords: Data Envelopment Analysis; Resource Allocation; Energy Saving and Emission Reduction; Green Economy Development

1.

Introduction

Currently, China is experiencing rapid development through industrialization and urbanization. *

Corresponding author Email address: [email protected] (Mingjun Li)

Journal Pre-proof The massive consumption of resources and the excessive discharge of pollutants are both critical negative effects brought by the rapid development of the traditional industrial economy. Long-term research shows that we can effectively break through bottlenecks in resource and environment only through vigorously developing a green economy. In 2015, the Chinese government included Green Development as one of China’s core development goals and policies in its 13th Five-Year Plan. It also proposed specific plan goals, including a 20% reduction in energy consumption per unit of GDP; a 15% increase in the proportion of renewable and clean energy consumption; a 10% reduction in major pollutant emissions and so on. Thus, the concept of

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green development is not only an evaluation and analysis of the current development of the green

understanding the existing green development level.

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economy but also a scientific approach to improving the efficiency of green development based on

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Green development research points out that the green development of a region is mainly improved through energy conservation, emission reduction, and pollutant treatment. Firstly, we

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must optimize resource allocation by a scientific method. Although the total resources of China are

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relatively abundant, the per capita resources are low; in particular, the main energy sources such as water resources, oil, and gas reserves per capita are far below the world average. Therefore,

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optimizing resource allocation and reducing waste is a major method to improve the efficiency of green development. Secondly, because of the lack of resources and the constraints of the traditional industry’s development and technology, China’s discharge of wastewater and

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generated solid wastes have also remained high, which has put great pressure on the ecological

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environment. Based on this, the Chinese government has gradually implemented the allocation and trading of emission rights, intending to rationally formulate distribution plans and improve the efficiency of pollution control. In summary, this paper will consider the allocation of resources and emission rights from the perspective of resource allocation to improve the efficiency of green development. In order to reflect the goals in the 13th Five-year Plan, we also consider the setting of the optimal emission-reducing amount and the fixed assets increasing amount. Green development can be regarded as one kind of sustainability management, there is plenty of literature on this stream. From the energy saving aspect, Sun et al. (2018), Li et al. (2019a) and Ji et al. (2017) did study on China’s energy consumption among provinces and enterprises. Wu et al. (2018) and Ji et al. (2019) measure China’s energy efficiency considering undesirable output. From emission aspect, studies are aim on carbon emission regulation (Li et al.,

Journal Pre-proof 2018). Furthermore, Li et al. (2019b) examine the role of innovative technologies in green supply chains from an enterprise perspective. In the paper, we mainly study green development from the resource allocation aspect. As one of the classic applications of sustainability management, resource allocation has great practical value (Korhonen and Syrjanen, 2004; Ji et al., 2017). Data Envelopment Analysis (DEA) brought a new perspective to the resource allocation problem. Existing DEA studies on resource allocation can be divided into three different categories: resource allocation and objective setting (Bi et al., 2011; Song et al., 2019), centralized resource allocation (Lozano and Villa, 2004; Song et. al., 2019), and other perspectives (Jin et al., 2019; Cui

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and Song, 2019; Chen et al., 2019). Yu et al. (2019) studied the input-oriented BCC model used to

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evaluate the efficiency of the primary carbon emission allowance allocation scheme in the “13th Five-Year Plan”. Ye et al. (2019) established a dual-objective programming model that considered

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both the economic and energy goals, while the environmental goal was reflected in constraints. Besides, there are studies bring new extended DEA method to allocation problems (Ji et al., 2018;

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Ji et al., 2019; Wu et al., 2016, Liu et al., 2019).

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In the literature, the DEA models for resource allocation have two assumptions. One is that the efficiency of each DMU may be different after resource allocation. The second is that the

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efficiency of each DMU is constant regardless of how resources are allocated. These two assumptions about resource allocation have certain limitations: First, models based on constant efficiency assumptions may be unreasonable because, for most production systems, efficiency

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changes as production size changes. Therefore, it is necessary to consider efficiency changes due

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to resource allocation. Second, most studies based on variable efficiency assumptions after resource allocation assume that each unit can be produced on an efficient boundary formed by some efficient DMUs. Such studies did not consider the technical heterogeneity of each DMU, and they set output targets that might not be easily achieved for some DMUs (Sun et al., 2018). In reality, input resources cannot always be flexibly allocated or changed because of certain special attributes. For example, some resources may have fixed characteristics that cannot be easily changed or transferred, such as land resources, while others can be flexibly changed. Furthermore, some resources may be scarce, which forces decision makers to consider the efficiency of the organization when allocating; it is necessary to allocate scarce resources to the most needy DMUs. In addition, some of the allocated input resources have fixed features that are not consumed during production, such as equipment investment. Other features are more flexible and can be arbitrarily

Journal Pre-proof changed in each production period. This paper aims to select the resource allocation model that best fits the green development essence and to apply the latest data to solve practical problems. According to the improvement method of green development efficiency and the analysis of existing resource allocation models explained above, we will mainly consider three points in the selection of models and indicators. First, input indicators should be classified by their attributes and construct constraints, respectively. Second, the technical heterogeneity between DMUs should be considered. Thus, we assume that technical efficiency cannot be improved in the short term. There are already

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researchers applied heterogeneity assumptions in the DEA study (Sun et al., 2019, Wu et al. 2019).

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Third, to fully characterize the essence of green development, the choice of the objective function in this article cannot be single, multi-objective functions must be considered. Multiple-objective

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linear programming (MOLP) is applied to divide the objective of the central decision-making unit (CDMU) into maximizing output, minimizing additional resource input, and maximizing

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organization efficiency. MOLP has been considered in several studies and can be transformed into

Preliminaries

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2.

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a single objective linear programming model (Wu et al., 2012).

We select the constant technical efficiency assumption first. The technical efficiency of each

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province does not change easily in a short period. To ensure the fairness of allocation, we consider

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the heterogeneity of technical efficiency and group DMUs according to their technical efficiency. Secondly, according to the characteristics of green development efficiency and the role of input indicators in allocation, we classify each input indicator according to whether it is reallocated and variable.

2.1.

