Zero-sum Gains Data Envelopment Research Articles

An integrated adaptive allocation model for unified optimization of conventional and unconventional water resources based on fairness and efficiency

Unconventional water (UW) use has pros and cons, presenting the challenge of matching water utilization with regional water use characteristics. This study proposed the concept of amount-centered adaptive water allocation and built an integrated adaptive allocation model that includes conventional water (CW) and UW adaptability. The model consists of two modules. The first module introduces the regional composite index and inequality index to match CW and UW allocation amount with the sub-region’s characteristics. The second module defines the efficiency of CW and UW allocation, employs the Zero-Sum Gains Data Envelopment Analysis to find the solution set with the highest efficiency on the Pareto front, and further modifies it to reach the optimal allocation efficiency. Then the proposed model was applied to Jiangsu Province, China. Empirical and comparative analyses of the 54 weighting plans proved the validity and practicability of the model. The results showed: (1) The model tallies with the principles of fairness and efficiency and reduces the spatial heterogeneity of water shortage risk; (2) When available water supply decreases by over 20% due to future water-related emergency incidents, CW allocation would first reach its upper limit, while UW fails to effectively bridge the supply–demand gap; (3) Only by improving the maximum UW consumption by over 40% can the future risk of extreme water shortages be effectively addressed. The model proposed in this study has excellent practicality and application potential, providing a novel perspective for incorporating UW into the unified management of water resources.

Principles and Optimization of China’s Unconventional Water Management: From a Brand-New Perspective of Responsibility Allocation

Unconventional water includes reclaimed water, harvested rainwater, desalinated seawater, and mine water. Unconventional water use is considered more of a “mandatory responsibility” in China. The initial allocation of unconventional water emphasizes quantity-centered responsibility allocation while the minimum utilization reflects this responsibility. The unconventional water use responsibility (UWUR) should be tailored to the characteristics of each area, moving away from a ‘more is better’ mindset. However, there is a large research gap in this field. This paper first presented six fundamental principles for unconventional water allocation. Ensuring fairness in allocation involves aligning the allocated amount with urban water usage characteristics. Hence, based on four key features, this paper integrated various socioeconomic and environmental factors to build an initial allocation model. To enhance efficiency, an optimal allocation model was constructed using the zero-sum gains–data envelopment analysis (ZSG-DEA) method. The models were then applied to Jiangsu Province, China, to verify their applicability. The results showed that the projected minimum UWUR allocation (unit: 100 million m3) for each city in 2025 is 1.482 (Nanjing), 1.501 (Wuxi), 0.919 (Xuzhou), 1.029 (Changzhou), 2.977 (Suzhou), 1.497 (Nantong), 0.818 (Lianyungang), 0.766 (Huai’an), 0.875 (Yancheng), 0.920 (Yangzhou), 0.790 (Zhenjiang), 0.858 (Taizhou), and 0.766 (Suqian). The rational and feasible results indicated that the allocation framework proposed in this paper has a certain practicability. Lastly, this paper considered the differences in unconventional water utilization conditions across 13 cities and proposed corresponding measures to improve the utilization. This paper represents a tentative exploration of unconventional water allocation in China and offers theoretical and practical insights for policy-makers to improve territorial spatial planning and sustainable water management.

Allocation scheme selection for transportation carbon allowance -evidence from China's top ten economic regions

Establishing a scientific allocation scheme for transportation carbon allowance (TCA) is an inevitable requirement of China's sustainable development. Previous studies on the allocation problems of TCA considered the single goal, but this study constructs an allocation model of TCA under the framework of zero-sum gains data envelopment analysis and a spatial simultaneous panel. Furthermore, a profit maximization function model is used to measure the allocative efficiency and the differences in regional abatement costs of three different transport allocation mechanisms in China's top 10 economic regions from 1998 to 2019. Empirical results revealed four key results. (1) The efficient scheme is beneficial to regions with a high level of economic development and high-carbon emission efficiency, but it is easy to cause widening regional wealth disparities. (2) The equitable scheme is beneficial to regions with low transportation carbon emission efficiency, immature transportation structures, and green transportation technology, but it is easy to cause an unsuitable punishment effect. (3) Compared with the above two schemes, the comprehensive scheme is beneficial to more regions because it can both minimize the average marginal abatement costs and mitigate regional development inequalities. (4) With the gradual improvement of the national transportation carbon trading market, the comprehensive scheme is more sustainable and should be used more in the future. This study contributes to the formulation and implementation of energy allocation policies in the transportation sector.

