孙冬营++王慧敏++于晶
摘要水资源短缺是我国面临的十分重要的资源问题,随着人口的不断增长,对水资源的需求也逐渐增加。水资源短缺已成为经济发展和社会和谐的一个主要瓶颈,如何将一个流域有限的水资源合理地分配给流域内不同的行政区域、区域内不同的产业是水资源规划与管理领域学术研究的核心内容。流域是一个自然形成的空间范围,往往涉及多个不同的行政区域,流域水资源分配牵涉到流域内不同利益主体,公平有效地进行流域水资源配置以达到水资源的可持续利用已经成为流域经济发展和社会稳定的重要因素。本文采用流域水资源分配的二次配置模型,在流域水资源初次分配当中考虑公平,建立基于用水主体需求的水资源分配优化模型,使得各主体需水量和分配水量的离差平方和最小,并得到初始水资源分配结果;在流域水资源二次分配当中考虑效率,建立流域水资源二次分配的模糊联盟合作博弈模型以最大化流域整体收益,并将由合作带来的流域整体收益的增加部分采用模糊夏普利值的方法分配给参与模糊联盟的各个用水主体,同时流域水资源得到有效再分配。最后,将上述流域水资源二次分配模型运用到一个算例当中,验证了模型本身的有效性和适应性。模糊联盟合作博弈模型对于促进流域水资源规划与管理具有借鉴意义。
关键词合作博弈;模糊联盟;水资源配置;优化
中图分类号文献标识码A文章编号1002-2104(2014)12-0153-06doi:10.3969/j.issn.1002-2104.2014.12.021
水资源是人类社会赖以生存和发展的基本要素和战略性资源。伴随着社会经济的快速发展,人们对水资源的需求也不断增加,水资源已经成为新时期我国最为稀缺的自然资源之一。同时,水资源短缺、水污染、水生态恶化等问题已经成为国民经济发展的瓶颈,严重制约着经济社会的可持续发展。流域水资源配置是一个涉及多个行政区域、多个业务部门以及多个目标的复杂决策问题。如何将有限的水资源分配给用水主体、使得水资源的利用得到最大化效益,成为研究人员研究的热点问题。由于各个利益主体目标的不完全一致性,在流域水资源配置过程中常常发生国家之间、区域之间以及行业之间的用水冲突。在流域水资源配置过程中,如何处理公平与效率的关系使得各利益主体个体收益不减少的情况下增加整体收益不仅关系到每一个用水主体,同时也是水资源主管部门所关心的核心问题,更影响着社会和谐与稳定。本文尝试研究利用流域水资源二次配置模型,在初次配置中考虑公平,在二次配置中考虑效率。流域水资源配置研究在国内外都取得了一定进展。罗其友等[1]重点研究了黄河流域农业水资源在不同区域不同作物间的合理配置问题;陈晓宏等[2]采用大系统“分解协调”原理提出多层次优化的水资源优化配置模型,在模型中考虑了防洪、供水、航运等多种约束;王浩等[3]提出水资源“三次平衡”和水资源可持续利用思想并进行了详细阐述;陈西庆等[4]提出在长江流域实行流域综合管理使水资源利用和管理在流域层面上达到优化状态,并确定了流域各行政区管理机构与用水户共同协商决策的原则,开启了对流域各主体协商管理水资源的研究;王勇[5]从负外部性的角度探讨了流域水资源配置,并对比了流域管理中的科层协调机制、市场协调机制和府际治理协调机制,表明三者的结合成为淮河治污的最佳选择;史银军等[6]针对内陆河流域水资源多次转化多次利用的特点,建立以水资源转化过程为基础的流域水资源优化配置模型,并引入进化算法求解计算实现水资源的流域配置和行政区配置的统一,便于水资源统一管理;吴丹等[7]建立流域初始水权配置的双层优化模型使得流域水资源得到合理配置,减少了区域之间的用水矛盾,并基于交互式群决策方法对模型进行求解。Koos De Voogt等[8]使用一个半分布式水文模型对流域水资源配置对水资源可用性和作物产量的影响进行评估,发现在灌溉季节湿地需水的增加减少了作物产量;ClaudiaRingler等[9]使用一个集成经济-水文的流域模型分析水资源分配政策的产生发展和应用,并在这个模型框架下考虑政治因素对水资源配置的影响;Devaraj de Condappa等[10]开发一个决策支持系统用于沃尔特河流域跨界水资源管理,该系统综合了水文模型、水资源评估与规划模型和水资源配置模型并考虑潜在的气候变化的影响;Mojtaba Sadegh等[11]利用合作博弈模型研究跨流域水资源转移的最优化,但并未考虑因此而产生的跨流域调水所产生的费用问题;D. Haro等[12]将非线性引入传统的网络流模型用于流域水资源配置,三种不同网络流算法用于配置问题的求解,结果表明OutofKilter具有最好的鲁棒性(robustness)。
总结已有的国内外研究,我们可以发现已有的水资源配置研究主要集中在优化算法模型、决策支持技术的研究上,却很少考虑到水资源配置过程中涉及的不同用水主体之间的关系,水资源配置目的在于最大化流域整体利益并使得相关利益主体参与水资源配置的积极性得到提高。对于流域水资源配置过程中的利益主体间的关系的研究有助于减少配置过程中可能产生的矛盾和冲突,提高主体参与水资源配置积极性,并最终达到流域水资源在整个流域层面得到和谐配置。由于合作能够给局中人带来更多的利益,所以合作博弈常被用来研究公共池塘资源的分配,比如水资源。合作博弈理论研究局中人中的联盟关系以及联盟利益分配问题,这与流域水资源配置实践相符合。采用合作博弈的方法配置流域水资源,可以充分考虑各个主体决策的策略。本文采用模糊联盟合作博弈的方法给出流域水资源配置的一个框架:第一步基于公平的初始水资源配置;第二步基于效率的水资源二次分配。最后将所提出的方法用于一个算例分析,结果表明该方法确实提高了流域整体收益并增加了各参与主体的收益。