Identification for production technology

Most existing models for resource allocation problems are based on the assumption that allocating additional input resources could project each DMU to the efficient frontier of the production possibility set formed by all the DMUs (Fang, 2013; Korhonen and Syrjanen, 2004; Lozano and Villa, 2004; Wu et al., 2013). Being on the frontier is thought to bring the optimal output revenue. The frontier assumption may be reasonable in the long term because inefficient DMUs can learn

Journal Pre-proof from or imitate efficient DMUs to improve their technology. However, in the short-term, real-world context, simply increasing or decreasing input resources may not be sufficient to make a DMU’s production technology efficient. Even after resource allocation, the DMU continues to use its original technology to produce, so the evaluation of its original technology is a key issue. Here, a context-dependent DEA is introduced to identify the actual production technology. Therefore, we define a new production possibility set that describes the possible short-term production changes for each unit. We use a context-dependent DEA technique (Seiford and Zhu, 2003; Zhu, 2003) to

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measure the relative attractiveness of a DMU compared to others. The set of DMUs can be divided

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into different levels of efficient frontiers. For example, VRS has been assumed in the BCC model because each level of efficient frontier in the VRS better describes each production method. If we

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remove the original efficient frontier, the remaining inefficient DMUs can be used to determine a new second-level efficient frontier. If we remove the second-level efficient frontier, we can form a

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third-level efficient frontier, and so on, until there are no remaining DMUs. Each such efficient

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frontier can provide an evaluation context to compare the original technologies of the DMUs. All DMUs at the same efficient frontier are said to be on the same layer DMUs, and it is reasonable to

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expect all DMUs on a given layer k will have some common attributes. The following algorithm identifies the DMUs in the same layer.

Algorithm 1: Algorithm for context-dependent DEA technique.

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1. We start with Layer 1, so set k = 1 . Use the BCC DEA model to evaluate the entire set of

frontier).

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DMUs, E1 , to obtain the first-layer efficient DMUs, set L1 (the first-layer efficient 2. Exclude the k -layer efficient DMUs from future DEA runs. E( k 1) = Ek  Lk . If E( k 1) =  , the algorithm stops; else go to step 3.

3. Evaluate the new subset of “inefficient” DMUs, E( k 1) , to obtain a new set of (k  1) -layer efficient DMUs L( k 1) (the new-layer efficient frontier). 4. Let k = k  1. Go to step 2. Since DMUs on the same efficient frontier have similar performance in production, here we assume that DMUs in the same layer have the same technology. As the input increases or decreases, the DMUs have performance similar to other DMUs in the same layer. Therefore, those

Journal Pre-proof DMUs can produce their products on their own changed production possibility set after allocating additional resources to them. The changed production possibility set based on layer k is given here.

TBCC = {( x, y)  L(k ) |

 x

jL ( k )

j ij

 x,

 y

jL ( k )

j

ij

 y,



jL ( k )

j

= 1,  j  0}

(1)

After allocating additional input resources, the changed production possible set defines each DMU’ s feasible production region.

Classification for input indicator

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2.2.

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We classify the input resources into three groups: nonallocated constant inputs, allocated constant inputs, and allocated variable inputs. The characteristics of each kind of input resource are as

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follows. The nonallocated constant inputs are unchangeable inputs for each DMU, so they are neither exhausted nor increased by allocation; they remain unchanged in the next production

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period. An example of a nonallocated input is the land occupied by the DMU. An allocated

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constant input for a DMU will not be consumed in production so it will not decrease, but it may increase during the next production period if a central control unit allocates more of this input to

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the DMU from a fixed available amount. Large-scale equipment is an example of this type of input. The last group is allocated variable inputs that are used up in production in the current period but for which there is a ready supply. Amounts of this type of input can increase or decrease for

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each DMU. In short, nonallocated constant inputs will never change, allocated constant inputs will

3.

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never decrease but may increase, and allocated variable inputs may increase or decrease.

MOLP model for resource allocation based on regional green

development efficiency Corresponding to the green development goals set in the 13th Five-Year Plan, we choose a multi-objective program that takes into account changes in inputs/ outputs and the effectiveness of an organization. In this section, in order to allocate the additional resources effectively, we follow the DEA-based bi-objective LP model (Wu et al., 2016) to simultaneously maximize total changed output production and minimize the total allocated variable input resource consumption. Suppose there are n DMUs controlled by a centralized decision making unit (CDMU) in

Journal Pre-proof the

organization.

X J =  x1 j , x2 j ,

For

each

j ,

DMU j

uses

w

nonallocated

xwj  , m allocated constant inputs FJ =  f1 j , f 2 j , T

variable inputs U J =  u1 j , u2 j ,

constant

inputs

. f mj  , and t allocated T

uti  to produce s outputs YJ =  y1 j , y2 j , T

ysj  . Suppose that T

for the next period of production the organization has total additional inputs Ri , i = 1, 2, each allocated constant input resource and total additional inputs Ei , i = 1, 2,

m for

t , for each

allocated variable input resource. The CDMU desires to allocate a proper proportion of these

possibility set will not change after the resource allocation. s

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n

Max yrq

(I )

q=1 r=1 t

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n

Min uiq

( II )

q=1 i =1



jq ij



jq ij



jq

jL ( k )

jL ( k )

jL ( k )

x  xiq

i = 1,

f  fiq  fiq

u  uiq

, w k = 1, i = 1,

i = 1,

yrj  yrq  yrq

, p,q  L(k ) (2.1)

re

jq ij

, m k = 1,

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

jL ( k )

,t

k = 1,

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s.t.

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resources to each DMUs to maximize the objectives. In this paper, we assume that the production

r = 1,

, p,q  L( k ) (2.2)

, p,q  L( k ) (2.3)

, s k = 1,

, p,q  L( k ) (2.4)

ur

f iq = 0 when f iq  f iqMpss i = 1, , m, q = 1, , n (2.5) f iq  f iq  f iqMpss when f iq  f iqMpss i = 1, , m, q = 1, n

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f

iq

= Ri

i = 1,

, m (2.7)

 Ei

i = 1,

, t (2.8)

, n (2.6)

q =1 n

u

iq

q =1



jL ( k )

jq

= 1 k = 1,

, p  L(k ) (2.9)

f iq  i fiq i = 1, , mq = 1, , n (2.10)  jq  0 uiq  0 j  L(k ) k = 1, , p i = 1,

(2) ,m

where L ( k ) denotes the set of observed DMUs that belong to layer k . Here f iq , uiq , and yiq denote the change amounts of constant input i , variable input i , and output r respectively.

In model (2), maximizing the sum of the total output changes of all DMUs in the next

Journal Pre-proof period models the fact that bringing the highest amount of production is the primary objective of resource allocation for a centralized organization’s CDMU. We also minimize the sum of allocated variable inputs allocated to all DMUs in the next period because the secondary objective of the CDMU is to save resources if that is possible while maintaining maximum organizational output. Constraints (2.1)-(2.4) guarantee that each DMU’s new production is in its own changed production possibility set. Constraints (2.7) and (2.8) denote that the total allocated resources among all DMUs cannot exceed the total additional input resources. Constraint (2.9) indicates that VRS is assumed in this model. To guarantee that the proportional scaling is managerially feasible,

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according to (Korhonen et al., 2004), we limit the change in constant inputs to be fiq  i fiq .

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These constraints eliminate solutions in which all resources are allocated to only a few DMUs with advanced technology, which reflects the idea that the CDMU should be fair to all DMUs.