CO2 Emission Allocation for Urban Public Buildings Considering Efficiency and Equity: An Application at the Provincial Level in China

China is currently recognized as the leading global energy consumer and CO2 emitter. A significant amount of carbon emissions can be attributed to urban public buildings. Establishing an equitable and efficient carbon emission allocation mechanism is a crucial step to meeting the ambitious targets in China’s 2030 carbon peak plan. In this study, we estimate the total amount of CO2 emissions from urban public buildings by 2030 and propose a preliminary scheme of carbon quota assignment for each province. By means of applying the zero-sum gains data envelopment analysis (ZSG-DEA) model, the carbon emission quotas allocation of urban public buildings in China’s 30 provinces is proposed, and the corresponding pressure to reduce provincial carbon emissions is analyzed. The results indicate that Qinghai has the lowest carbon emission rate (0.01%) for urban public buildings, while Guangdong has the highest (9.06%). Among the provinces, Jiangsu, Jiangxi, and Tianjin face the least pressure in reducing carbon emissions from urban public buildings. On the other hand, Hebei, Beijing, and Anhui are under great pressure to decrease carbon emissions. Notably, Hebei is predicted to have the highest emission reduction requirement of 95.66 million tons. In terms of pressures on carbon emissions reduction for urban public buildings, Jiangsu, Jiangxi, and Tianjin exhibit the least pressure. Hebei, Beijing, and Anhui are facing intense pressure to decrease carbon emissions. These findings offer policymakers valuable insights into developing a fair and efficient carbon allowance allocation strategy, while also contributing to China’s efforts to mitigate carbon emissions and combat climate change.

Optimized allocation of renewable energy quota in Chinese provinces

A fair and efficient renewable energy quota allocation scheme is essential for China to implement the Renewable Portfolio Standards policy. Therefore, based on the principles of fairness and efficiency, this paper comprehensively considers the differences among provinces and then proposes and adopts an improved zero-sum gains data envelopment analysis method to reallocate quotas. Furthermore, for verifying the superiority of the proposed method, this paper establishes a composite index based on the Gini coefficient and the Theil index to compare the rationality of the distribution results. Finally, this paper discusses the relevant advice for the development of renewable energy. The results validate that the proposed method is superior to the traditional method. Additionally, according to the final quota distribution scheme, there are fewer renewable energy quotas in the northern provinces and more in the southern provinces. The quota of most provinces is lower than 50 × 109 kWh, while Guangdong, Sichuan, Yunnan, Jiangsu, and Hunan are the five provinces with the most renewable energy quota of over 100 × 109 kWh. In general, this study provides a more rational renewable energy quota redistribution approach, which will help the government to establish an efficient and fair mechanism of renewable energy quota allocation.

Extending the zero-sum gains data envelopment analysis model

Extending the zero-sum gains data envelopment analysis model

IMPROVING THE EFFICIENCY OF UNIVERSITY LIBRARIES IN MALAYSIA USING ZERO-SUM GAINS DEA MODEL

Measuring the efficiency and optimizing available resources are vital for library management. This research empirically examines the measurement of efficiency of 10 public university libraries in Malaysia and provides an opportunity for inefficient libraries to improve their efficiency by proposing the appropriate number of resources. Data encompassing the number of staff, materials availability, and material circulation were gathered between 2016 and 2019. This study implements the zero-sum gains data envelopment analysis (ZSG-DEA) model to improve the efficiency. The findings show that in the early stage, five libraries were efficient in 2016 and 2018 while six libraries were efficient in 2017 and 2019. Comparable efficiency scores between conventional DEA and ZSG-DEA can be seen as all the inefficient libraries manage to attain better efficiency scores. Overall, all inefficient libraries can increase their efficiency rates. Despite the scores still not achieving the highest rate of efficiency, this study may assist librarians on managing library operations efficiently.