孙冬营等:基于模糊联盟合作博弈的流域水资源优化配置研究中国人口·资源与环境2014年第12期1流域水资源优化配置模糊合作博弈模型
所采用的方法的应用过程如图1所示。
图1流域水资源配置模糊联盟合作博弈模型
应用框架
Rm表示第m个月水库S释放的水量,Dm表示第m个月总的需水量,共有M个月,i表示第i个用水主体,共有N个用水主体。Xi,m表示第m个月分配给第i个用水主体的水量,di,m表示第m个月第i个用水主体的需水量。Ifm表示第m个月维持河道环境所需的径流,Im表示第m个月水库上游来水量。Rmax表示水库能够释放的最大水量,Sm表示水库在第m个月初的存量,S1表示水库初始存量,Smin和Smax分别表示水库的死库容和最大库容。
方程(2)确保水资源按照用水主体需水量的相同比例分配给不同用水主体,本模型所得到的分配水量Xi,m将作为二次分配模型的输入部分。
1.2流域水资源二次配置模型
合作博弈研究联盟之间的相互作用以及联盟收益如何在盟友之间进行分配的问题,水资源配置问题往往也是复杂的多主体决策问题,用合作博弈去解决水资源配置问题具体先天优势[13]。在常规联盟(Crisp Coalition)中,要求局中人携带自己的全部资源参与某个联盟,根据Shapley的定义,联盟中某个局中人的收益决定于其对该联盟的贡献。根据Aubin(1974)提出的模糊联盟(Fuzzy Coalition)的含义,在模糊联盟中,局中人只需要携带部分资源参与各个联盟,其收益等于该局中人参与各个联盟获得的收益之和。具体来说,模糊联盟不要求局中人携带自身拥有的全部资源参与某个联盟,而是允许其携带自身拥有的部分资源参与不同的联盟。常规联盟和模糊联盟的区别在于,在常规联盟中,局中人只能参与某一个联盟;而在模糊联盟中,局中人可以同时参与多个联盟。模糊联盟产生的实际背景在于,实际问题当中,局中人并不是将其所有的资源贡献给联某个盟,只是将一部分资源贡献给该联盟,也就是以不同的参与率参与不同的联盟。在水资源二次分配模型中,首先,各用水主体携带一定数量的水资源参加不同的模糊联盟,使得整个流域系统的收益达到最大,然后将最大化的收益按照一定的方法分配给各个参与联盟的用水主体,同时各个用水主体的水资源也将在不同的模糊联盟间进行再分配。对于一个模糊联盟所拥有的资源如何在模糊联盟中各个参与主体之间的分配,模糊联盟并没有定义,相反地,模糊联盟研究的是收益的增加部分在局中人之间的分配。在实际问题当中,各个局中人之间的合作往往是多个维度的,也即除了在水资源分配当中的合作,还有其他合作途径,而这些不同的合作途径又往往互相作用并最终达到一个动态平衡状态。
为了最大化流域整体收益,我们需要确定各个用水主体参与各个模糊联盟的参与率。这里参与率指的是用水主体携带多少比例的初始水资源参加某个模糊联盟。目标函数与约束如下:
在这里T代表流域整体收益,也即总的流域水资源收益。v(s)代表联盟s的收益,其中B(s)表示联盟s的收益参数即单位水产生的收益,C(s)表示联盟s对水资源的最大需求能力,x(s)表示参与联盟s的用水主体携带的水资源总量。pri(s)代表第i个用水主体参与联盟s的参与率,其最大值为1表示携带全部初始水资源参与联盟s,最小值为0表示不参与联盟s,且每个用水主体参与各个联盟的参与率之和为1,也即全部水资源都被用来参与再分配。v(i,s)代表第i个用水主体独立使用其用于参与联盟s的水资源所产生的收益,其中b(i)表示第i个用水主体的单位水资源收益参数,而Xi表示第i个用水主体的初始水资源量。φi(s)代表第i个用水主体参与联盟s所获得的收益,必须满足个体理性也即从参与联盟s中获得的收益必须不小于这部分水资源独立使用时产生的收益。
在求解上面的模型之后,可以使用不同的收益分配方法将系统总的净收益分配给各个用水主体,主要有模糊夏普利值、模糊最小核与模糊弱最小核,本文采用模糊夏普利值来分配收益。
3结论
在现实问题当中,流域不同灌区之间对水资源的需求可能并不是同时发生的,比如,由于作物种类的不同而产生的灌溉时间的差异以及降雨的时空差异也会产生对水资源需求的不同步性;而流域上下游之间因为产业结构的不同也会产生对水资源需求的不同步性;另外流域内区域之间的水资源合作联盟可能建立在其他形式的经济合作基础之上,就像本文算例中所说,区域B可以为区域A加工农产品而区域C可以为区域A和B提供服务和产品。所以考虑到这些因素,流域不同区域用水主体之间的合作就成为可能。合理有效地在流域范围内利用水资源有助于提高水资源的利用效率,减少水资源浪费。