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It is assumed that the allocated constant input resource F is very valuable for production

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but is scarce due to cost and availability. The CDMU expends lots of effort and funding to obtain these resources, so decision makers naturally want to get a return on that investment as quickly as

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possible. Therefore, we assume that this type of resource should be fully allocated. Recognizing the enormous value of allocated constant input resources, we want to ensure that they are allocated

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to those DMUs that really need them, so we apply the concept of the new MPSS (Zhu and Shen., 1995), which is represented by constraints (2.5) and (2.6). The notation f iqMPSS indicates the m by DMU q in the field of new MPSS. For each layer, there

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maximum value of input i = 1, 2,

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is only one such maximum value, i.e., the DMUs in the same layer have the same maximum value. The maximum value in each layer can be calculated by the following Algorithm 2 (Zhu and Shen., 1995).

Algorithm 2: Algorithm for calculating maximum f iqMPSS using the MPSS concept. 1. Calculate the efficiency of the DMUs in each layer using the FGL model 2. Find the efficient DMUs in each layer using the FGL model. 3. Calculate the biggest value for each input i among the efficient DMUs in each layer, and also the maximum value in each layer, which is denoted by f iqMPSS , i = 1, 2,

m

Also, to maximize satisfaction within the organization, an additional one unit of input should be allocated to the DMU that brings greater satisfaction to the organization while maintaining maximum output. Based on this setting, we define this output growth rate as the

Journal Pre-proof effectiveness of the DMU, and the effectiveness of the organization is expressed as follows. Definition 1. The effectiveness of an organization is defined as the output growth rate for all DMUs. This is a benefit index that can be calculated as: n

s

 = 

yrq

q=1 r=1

(3)

yrq

The organization should consider not only the change of total output and consumption of input resources but also the effectiveness of the resource allocation. Therefore, the objective function of model (2) can be replaced by the following. s

(I )

n

t

Min uiq q=1 i =1 s

(4)

yrq

( III )

re

q=1 r=1

yrq

( II )

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n

Max 

ro

q=1 r=1

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n

Max yrq

Model (2) is a multiple-objective programming problem in DEA (Amirteimoori and Emrouznejad,

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2012; Amirteimoori and Kordrostami, 2012; Keshavarz and Toloo, 2014, 2015). Following the multiple-objective programming method (Amirteimoori and Kordrostami, 2012), we can

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programming model (5):

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transform the multiple-objective programming model (2) into the following single-objective

Journal Pre-proof n

s

n

t

n

s

Max yrq  w1 uiq  w2  q=1 r=1

s.t.



jq ij



jq ij



jq ij



jq

jL ( k )

jL ( k )

jL ( k )

jL ( k )

q=1 i =1

x  xiq

i = 1,

f  fiq  fiq

u  uiq

i = 1,

yrj  yrq  yrq

yrq

q=1 r=1

, w k = 1,

i = 1,

yrq

, p,q  L(k ) (5.1)

, m k = 1,

,t

k = 1,

r = 1,

, p,q  L(k ) (5.2)

, p,q  L(k ) (5.3)

, s k = 1,

, p,q  L(k ) (5.4)

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fiq = 0 when f iq  f iqMpss i = 1, , m, q = 1, , n (5.5) fiq  fiq  f iqMpss when f iq  f iqMpss i = 1, , m, q = 1,

f

iq

= Ri

i = 1,

, m (5.7)

 Ei

i = 1,

, t (5.8)

n

u

iq

-p

q =1

q =1

jq

= 1 k = 1,

, p  L(k ) (5.9)

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

jL ( k )

, n (5.6)

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n

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fiq  i fiq i = 1, , mq = 1, , n (5.10)  jq  0 uiq  0 j  L(k ) k = 1, , p i = 1,

(5)

,m

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The constraints of single-objective model (5) are the same as model (2). In the objective function of model (5), w1 (0 < w1 < 1) and w2 (0 < w2 < 1) are the weights of input resources and

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effectiveness, respectively. The weight selection has a large impact on the optimal solution. Different studies have used different methods to choose the weights (Amirteimoori and

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Emrouznejad, 2012; Amirteimoori and Kordrostami, 2012). In this paper, we consider the real factors and maximize the total output as the main goal. Considering the importance of green development, minimizing the input of resources is the secondary goal, and organizational effectiveness is the third goal. Therefore, it is assumed that w1 > w2 . It is worth noting that CDMUs may have varying preferences for input resources and effectiveness, and can set different weights. We also consider the effects of different weights in the model analysis section of this paper, and do a numerical analysis of the settings of w1 , w2 . In summary, we use model (5) to establish a comprehensive resource allocation scheme that considers multiple objectives according to the needs of a CDMU. This model is realistic about the difference of the objective selections of CDMUs, thus giving a more scientific and rational resource allocation plan.

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4.

Indicator selection and results analysis

4.1.

Indicator selection and group

In keeping with previous research on the characteristics of Chinese industry, we select the indices of industrial labor force of year-end (ILF, unit: 10 thousand persons ), industrial water consumption (IWC, unit: 100 million m3 ), annual electricity consumption (AEC, unit: 10 thousand KWH), industrial energy consumption (IEC, unit: 10 thousand ton standard coal), and

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fixed asset investment (FAI, unit: 10 thousand yuan) as inputs, and we select the indices of industrial SO2 emitted (SO2, unit: ton), industrial wastewater discharged (IWWD, unit: 10

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thousand ton), industrial solid wastes generated (ISWG, unit: 10 thousand ton), gross industrial

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output value (GIOV), GDP as outputs. We first consider how the CDMUs’ additional fixed asset investment is allocated to each province. Fixed assets are not consumed in the production process,

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so the fixed assets will only increase, never decrease. According to the input classification in the model preliminaries, fixed asset investment increases the fixed assets which are an allocated

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constant input. Secondly, the emissions of “three wastes” are the undesired outputs of the green development, which can be regarded as a special input resource. The state can control the

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emissions of each province by allocating emission rights, and the emissions of each DMU can be increased or decreased for the next stage, so the emission right is an allocated variable input. The

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remaining input resources are not allocated, thus classified as nonallocated variable inputs. This

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study uses data of 30 provinces in China to measure the efficiency of regional green economic development. The sources of the data are the China Statistical Yearbook and China Environmental Statistical Yearbook. The classification of input, output, and initial efficiency values of the regional green development production in 2015 are given in Table 1 and Table 2

Table 1: Input of regional green development of production period in 2015 Nonallocated input (X)

Allocated constant input (F)