An alternative ranking of DMUs performance for the ZSG-DEA model

The Zero-Sum Gains Data Envelopment Analysis (ZSG-DEA) model was developed to evaluate the performance of Decision Making Units (DMUs) under output interdependency, which is evident when the total (over DMUs) observed output is a priori fixed. In this paper, we take a closer look at the derivation and interpretation of the ZSG-DEA efficiency scores and we explain why these are not really comparable across DMUs. Moreover, we verify that DMUs' ranking based on their ZSG-DEA efficiency scores is in fact incompatible with output interdependency, which requires total potential output of DMUs to be equal to their total observed output. Then, we propose an alternative metric of DMUs’ performance that is both consistent with output interdependency and comparable across DMUs. This metric is used for classifying DMUs into three (high, average or low performance) groups and for ranking them within these groups. To illustrate its empirical applicability, we use data from the Olympic Games, where output interdependency is clearly evident since the total number of awarded (gold, silver, and bronze) medals is a priori fixed.

Optimal allocation of CO2 emission quotas at the city level in Bohai Rim Economic Circle based on multi-objective decision approach.

As the most developed city circle in northern China, allocating CO2 emission quotas at the Bohai Rim Economic Circle (BREC) city level is essential for developing specific abatement policies. Thus, with reflecting multi-principles (fairness, efficiency, sustainability, and feasibility), this paper formulates the CO2 emission quota allocation among cities in BREC in 2030 based on the multi-objective decision approach. We first propose three allocation schemes based on the principles of fairness, efficiency, and sustainability, which are conducted by entropy method, zero-sum gains data envelopment (ZSG-DEA) model, and CO2 sequestration share method, respectively. Then, the CO2 allocation satisfaction is defined and used to measure the feasibility principle which is integrated as the objective function of the multi-objective decision model together with three allocation schemes to obtain the optimal allocation results. The results show that Beijing, Tianjin, Dalian, Shijiazhuang, Yantai, Weifang, and Linyi enjoy the largest CO2 emission quotas, having 1179.94 Mt in total and accounting for 31%. Beijing has the highest quotas, and Laiwu has the lowest emission quotas. Cities with large energy consumption and less CO2 sequestration capacity, such as Tianjin, Handan, and Tangshan, experience a decrease in the emission quota shares from 2017 to 2030, indicating that these cities would undertake large emission reduction obligations. Sensitivity analysis shows that Beijing, Zibo, and Jinan are more sensitive to minimum satisfaction changes, and the total satisfaction experiences an increase first and declines thereafter. Based on the results above, cities with large pressure to reduce CO2 emissions should not only promote economic development but also improve the capacity of CO2 sequestration by enhancing environmental protection to realize emission reduction targets.

Two-step allocation of CO2 emission quotas in China based on multi-principles: Going regional to provincial

In order to ensure the implementation of the emission trading scheme (ETS), the allocation of CO2 emission quotas in China’s provinces is of significant importance. Unlike previous studies that allocated CO2 emission quotas directly to Chinese provinces, we propose a two-step allocation scheme of “country to region” and “region to province” to formulate the provincial CO2 emission quotas allocation. In the first step, considering the regional coordination development, the Shapley value method is used to assign the CO2 emission quotas to China’s eastern, central, and western regions by simulating the regional collaborative abatement. In the second step, we use the entropy method to obtain the initial CO2 emission quotas for each province combining the principles of fairness, efficiency, feasibility, and sustainability. Then, a zero-sum gains data envelopment analysis (ZSG-DEA) model is applied to evaluate initial allocation efficiency and reallocate the CO2 emission quotas to realize efficiency optimization within the region. The results show that the eastern region obtains the largest CO2 emission quotas, followed by central and western regions. The energy-abundant and economic-prosperous provinces, such as Shandong, Hebei, Inner Mongolia, and Xinjiang, face great pressures on CO2 reduction. Compared with existing literature, the proposed scheme’s regional allocation results are more balanced, which will narrow the gaps of regional economic development. Since the emission reduction pressure varies in provinces, developing differentiated policies is critical to realizing China’s reduction targets. By considering regional fairness, this paper provides a reference for allocating CO2 emission quota among provinces to improve adaptability to the current conditions of China.

A note on the zero-sum gains data envelopment analysis model

In the case of the proportional output reduction strategy with a single output, the Variable-Returns-to-Scale (VRS) Zero-Sum Gains Data Envelopment Analysis (ZSG-DEA) efficiency scores can be obtained from the VRS conventional DEA efficiency scores by means of the Target’s Assessment Theorem (TAT). Using TAT as a departure point, two relations for computing the ZSG-DEA efficiency scores appear in the literature. Our objective in this note is to compare, contrast and challenge them on both theoretical and empirical grounds. For the latter, three different data sets are used.