通过建立基于需水的流域水资源初始分配模型,保证水资源在初次分配中保证公平,而流域水资源的二次分配确保流域整体利益得到最大化,效率成为关键因素。在流域水资源二次分配过程中,提高流域整体利益的同时并没有减少每个区域的收益,满足各主体参与联盟的个体理性,并根据模糊夏普利值计算出各个参与主体获得的收益。算例分析表明,所建立的模型有效,对于实际的水资源分配具有一定的借鉴意义。
(编辑:于杰)
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Study on Optimal Allocation of Water Resources in Basin
Based on Cooperative Game Under Fuzzy Coalition
SUN Dongying1,2WANG Huimin1,2Yu Jing3
(1. State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China;
2. Institute of Management Science, Hohai University, Nanjing 211100, China;
3. Business school, Hohai University, Nanjing 211100, China)
AbstractWater shortage is an important resource problem faced by China, and nowadays the need for water resource is increasing with rising population. It has become the bottleneck of economic development and social harmony. How to allocate limited water resources among different regions and/or different industrials in a basin becomes one of the key topics in water resources planning and management. A basin is a naturally shaped area that usually involves multiadministrative. The allocation of water resources in a basin involves different stakeholders. As a result, equitable and effective allocation of water resources to obtain sustainable water usage is an important factor of the economic development and social stability. A model for water resources allocation with two steps is presented. The equality is considered in the initial water allocation in which an optimization model based on the water needs of water users and the results can be obtained by minimizing the sum of the squared deviations. The efficiency is taken into account in the second allocation, in which cooperative games with fuzzy coalitions is adopted to maximize the overall benefit of the basin. And the incremental benefits from cooperation is reallocated to related stakeholders by using the fuzzy Shapley value and water resources are reallocated among all coalitions at the same time. Finally, the proposed model is applied to a numerical example and the effectiveness and applicability of this model is examined. And there are some lessons can be obtained from cooperative games with fuzzy coalitions to improve water resource planning and management.