Province

ILF

IWC

AEC

IEC

FAI

Beijing

777.35

3.8

9527169

6853

79409699

Tianjin

294.78

5.3

8006009

8260

130480000

256.52

18.8

7971676

18927

122169796

Liaoning

612.41

21.4

11859009

21667

176403698

Jilin

291.37

23.2

3358652

8142

118104329

Shanghai

722.88

64.6

14055500

11387

63493886

Jiangsu

1547.88

239

26668022

30235

459051694

Zhejiang

1112.92

51.6

17455944

19610

266190881

Fujian

659.39

72.5

7454512

12180

212426978

Jiangxi

469.19

61.6

4303781

8440

168189589

Shandong

1222.51

29.6

21092740

37945

473814559

Henan

1099.43

52.5

11174675

23161

Hubei

781.71

93.3

8473007

ro

344762641

16404

261442180

Hunan

561.55

90.2

6589034

15469

248765510

Guangdong

1937.42

112.5

36428264

30145

294044165

Hainan

102.10

3.2

977679

1938

18483389

Chongqing

986.87

32.5

7590866

8934

153679690

Sichuan

1026.62

55.4

8429568

19888

228335056

Guizhou

241.16

25.5

1334960

9948

86413506

Yunnan

291.94

23

1013422

10357

78279349

Shaanxi

496.12

14.2

4263243

11716

152646896

Qinghai

41.55

2.9

1425438

4134

18360173

88.90

11.8

2107291

15651

20139732

Hebei

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Journal Pre-proof Inner

638.66

22.5

13920622

29395

281907744

shanxi

442.35

13.7

5476499

19384

136707323

Heilongjian

417.77

23.8

5617725

12126

92260840

Anhui

648.21

93.5

7955869

12332

235369526

Gaungxi

399.01

55.5

5804358

9761

157629997

Gansu

234.89

11.6

3178511

7523

82821228

Ningxia

110.70

4.4

2256405

5405

32224473

Xinjiang

ur

na

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re

-p

of

Mongolia

g

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Table 2: Output and initial efficiency of regional green development of production period in 2015

SO2

IWWD

ISWG

GIOV

GDP

Efficiency(E)

Beijing

40347

8978

710

3710.88

23014.59

1

Tianjin

195395

18973

1546

6982.66

16538.19

1

Inner

1047351

35753

26669

7739.18

17831.51

1

Liaoning

1077990

83140

32434

11270.82

28669.02

0.99

Jilin

1167133

38772

5385

6112.05

14063.13

1

Shanghai

926035

46939

1868

7162.33

25123.45

1

Jiangsu

319643

206427

10701

ro

Province

Desirable output (Y)

27996.43

70116.38

1

Zhejiang

317480

147353

4486

17217.47

42886.49

1

Fujian

155360

90741

4956

10820.22

25979.82

1

Jiangxi

870175

76412

10777

6918

16723.78

1

Shandong

560083

186440

19798

25910.75

63002.33

1

Henan

440642

129809

14722

15823.33

37002.16

1

Hubei

337632

80817

7750

11532.37

29550.19

0.97

Hunan

517408

76888

7126

10945.81

28902.21

1

Guangdong

1358883

161455

5609

30259.49

72812.55

1

Hainan

1031667

6879

422

485.85

3702.76

1

Chongqing

506192

35524

2828

5557.52

15717.27

0.80

Sichuan

Jo

Undesired output (U)

559504

71647

12316

11039.08

30053.1

1

Guizhou

699102

29174

7055

3315.58

10502.56

1

Yunnan

431075

45933

14109

3848.26

13619.17

1

Shaanxi

31855

37730

9330

7344.62

18021.86

1

Qinghai

474805

8546

14868

893.87

2417.05

1

Xinjiang

725729

28402

7263

2740.71

9324.8

1

Hebei

702427

94110

35372

12626.17

29806.11

0.85

Shanxi

582558

41356

31794

4359.6

12766.49

0.69

-p

re

lP

na

ur

of

Mongolia

Journal Pre-proof Heilongjiang

671642

36410

7495

4053.77

15083.67

0.83

Anhui

476964

71436

13059

9264.82

22005.63

0.89

Guangxi

118046

63253

6977

6359.82

16803.12

1

Gansu

340969

18760

5824

1778.1

6790.32

1

Ningxia

718070

16443

3430

979.72

2911.77

1

Before considering the additional fixed assets investment, we determine the initial efficiency of 30 provinces. The evaluation shows that 23 of the 30 provinces are located on the

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production frontier, that is, they have efficiency 1. The remaining, inefficient seven provinces are

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Liaoning, Hubei, Chongqing, Hebei, Shanxi, Heilongjiang, and Anhui, whose efficiency values are 0.996, 0.97, 0.804, 0.853, 0.686, 0.826 and 0.89 respectively. The seven inefficient provinces

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are in North China, Central China, and Northeast China, and their efficiency values are all greater than 0.65. The lowest efficiency was found in Shanxi at 0.686, and Chongqing, Hebei, and Anhui

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are between 0.8 and 0.9. Liaoning and Hubei are larger than 0.9. Further, the efficiency of

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Liaoning is closer to 1 than the other six provinces.

We note that first, most of the 30 provinces are located in the production frontier, which

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shows that the economic development level of each region is quite different, but all of the provinces have implemented green development as a significant task effectively in the aspect of

ur

saving energy and protecting the environment. Second, among the seven inefficient provinces, Shanxi has experienced a deteriorating resource environment, and its coal-based economic

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development mode has become obsolete, resulting in very low efficiency. Liaoning Province is in the coastal area, resulting in economic transformation and development which has made Liaoning’s efficiency close to 1 in recent years. We consider the different frontier allocations to calculate the optimal allocation better. According to the above indicator data, we group the DMUs by their technical efficiency. Using Algorithm 1 and the BCC model, the results show that the 30 provinces can be divided into two groups (layers), that is, two different effective frontiers, with each effective frontier describing a production technology level. Group 1 consists of Beijing, Tianjin, Inner Mongolia, Jilin, Shanghai, Jiangsu, Zhejiang, Fujian, Jiangxi, Shandong, Henan, Hunan, Guangdong, Hainan, Guangxi, Hebei, Sichuan, Guizhou, Yunnan, Shaanxi, Qinghai, Xinjiang, Ningxia. The number of DMUs in Group 2 is less than in Group 1, which consists of Liaoning, Hubei, Chongqing, Hebei, Shanxi,

Journal Pre-proof Heilongjiang, Anhui. Firstly, Group 1 contains areas having China’s best economic development, including coastal provinces and cities, the Yangtze River Delta, the Pearl River Delta, and Beijing-Tianjin-Hebei. These regions have better economic development and financial strength than others in China. Even though the economic development of these regions is promoted by their many factories and enterprises, the local governments have a strong awareness of environmental protection as well as a strong ability to control pollution and save energy, so relevant legislation and supervision are powerful.

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Group 1 also contains some of China’s less developed areas, such as southwestern

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provinces, Xinjiang, Qinghai, and Inner Mongolia. The development of these regions is mainly based on primary industry and tertiary industry. The secondary industry is relatively scarce,

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environmental pollution is not serious, and green, livable cities (as identified by media) are also in these regions. Therefore, the environment in such regions is better and their resources are not

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overdeveloped; these reasons lead to high efficiency.

