Abstract: How to allocate environmental resources reasonably among various economic entities (Decision-Making Units, DMUs) to form an acceptable rights and responsibilities allocation scheme for environmental resources protection among all economic entities (DMUs) is a challenging issue in practical economic management. Data Envelopment Analysis (DEA) has the advantages of not needing to preset production function forms and error structures, and it is widely used in the evaluation of input-output efficiency and resource allocation. Therefore, this paper develops a goal-oriented DEA method for optimizing the allocation of environmental resources, in accordance with the principles of the Nash bargaining solution.
Firstly, this paper presents a weighted additive slack-based DEA model, which accounts for the public externalities based on the Directional Economic Environmental Distance Function (DEED), called the Adjusted Directional Economic Environmental Distance Function (ADEED). The DEED model only considers the private impact of undesirable output, whereas the ADEED model takes into account the fact that some undesirable outputs such as pollution emissions have public external effects on all economic entities (DMUs). Then, this paper constructs management Goal-Oriented ADEED (GOADEED) model by adding the objective constraint of total quantity controlling for the environmental resource into the ADEED model. Finally, by using the GOADEED model to calculate the Pareto optimal welfare under the constraint of management objectives, and by using the DEED model to calculate the disagreement points, a goal-oriented optimization allocation method for environmental resources conforming to the Nash bargaining solution is proposed.
In the empirical analysis, the environmental resources allocation method proposed in this paper is applied to address the issue of carbon reduction responsibility allocation among provinces in China, thereby demonstrating the effectiveness of the method. Each province is treated as a DMU, and each DMU has three inputs, namely, labor input, energy input and capital input. Additionally, each DMU has one desired output, which is Gross Domestic Product (GDP), and one undesirable output, which is carbon emission. The empirical data are collected from various public and authoritative institutions. Based on the collected data, the environmental resources allocation method proposed in this paper not only accurately allocates the carbon reduction tasks for each province, but also further calculates the amount of benefit compensation for each province relative to the allocation of carbon reduction responsibilities.
Overall, the environmental resource allocation method proposed in this paper can achieve equilibrium allocation of the environmental resource under the constraint of the total control goal for environmental resource set by managers, following the principle of the Nash bargaining solution. However, the DEED, ADEED, and GOADEED models require weighted information such as prices or costs of various input and output variables. In reality, this weighted information may not be available, especially for undesired outputs such as environmental pollution. Due to the absence of a trading market, it is particularly difficult to obtain information on prices or costs of undesired outputs such as environmental pollution. Therefore, it is necessary to adjust the ADEED model and GOADEED model into unweighted models, which is also a direction for further research.

Key words: data envelopment analysis, Nash bargaining solution, management goal oriented, environmental resources, allocation method, public externalities

摘要： 提出了符合纳什议价解原理的管理目标导向的环境资源优化配置的DEA模型。首先,在非期望产出私人影响的经济环境方向距离(DEED)函数模型的基础上,考虑环境污染等非期望产出对所有生产决策单位造成公共外部影响,构建加权可加的基于松弛变量的考虑公共外部影响的数据包络模型——调整的经济环境方向距离(ADEED)函数模型。其次,在ADEED中加入环境资源总量控制的目标约束式,从而构建管理目标导向的GOADEED模型。用GOADEED模型计算管理目标约束下的帕累托最优福利,用DEED模型计算无合作情景下的分歧点,进而提出了符合纳什议价解的目标导向的环境资源优化配置方法。最后,以我国各省区碳减排责任分配为例,说明该方法的可行性和有效性。本研究提出的方法可以在管理者设定的环境资源总量控制下,按照纳什议价解的原理,对环境资源进行均衡分配,从而实现环境资源的优化配置。

关键词: 数据包络分析, 纳什议价解, 管理目标导向, 环境资源, 分配方法, 公共外部影响