Allocation of carbon emission quotas in China’s provincial power sector based on entropy method and ZSG-DEA

The power sector accounted for almost 40% of China’s carbon emissions in 2017 and is the first industry that is included in the national carbon emission trading system, so the current paper carries out a study on allocating carbon emission allowances for the power sector. Different from previous studies, this article assigns carbon emission allowances to 30 provinces according to the principles of equality, efficiency, and sustainability rather than just using the principles of equality and efficiency. We first apply the entropy method to initially distribute emission allowances to 30 provinces. Then, a zero-sum gains data envelopment analysis (ZSG-DEA) model is used to test the efficiency of quota allocation and redistribute the carbon quotas across 30 provinces continuously until the quotas are optimally distributed. The results show that in 2030, Guangxi, Hainan and Shandong have the most emission quotas, while Heilongjiang, Jilin and Qinghai have the least emission quotas. By comparing the quota share of each province in 2017 with 2030, it is found that Hainan, Guangxi and Qinghai located in western China have small emission reduction challenges, while there are great difficulties for provinces Jiangsu, Shanxi and Shandong situated in the central and eastern China to cut down the emissions.

Provincial Carbon Emission Quota Allocation Study in China from the Perspective of Abatement Cost and Regional Cooperation

To achieve the carbon reduction target, the Chinese government not only requires a quota allocation scheme in line with the current development situation, but also needs to minimize the economic expenditure in the emission reduction work. Therefore, this study integrates the multi-index method and zero-sum gains–data envelopment analysis model to obtain a fair and efficient multi-criteria quota allocation scheme. To ensure the effectiveness of the scheme, the fairness and cost effect of the scheme are quantitatively tested. In addition, regional cooperation factors are introduced into the research framework to providing feasible practical measures. The results show that: (1) After optimization, the eastern region has the largest quota increment, accounting for 45% of the country’s quota. (2) The multi-criteria quota allocation scheme after secondary allocation is a more ideal scheme. The quota scheme not only meets the requirements of fairness and efficiency, but also has lower abatement costs. (3) Regional cooperation should be encouraged by China, especially the eastern region, which can alleviate the reducing emission pressure through cooperation. Although the western region needs to undertake additional emission reduction tasks, it can improve the utilization rate of local renewable resources and be conducive to long-term economic development. These results will provide a reference for China to achieve its carbon reduction targets.

Assessment and optimization of provincial CO2 emission reduction scheme in China: An improved ZSG-DEA approach

This paper applies the zero-sum gains data envelopment analysis (ZSG-DEA) model to assess the provincial CO2 emission reduction scheme of China in 2020 and then calculates optimized values for the provinces in 2030. Results from two standard optimization procedures to solve the ZSG-DEA model are compared. We also extend the current methods by improving the iterative approach and then introduce fairness to the efficiency-oriented approach for the 2030 case. We found that the choice of optimization procedures has only a minimal impact on the results, but the specification of model does matter. For 2020, a standard DEA approach shows that only 2 provinces out of 30 are efficient. According to the estimation results of the ZSG-DEA model, 12 provinces need to set higher reduction targets, whereas the other 18 provinces could have lower target values to achieve overall efficiency. These results are generally consistent across different optimization approaches. The improved approach is applied to further evaluate a number of scenarios in 2030, in which the adjustment values towards optimum can be calculated for each scenario. Furthermore, we show that the inclusion of fairness can significantly affect the adjustment targets, which is of great importance to policymakers

Analysis of the carbon emission reduction potential of China's key industries under the IPCC 2 °C and 1.5 °C limits

Carbon emission from human activities is one of the main factors inducing the on-going global warming. It is, therefore, essential to establish a shared responsibility in industry for carbon emissions reduction. In this study, we examined the allocation of carbon emission rights in China's six high-energy-consuming industries from the perspective of allocation efficiency. The initial carbon emission quota was iteratively optimized using the zero-sum gains data envelopment analysis (ZSG-DEA) model. Furthermore, a scenario-based method was used to predict the future of various industries under a 1.5 °C warming target. According to our analysis, the largest carbon emission quota was in the transport industry, at 19.61 Gt CO2 under a 2 °C target and 16.27 Gt CO2 under a 1.5 °C target. The electric power industry and the iron and steel industry show the greatest potential for emissions reduction, and significant effort is now needed to achieve the allocation efficiency target. A “high economic growth and low energy consumption” scenario was more conducive to the sustainable growth of industry. Emissions reduction should focus on the electric power industry and the transport industry. In addition, the use of energy-saving and emissions-reducing technologies in high-energy-consuming industries should be increased.