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Provinces grouping shows that geographical location does not determine group membership. Provinces in North China and Central China are in different groups, and Jiangxi and

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Hunan provinces in central China are in Group 1, while Anhui and Hubei province in the central region are in group 2. For the North China region, Beijing, Tianjin, and Inner Mongolia are in Group 1, while Shanxi is in Group 2.

ur

Consider Group 2’s Anhui and Hubei, both in the central region. Hubei has a solid

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industrial development foundation, and its GDP is ranked first in the central region, indicating that industrial development in Hubei accounts for a large part of the overall economic development, which inevitably leads to extensive environmental degradation and waste of resources caused by industrial development. Chongqing faces a similar situation. Anhui and Hebei are bordered by two of China’s major economic circles : the Yangtze River Delta and Beijing-Tianjin-Hebei, respectively. Although the government has introduced Anhui into the Yangtze River Delta and Hebei has been integrated into the Beijing-Tianjin-Hebei joint development in recent years, their main function is to carry out the industrial transfer of the economic circle. Most of the enterprises undertaking industrial transfer are heavy industry and highly polluting enterprises represented by the secondary industry. Although undertaking industrial transfer has increased the economic growth rate of Hebei Province and Anhui Province, it has inevitably brought a series of problems

Journal Pre-proof such as environmental pollution and waste of resources. For these two provinces, economic development cannot neglect the governance environment, especially under the concept of green development of China. The remaining provinces of Group 2 are Shanxi, Heilongjiang, and Liaoning. Shanxi, as China’s major coal province, has developed rapidly in the last century. However, due to the depletion of resources and the transformation of development methods in recent years, the economy of Shanxi is less developed, and the environment is deteriorating due to long-term development, so its efficiency is insufficient. As major provinces containing China’s heavy

of

industry development, Heilongjiang and Liaoning had extraordinary performance in the early days

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of China’s founding. However, over time, these provinces have been seriously affected by the changes in development concepts and methods, as well as the outflow of population in the three

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northeastern provinces. The incomplete transformation of development methods has led to a slowdown in development and a deterioration in the natural environment. Moreover, the three

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northeastern provinces mainly focus on the secondary industry and have failed to do a good job in

DEA-based MOLP model for resource allocation

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4.2.

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the supervision of environmental governance, resulting in a series of environmental problems.

In this section, according to the amount of the country’s advanced fixed assets investment, the

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additional investment will be temporarily rated at 10% of the total investment of the previous period, that is, R1 = 519400852.7 . Also, we assume that the CDMU’s total allocation of emissions

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for the next period is reduced by 2% compared with the previous period, namely

E1 = 17054118.76 , E2 = 1954610 , E3 = 320145.42 . First, we set the weights w1 , w2 to 0.8, 0.4; this setting is important because of the secondary objective of reducing the amount of allocated variable resources, i.e., reducing emissions. After determining the target and weight of resource allocation, we use model 5 to calculate the resource allocation results of the fixed asset investment and emission rights for each province after reconfiguration, as shown in Table 3

Table 3: Resource allocation results in the regional green development production period in 2015 Allocated constant input

Allocated variable input

(F)

(U)

Journal Pre-proof FAI

SO2

IWWD

ISWG

Beijing

0

40347

8978

710

Tianjin

39144000

195395

18973

1546

0

1047351

35753

26669

0

1167133

38772

5385

19048166

662981.3

39222.36

1704.715

Jiangsu

0

319643

206427

10701

Zhejiang

79857264

317480

147353

4486

Fujian

63728093

155360

90741

4956

Jiangxi

0

870175

76412

10777

Shandong

0

560083

186440

19798

440642

129809

14722

517408

76888

7126

1358883

161455

5609

1031667

6879

422

342724.7

74009.18

7962.471

Inner

103428792

Hunan

0

Guangdong

0

ro

-p

Henan

re

Shanghai

lP

Jilin

of

Mongolia

5545017

Sichuan

3212062

Guizhou

0

699102

29174

7055

Yunnan

0

431075

45933

14109

0

31855

37730

9330

0

474805

8546

14868

0

725729

28402

7263

47288999

151446.9

27542.21

5386.594

Gansu

24846368

376322.8

17935.67

5397.64

Ningxia

9667342

718070

16443

3430

Liaoning

52921109

1077990

83140

32434

0

337632

80817

7750

24175421

506192

35524

2828

Hebei

0

702427

94110

35372

Shanxi

0

582558

41356

31794

Xinjiang Guangxi

Hubei Chongqing

ur

Qinghai

Jo

Shaanxi

na

Hainan

Journal Pre-proof Heilongjiang Anhui

0

671642

36410

7495

46538218

476964

71436

13059

The additional fixed assets investment was allocated to 13 provinces and cities, which respectively are Tianjin, Shanghai, Zhejiang, Fujian, Henan, Hainan, Sichuan, Guangxi, Gansu, Ningxia, Liaoning, Chongqing and Anhui. After additional fixed assets investment and reallocation of emission rights, Henan received the most additional fixed assets investment, with the least amount going to Hainan. It can also be found that the allocation of the additional fixed

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assets investment is mainly distributed to the central and eastern regions of China, which are

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densely populated, indicating that such regions have great development potential. However, only the gross industrial output value of Shandong and the GDP of Shaanxi and Gansu have increased

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in the final desirable output. In the 30 regions, considering two desirable outputs, we find that in a total of 60 desirable output variables, only three have changed. This result should be better. It

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seems insufficient to add only 10% to the fixed assets. This requires us to explore the

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circumstances under which additional fixed assets investment is optimal. We explore the optimal additional fixed assets investment and the optimal allocation of emission rights in the next section.

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Using Table 3, we can compare data before and after allocation. It can be seen that the allocation of emission rights has not changed in most provinces, but there are four provinces,

ur

Shanghai, Sichuan, Guangxi, and Gansu, in which the three waste emission rights allocations have changed. We can see that for industrial SO2, industrial wastewater discharged, and industrial solid

Jo

waste generated, the reductions of emission rights for Shanghai were 263053.7425, 7716.64, and 163.285, respectively. The reductions in Sichuan Province were 216779.29, -2362.17, and 4353.53 respectively (a negative reduction indicates an increase in emission rights). The reductions of Guangxi Province were -33400.89, 35710.8, and 1590.41. From Table 2, we can see that the total emissions of industrial SO2, industrial wastewater, and industrial solid waste in the 30 provinces were 16991083.64, 1952604.41 and 320145.42, respectively. The allocations of three waste emission rights are less than or equal to the target value E1 = 17054118.76 , E2 = 1954610 ,

E3 = 320145.42 , and only the gross industrial output value of Shandong and the GDP of Shaanxi and Gansu have increased. Therefore, the economic benefits brought by the resource allocation are very limited and far from ideal. The allocation of emissions in the next period is not accurate enough to reduce emissions by 2% compared with the previous period, which requires us to

Journal Pre-proof optimize the allocation of three wastes emission rights under the condition of optimal fixed assets investment. Therefore, we will give an optimal allocation of the three wastes emission rights in the next section. Also, in order to verify the effect of weight on the result of resource allocation, we use numerical analysis to do a sensitivity analysis on the weights w1 , w2 and observe the impact on the result of resource allocation,as shown in table 4. The results show that the change of weight has no significant impact on the results of resource allocation, so we still set the weight to

of

w1 = 0.8, w2 = 0.4 in the subsequent analysis.