Key wordscooperative game; fuzzy coalition; water resources allocation; optimization
Based on Cooperative Game Under Fuzzy Coalition
SUN Dongying1,2WANG Huimin1,2Yu Jing3
(1. State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China;
2. Institute of Management Science, Hohai University, Nanjing 211100, China;
3. Business school, Hohai University, Nanjing 211100, China)
AbstractWater shortage is an important resource problem faced by China, and nowadays the need for water resource is increasing with rising population. It has become the bottleneck of economic development and social harmony. How to allocate limited water resources among different regions and/or different industrials in a basin becomes one of the key topics in water resources planning and management. A basin is a naturally shaped area that usually involves multiadministrative. The allocation of water resources in a basin involves different stakeholders. As a result, equitable and effective allocation of water resources to obtain sustainable water usage is an important factor of the economic development and social stability. A model for water resources allocation with two steps is presented. The equality is considered in the initial water allocation in which an optimization model based on the water needs of water users and the results can be obtained by minimizing the sum of the squared deviations. The efficiency is taken into account in the second allocation, in which cooperative games with fuzzy coalitions is adopted to maximize the overall benefit of the basin. And the incremental benefits from cooperation is reallocated to related stakeholders by using the fuzzy Shapley value and water resources are reallocated among all coalitions at the same time. Finally, the proposed model is applied to a numerical example and the effectiveness and applicability of this model is examined. And there are some lessons can be obtained from cooperative games with fuzzy coalitions to improve water resource planning and management.
Key wordscooperative game; fuzzy coalition; water resources allocation; optimization
Based on Cooperative Game Under Fuzzy Coalition
SUN Dongying1,2WANG Huimin1,2Yu Jing3
(1. State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China;
2. Institute of Management Science, Hohai University, Nanjing 211100, China;
3. Business school, Hohai University, Nanjing 211100, China)
AbstractWater shortage is an important resource problem faced by China, and nowadays the need for water resource is increasing with rising population. It has become the bottleneck of economic development and social harmony. How to allocate limited water resources among different regions and/or different industrials in a basin becomes one of the key topics in water resources planning and management. A basin is a naturally shaped area that usually involves multiadministrative. The allocation of water resources in a basin involves different stakeholders. As a result, equitable and effective allocation of water resources to obtain sustainable water usage is an important factor of the economic development and social stability. A model for water resources allocation with two steps is presented. The equality is considered in the initial water allocation in which an optimization model based on the water needs of water users and the results can be obtained by minimizing the sum of the squared deviations. The efficiency is taken into account in the second allocation, in which cooperative games with fuzzy coalitions is adopted to maximize the overall benefit of the basin. And the incremental benefits from cooperation is reallocated to related stakeholders by using the fuzzy Shapley value and water resources are reallocated among all coalitions at the same time. Finally, the proposed model is applied to a numerical example and the effectiveness and applicability of this model is examined. And there are some lessons can be obtained from cooperative games with fuzzy coalitions to improve water resource planning and management.
Key wordscooperative game; fuzzy coalition; water resources allocation; optimization