University library performance management: Applying zero-sum gains DEA models to resource allocation

The management of university libraries faces major challenges in evaluating its performance since in many cases this assessment is performed inappropriately. One of the challenges is the lack of fair approaches to reallocate resources in university library systems. In this context, data envelopment analysis (DEA), a flexible technique that allows the use of multiple inputs and outputs to assess the performance of productive units, may prove useful. In DEA, in addition to the so-called classic models, there are the zero-sum gains (ZSG) models that, when used together, assist in resource allocation. This work aims to develop a powerful approach to help the manager to assess the performance of libraries as well as allow the reallocation of resources within an integrated library system of a university in Brazil. This two-step approach is based on the classic CCR model in the first stage and the ZSG CCR DEA (zero-sum gains data envelopment analysis CCR) model on the next stage, both oriented to inputs. The results show increases in the efficiency of libraries through the redistribution of resources. This approach is invaluable to the management of library systems since it provides an instrument for improving resource utilization.

Efficient allocation of coal de-capacity quota among Chinese provinces: a zero-sum gains data envelopment model

An efficient coal de-capacity quota allocation scheme is key for accelerating China’s coal supply-side structure reform. This paper allocates the coal de-capacity quota from the perspective of effi...

Efficient allocation of CO2 emissions in China: a zero sum gains data envelopment model

The appropriate allocation of CO2 emission quotas can build up a solid foundation for future emissions trading. Building CO2 emissions allocation mechanism has significant practical implications. Based on radial zero sum gains data envelopment (ZSG-DEA) allocation model, this paper uses a non-radial ZSG-DEA model to allocate CO2 emissions between different Chinese provinces. Unlike previous studies treating CO2 as the input variable, we treat CO2 as the undesirable output variable. The modified model can better reflect macro-production process while earlier relevant models treated CO2 emissions as inputs. This paper contributes to the existing resource allocation method and allocates China's provincial CO2 emissions from the view of technical efficiency. The results of our paper reveal that (1) between 2006 and 2010 the cumulative optimal amounts of CO2 emissions were higher than the actual amounts in 12 provinces, and lower in other 18 provinces. (2) Several energy-abundant provinces such as Shanxi and Inter Mongolia need to take more responsibilities in CO2 emissions reduction. (3) After the ZSG-DEA allocation, all provinces' CO2 emissions are on ZSG-DEA frontier, which reflects the overall “Pareto Optimality”.

Regional allocation of CO2 emissions allowance over provinces in China by 2020

The mitigation efforts of China are increasingly important for meeting global climate target since the rapid economic growth of China has led to an increasing share in the world's total CO2 emissions. This paper sets out to explore the approach for realizing China's national mitigation targets submitted to the UNFCCC as part of the Copenhagen Accord; that is, to reduce the intensity of CO2 emissions per unit of GDP by 40–45% by 2020, as well as reducing the energy intensity and increasing the share of non-fossil fuel consumption, through regional allocation of emission allowance over China's provinces. Since the realization of China's mitigation target essentially represents a total amount emission allowance allocation problem, an improved zero sum gains data envelopment analysis optimization model, which could deal with the constant total amount resources allocation, is proposed in this study. By utilizing this model and based on several scenarios of China's economic growth, CO2 emissions, and energy consumption, a new efficient emission allowance allocation scheme on provincial level for China by 2020 is proposed. The allocation results indicate that different provinces have to shoulder different mitigation burdens in terms of emission intensity reduction, energy intensity reduction, and share of non-fossil fuels increase.

Uniformization of frontiers in non-radial ZSG-DEA models: an application to airport revenues

We propose in this paper an extension to the Zero Sum Gains Data Envelopment Analysis model (ZSG-DEA). The proposed approach takes into account, simultaneously, non-radial projections and cone-ratio weights restrictions. We developed an iterative approximate algorithm to solve this model, as in the case study it is oriented only to the constant sum output. The theoretical approach is applied to the concession of discounts and surcharges problem, in terms of airport fees.