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Table 4: Sensitivity analysis

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w1 = 0.5 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

SO2

16991

16991

16991

16991

16991

16991

16991

16991

16991

16991

084

084

084

084

084

084

084

084

084

084

IW

19526

19526

19526

19526

19526

19526

19526

19526

19526

19526

WD

10

10

10

10

10

10

10

10

10

10

ISW

32014

32014

32014

32014

32014

32014

32014

32014

32014

32014

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

06

06

06

06

06

06

06

06

06

06

Jo

ed of GIO V Add

lP

82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896

ur

Add

na

G

re

w2

513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59

ed of

86

86

86

86

86

86

86

86

86

86

w2

0.06

0.12

0.18

0.24

0.3

0.36

0.42

0.48

0.54

0.6

SO2

16991

16991

16991

16991

16991

16991

16991

16991

16991

16991

084

084

084

084

084

084

084

084

084

084

GDP

w1 = 0.6

Journal Pre-proof IW

19526

19526

19526

19526

19526

19526

19526

19526

19526

19526

WD

10

10

10

10

10

10

10

10

10

10

ISW

32014

32014

32014

32014

32014

32014

32014

32014

32014

32014

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

G Add

82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896

ed of

06

06

06

06

06

06

06

06

06

06

GIO V 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 86

86

86

86

86

86

w2

0.07

0.14

0.21

0.28

0.35

SO2

16991

16991

16991

16991

084

084

084

084

IW

19526

19526

19526

WD

10

10

10

ISW

32014

32014

5.4

5.4

GDP

86

86

86

re

0.42

0.49

0.56

0.63

0.7

16991

16991

16991

16991

16991

084

084

084

084

084

084

19526

19526

19526

19526

19526

19526

19526

10

10

10

10

10

10

10

32014

32014

32014

32014

32014

32014

32014

32014

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

ur

na

lP

16991

82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896

ed of

06

GIO

Jo

Add

-p

w1 = 0.7

G

86

ro

ed of

of

Add

06

06

06

06

06

06

06

06

06

V Add

513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59

ed of

86

86

86

86

86

86

86

86

86

86

w2

0.08

0.16

0.24

0.32

0.4

0.48

0.56

0.64

0.72

0.8

SO2

16991

16991

16991

16991

16991

16991

16991

16991

16991

16991

084

084

084

084

084

084

084

084

084

084

GDP

w1 = 0.8

Journal Pre-proof IW

19526

19526

19526

19526

19526

19526

19526

19526

19526

19526

WD

10

10

10

10

10

10

10

10

10

10

ISW

32014

32014

32014

32014

32014

32014

32014

32014

32014

32014

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

5.4

G Add ed of

82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 82.896 06

06

06

06

06

06

06

06

06

06

GIO V

86

86

86

86

86

86

86

86

86

86

-p

GDP

Extension of DEA-based MOLP model for resource allocation

re

4.3.

of

ed of

513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59 513.59

ro

Add

In the above section, we tentatively determined reallocated additional investment R1 and the total

lP

investment resource of redistribution Ei , i = 1, 2,3 . However, this setting is subjective. We should also consider optimal additional fixed assets investment and the optimal amount of emissions.

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(1) Optimal additional fixed assets investment In this section, we discuss the optimal additional fixed assets investment based on fixed

ur

assets as allocated constant inputs. In this regard, we use the following definition: when the

Jo

additional resource allocation results no longer increase with any further increase in additional investment, the current amount is the optimal additional investment. In this case, the secondary objective of the CDMU is to maximize resource-saving while maintaining the maximum organizational output. When we have reached the optimal additional investment, no matter how the total of additional fixed assets increases, further investment will not change the allocation and efficiency of each province. In fact, if the fixed assets investment increases too much, it will only waste resources. Therefore, we focus on the optimal additional fixed assets investment in this section. Based on model 5, we give Algorithm 3 to obtain the optimal fixed assets investment. Algorithm 3: Calculation of optimal additional fixed assets investment. 1. k = 1 . 2. R1k = R *0.05* k , R1k 1 = R *0.05*(k  1) .

Journal Pre-proof 3. Running resource allocation model (3), obtain f i k ; f i k 1 . 4. If fi k 1 = fi k , the algorithm stops, getting R1* = R *0.05* k . 5. Else, k = k  1; back to step 2. Considering the special characteristic of the China’s additional fixed assets investment, we choose 5% as the minimum benchmark and 5% as the promotion of each level to get the optimal additional fixed assets investment. We can obtain the optimal additional fixed assets investment through Algorithm 3, and the number of provinces with changed allocations under different

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additional fixed assets investment ratios, specializing that 8 provinces under 5% additional investment ratio, 13 provinces under 10%, 19 provinces under 10% and 25 provinces under 20%.

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When the additional investment is 5%, the additional fixed investment is divided into eight provinces, i.e., Tianjin, Shanghai, Fujian, Hainan, Sichuan, Guangxi, Gansu and Liaoning. while

-p

the other provinces’ changes are all zero. Seven of the eight provinces are in Group 1, the

re

exception being Liaoning. Fujian has the most fixed assets, and Hainan has the least. That is, Fujian has the greatest development potential, and Hainan has the smallest. The eight provinces

lP

are located in different regions of China: North China, East China, Southeast China, South China, Southwest China, Northwest China, and Northeast China. These are mainly the provinces with

na

better development in these areas. Tianjin, as the economic center of the Bohai Rim region and a major member of the Beijing-Tianjin-Hebei economic circle, is bordered by Bohai in the east and

ur

Beijing in the west, which has unique regional advantages of China. Shanghai, as the major city in China, is the “leader” of the Yangtze River Delta urban agglomeration; it has a large radiation

Jo

range and it has great potential for development because of its unique aggregation effect. In addition, it is noteworthy that Shanghai and Tianjin were the earliest cities in China to establish free trade zones.

As the largest province in southwest China, Sichuan has developed rapidly in recent years. Although the development of Northeast China has slowed down in recent years, Liaoning is still the largest and best-developed province in Northeast China. Fujian is in the southeast of China, in which the total economic volume is general, and the secondary and tertiary industries are its main industries. However, the additional fixed assets investment will accelerate the development of the secondary industry, and the development of the tertiary industry will also promote the development of the secondary industry. Guangxi and Gansu, despite their small economic volume, have developed rapidly in recent years, and their economic growth rates are also upstream level,

Journal Pre-proof indicating good performance. In summary, when the additional fixed assets investment is only 5% of the original total fixed assets, under this model, the CDMU will allocate the additional fixed assets to the above provinces, which will maximize the overall efficiency and obtain the highest earnings. From another point of view, the above provinces have great potential for development. If they receive allocations of new funds, the overall marginal benefit will be the highest, that is, the maximum benefit will be realized with certain inputs. When k = 2, the additional investment is 10%. This additional investment adds Zhejiang, Henan, Chongqing, Ningxia, and Anhui to the 5% case list of provinces receiving more

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investment. Chongqing and Anhui are in Group 2, and the other three are in Group 1. The

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additional investment is mainly allocated to Anhui, Henan, and Zhejiang, with Henan getting the maximum. Three of these provinces are in the central region of China, which shows that China’s

-p

central region has great development potential. Henan, Anhui, and Chongqing belong to the densely populated areas of China, and their labor supply is sufficient, which gives them great

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potential. Zhejiang is located in the economic circle of the Yangtze River Delta, in which

lP

economic development is better than in the above-mentioned provinces; it has more abundant resources and potential to develop industry. Ningxia is in the northwest of China, with a weak

na

economy and a small population but, even there, appropriate additional investment will bring great benefits.

When k = 3, the additional investment is 15%. This level of investment adds Jiangxi,

ur

Guangdong, Guizhou, Shaanxi, Qinghai, and Shanxi to the 10% case list of provinces that get

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increased allotments. Except for Shanxi, the added provinces are in Group 1. We can see that most of the additional investment goes to Guangdong, and the least goes to Qinghai. Guangdong is located in the Pearl River Delta, with strong economic strength and a good foundation for secondary industry, so it gets the most allocation. Jiangxi, Shanxi, and Guizhou are in the central, north, and southwest regions of China, respectively. The economic base of these regions is relatively weak, but the economic growth rate is relatively high, so they are worthy of some additional allocation. When k = 4, the additional investment is 20%. This adds six provinces to the 15% case list: Beijing, Inner Mongolia, Jilin, Hunan, Jiangsu, and Xinjiang. These newly added provinces are all in group 1. They have limited potential for the development of secondary industry and tend to be saturated. When the additional fixed assets investment exceeds 20%, these provinces will get new

Journal Pre-proof investment. It can be seen that with increasing additional investment, the economic growth areas will be considered because these areas have great potential and bright prospects for development. However, some developed coastal areas are not priority allocation regions, indicating that their development has reached saturation. Shandong, Yunnan, Hubei, Heilongjiang, and Hebei provinces do not appear in the above lists, indicating that if these provinces continue to add fixed assets investment, that will not bring positive effect; blindly increasing investment will only bring a waste of resources. For these provinces, the best choice is to change the development thinking, save energy, and control the waste of resources.

of

(2) Optimal emission rights resource allocation

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Similar to the process of finding optimal additional fixed assets investment, we also give Algorithm 4 to obtain the optimal allocation of emission rights.

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Algorithm 4: Calculation of optimal emission rights resource allocation. 1. k = 1 .

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2. Ei k = Ei 0  Ei 0 *0.01* k ; Ei k 1 = Ei 0  Ei 0 *0.01*(k  1) .

4. If

fi k 1 = fi k

lP

3. Running resource allocation model (3), obtain f i k ; f i k 1 . , the algorithm stops, getting

Ei* = Ei 0 *0.05* k

.

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5. Else, k = k  1; back to step 2.

We have obtained the optimal additional fixed assets investment in the previous section.

ur

Thus, we set the additional input of fixed assets to Ri* 0 = 1038801705 in this section, and based

shown in Table 5.

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on that, we can get the optimal allocation of emission rights by using Algorithm 4. The results are

Table 5: Regional Green Development Emissions Resource Reallocation and Efficiency in 2015 Allocated variable input

Desirable output (Y)

(U) SO2

IWWD

ISWG

GIOV

GDP

E

Beijing

40347

8978

710

3710.88

23014.59

1

Tianjin

195395

18973

1546

6982.66

16538.19

1

Inner Mongolia

1047351

35753

26669

7739.18

17831.51

1

Jilin

1167133

38772

5385

6112.05

14063.13

1

Journal Pre-proof 662981.2575 39222.357 1704.7147

7162.33

25123.45

1

319643

206427

10701

27996.43

70116.38

1

Zhejiang

317480

147353

4486

17217.47

42886.49

1

Fujian

155360

90741

4956

10820.22

25979.82

1

Jiangxi

870175

76412

10777

6918

16723.78

1

Shandong

560083

186440

19798

25993.64606

63002.33

1

Henan

440642

129809

14722

15823.33

37002.16

1

Hunan

517408

76888

7126

10945.81

28902.21

1

Guangdong

1358883

161455

5609

30259.49

72812.55

1

Hainan

1031667

6879

422

485.85

3702.76

1

11039.08

30053.1

0.9982

7055

3315.58

10502.56

1

342724.7093 74009.178 7962.4714 699102

29174

Yunnan

431075

45933

14109

3848.26

13619.17

1

Shaanxi

31855

37730

9330

7344.62

18411.46532

1

Qinghai

474805

8546

14868

893.87

2417.05

1

Xinjiang

725729

28402

7263

2740.71

9324.8

1

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Guizhou

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Sichuang

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Jiangsu

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Shanghai

151446.8991 27542.214 5386.5939

Gansu

376322.7724 17935.667

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Guangxi

16927.11325 0.9993

5397.64

1778.1

6790.32

1

3430

979.72

2911.77

1

718070

Liaoning

1077990

83140

32434

11270.82

28669.02

0.8934

Hubei

337632

80817

7750

11532.37

29550.19

1

506192

35524

2828

5557.52

15717.27

0.8042

702427

94110

35372

12626.17

29806.11

0.8628

Shanxi

582558

41356

31794

4359.6

12766.49

0.6777

Heilongjiang

671642

36410

7495

4053.77

15083.67

0.8446

Anhui

476964

71436

13059

9264.82

22005.63

0.8896

275132.18

722255.08

Total

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Hebei

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Ningxia

Chongqing

16443

6359.82

16991083.64 1952610.4 320145.42

From Table 5, we can see that the total industrial SO 2 emissions are 1691083.64, the total industrial wastewater discharged is 1952610.41, and the total industrial solid wastes generated is

Journal Pre-proof 320145.42. These are all less than the before allocation: 17402162, 1994500, and 326679. The total emission of three undesired outputs in the 30 provinces is within the scope of the three waste discharge allowances (18272270.1, 2094225, 343012.95). Sichuan, Guangxi, Liaoning, Chongqing, Hebei, Shanxi, Heilongjiang, and Anhui are inefficient DMUs. Compared to the efficiency before allocation, Hubei has been pulled to the frontier of production, becoming efficient. This may have been caused by the other provinces being allocated additional fixed investment, while Hubei did not. This can happen because the increase in the allocation of invariable investment makes the efficiency of other DMUs decrease relatively, thus making Hubei

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more efficient.

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Sichuan and Guangxi received 685005.168 million and 472889.991 million respectively in the allocation, but they belong to the western region of China, where the economy is

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underdeveloped. Therefore, when the additional fixed investment is allocated, their input increases and their efficiency is reduced. Therefore, they will change from efficient DMUs to relatively

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inefficient DMUs. Other formerly efficient provinces (Beijing, Tianjin, Inner Mongolia, Jilin,

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Shanghai, Jiangsu, Zhejiang, Fujian, Jiangxi, Henan, Hunan, Guangdong, Hainan, Guizhou, Shaanxi, Qinghai, Xinjiang, Gansu, and Ningxia) have also been allocated additional investment,

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but some of these belong to densely populated areas, and therefore, have sufficient labor force supply, larger development potential, and strong productivity. Also, some are coastal cities that have strong economic production capacity. Therefore, the increase of additional fixed investment

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can stimulate the improvement of their production capacity and maintain high efficiency. At the

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same time, Shandong and Yunnan are not allocated any additional fixed investment, so their production capacity will remain unchanged, and they will still be efficient. The results of comparing the data before and after allocation are shown in Figure 1.

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Figure 1: Comparison of SO2, wastewater discharged and solid wastes generated before and after allocation.

By comparing the figures for industrial SO2 emissions, industrial wastewater discharged,

Journal Pre-proof and industrial solid waste generated, it can be seen that among the 30 provinces surveyed in China, only Shanghai, Sichuan, Guangxi, and Gansu are affected by the three wastes emissions after the reallocation of additional fixed assets investment. These four provinces experience a reduction in emissions of the three wastes. Unlike Shanghai, the other three provinces belong to the western region of China, which leads to the conclusion that most of the western regions have not developed well, but they do take into account environmental concerns and coordinated development in economy and environment, which is a more stable development strategy. Shanghai is a major city located in eastern China, and it has great influence and strong

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productivity. It can control the emission of three wastes well by increasing additional fixed assets

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investment under its current conditions of mature and efficient production. Sichuan is an important distribution center of various products and commodities in the western region (especially in the

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southwestern region), its secondary and tertiary industries are well developed, and its economic strength is great. However, Sichuan has significant regional differences, unstable climate, and

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poor environmental quality; thus, more resources and financial investments are needed to improve

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its environmental quality. After reallocation of additional fixed assets investment, Sichuan’s environment has been improved, and the emissions of the three wastes have been reduced.

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However, its production efficiency has been reduced, which causes it to become evaluated as inefficient. That is, it is necessary to sacrifice certain resources to improve the environment but reduce production effectiveness at the same time. Guangxi is located in South China, where the

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secondary and tertiary industry are relatively underdeveloped, but the environment is better than

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other provinces. After reallocation of additional fixed assets investment, it can make full use of resources and reduce the emission of the three wastes. Table 5 shows the efficiency change of Guangxi: that there is almost no impact on production, and its production efficiency is close to efficient. The special geographical position of Gansu makes the allocation of resources and investment insufficient, especially because of the secondary and tertiary industry, which develops more slowly than the industry in the more developed provinces. Therefore, under the condition of increasing investment, the effect of reallocating additional fixed investment to Gansu is remarkable, and the emission of three wastes is reduced. Its production efficiency value remains equal to 1.

5.

Conclusions and policy suggestions

Journal Pre-proof This paper analyzes the improvement of green development efficiency from the perspective of resource allocation. Firstly, we consider the regional heterogeneity of technical efficiency of each province and different resource reallocation possibilities to group the areas and input indicators. Secondly, we allocate additional fixed assets investment and emission rights in the green development production for 30 regions in China 2015 by using a multiple-objective DEA model and considering a multiple-objective function. Finally, we obtain the optimal allocation scheme by an algorithm we provide. Conclusions and specific policy recommendations are as follows. The results indicate that there are obvious differences in technological efficiency among

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the different regions in China. We group the provinces according to their technical efficiency,

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which shows that areas of superior economic development, such as the Yangtze River Delta and the Pearl River Delta, have higher technical efficiency. These areas have strong environmental

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awareness and their governments have more funds and labor to invest in energy-saving and environmental protection actions. However, there are also some remote and underdeveloped areas

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with higher technical efficiency. These areas have no heavy industrial enterprises and good

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environmental conditions, which means they have no excessive development of nonrenewable energy. However, the central region and three northeastern provinces have low technical

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efficiency, which is related to having heavy industry as the main economic pillar, the pollution caused by heavy industry, and the lack of local government action to deal with pollutants. Based on our results, we give the following policy suggestions for governments to promote

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green development. First, the government should give priority to regions with large economic

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growth in allocating additional fixed assets investment. The government needs to consider the organizational effectiveness of fixed assets investment allocation because it is a scarce resource. Using our method to do the allocation, the additional investment is allocated to regions with faster economic growth because of their high development potential and capability to use the allocated fixed assets investment effectively. The areas that do not receive additional investment, including developed coastal areas, have basically saturated their own investment, while additional investment of some areas in the central region will only waste resources due to their low technical efficiency and inadequate capacity to deal with pollutants. The primary task of these areas should be to change their development thinking. Second, the allocation target of emission “resources” can be set slightly lower than the original total emissions. In terms of emission reduction, the government can adopt targeted

Journal Pre-proof emission reduction plans by setting emission targets. Up to an additional 20% of fixed assets investment can be used effectively to reallocate emission permits and reduce emissions. The DMUs that should reduce emissions include Sichuan, Guangxi, Gansu, and others. According to the actual technical efficiency of these provinces, they should reduce the existing “three wastes” emissions to achieve green development. In addition, the government’s emission permits should be reduced while remaining within a reasonable range. The technical efficiency of each province should be improved, and the total emission permitted should be scientifically and gradually reduced, based on improving the environmental awareness and the pollution treatment capacity of

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each province.

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In conclusion, the DEA model we chose is in line with the goals of the green development policy. The multi-objective functions correspond to the goals of the 13th Five-Year Plan for future

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green development planning. In particular, in the 13th Five-Year Plan, reductions in future emissions, reductions in energy consumption, and increases in investment are specified. In order to

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reflect these considerations, we use algorithms to try to find the optimal value of the decreasing

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and increasing amount. This makes the method used in this paper practical and can provide scientific advice for policymaking. Nonetheless, the methods and models in this paper have

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limitations. For example, cyclical dynamic changes are not considered. In reality, the achievement of green development goals requires multiple periods. For further study, we will further consider

1.

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Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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Graphical abstract

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Highlights:  The heterogeneity of technical efficiency of each province is considered.  The characteristics of input indicators, especially scarce resources, are taken into account.  The optimal allocation scheme is obtained by an algorithm.  Additional fixed assets investment should be allocated to regions with large economic growth.