不确定条件下环境友好型资源分配二层规划模型
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摘要
本文讨论了不确定条件下环境友好型的资源分配问题:其中总公司作为上层领导者在各下属工厂间合理分配资源,以期获得最大收益的同时降低对环境的污染程度;而作为下层从属者的各工厂决定各自产量以期获得最大利润。该问题中的产品价格、生产成本、资源成本等被考虑为随机变量,环境污染指数被考虑为模糊变量,因而本文构造了不确定条件下的机会约束二层资源分配模型。运用等价定理对模型进行转换,并采用交互式满意度法将二层模型转化为单层模型以便求解。最后通过数值算例证实了模型和算法的可行性与有效性。此外,由于模型含有影响模型解的参数,故基于满意度和置信水平分别进行了灵敏度分析,进一步验证了所提出模型的科学性。
In this paper,we discuss the environmental friendly resource allocation problem under the uncertain condition,where the leader is the head office,who allocates the resource properly to maximize the profit and minimize the pollution; the follower is the processing plants,who decide the production amount of every products to get their best profit. In this problem,we suggest that the products' price,the capacity and the cost obey random distribution,and the environment pollution factors are fuzzy variables. Based on the above statement,an uncertain chance constrained bi-level resource allocation model is constructed. In order to make the model solvable,we then convert the uncertain model into the equivalent model,and adopt the interactive satisfied method to transform the bi-level model into a kind of single level model. At last,we use a numerical example to test and verify the feasibility and efficiency of the model and the solution method. Besides,there are confidence levels and satisfied degrees in the models which may affect the result to some extent,hence we also proceed the sensitivity analysis to show the relationship between the result and the confidence levels and satisfied degrees,respectively.
In this paper,we discuss the environmental friendly resource allocation problem under the uncertain condition,where the leader is the head office,who allocates the resource properly to maximize the profit and minimize the pollution; the follower is the processing plants,who decide the production amount of every products to get their best profit. In this problem,we suggest that the products' price,the capacity and the cost obey random distribution,and the environment pollution factors are fuzzy variables. Based on the above statement,an uncertain chance constrained bi-level resource allocation model is constructed. In order to make the model solvable,we then convert the uncertain model into the equivalent model,and adopt the interactive satisfied method to transform the bi-level model into a kind of single level model. At last,we use a numerical example to test and verify the feasibility and efficiency of the model and the solution method. Besides,there are confidence levels and satisfied degrees in the models which may affect the result to some extent,hence we also proceed the sensitivity analysis to show the relationship between the result and the confidence levels and satisfied degrees,respectively.
引文
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[2]Shimizu K,Aiyoshi E.Hierarchical multi-objective decision systems for general resource allocation problems[J].Journal of Optimization Theory and Applications,1981,35(4):517-533.
[3]仲伟俊,徐南荣.具有合作关系的多人递阶资资源分配问题研究[J].系统工程理论与实践,1993,13(2):11-16.
[4]刘新旺,达庆利.一种多人递阶资源分配问题的模糊满意解[J].系统工程理论与实践,2000,22(4):51-56.
[5]曾玲,高金伍.带模糊参数的递阶资源分配问题[J].系统工程理论与实践,2004,11:10-19.
[6]Arora S R,Ritu Gupta.Interactive fuzzy goal programming approach for bilevel programming problem[J].European Journal of Operational Research,2009,194(2):368-376.
[7]Gang J,Tu Y.A multi-objective bi-level location planning problem for stone industrial parks[J].Computers&Operations Research,2015,56:8-21.
[8]Asaduzzaman S,Maheswaran M.Decentralized management of bi-modal network resources in a distributed stream processing platform[J].Journal of Parallel and Distributed Computing,2011,71(6):774-787.
[9]邓胜岳,周立前,汪新凡.上层含约束条件且具有模糊决策变量的二层多随从线性规划[J].控制与决策,2014,29(10):1803-1808.
[10]Xu J,Yao L.Random-like multiple objective decision making[J].Springer,2011.
[11]Xu J,Zhou X.Fuzzy-like multiple objective decision making[J].Springer,2011.
[2]Shimizu K,Aiyoshi E.Hierarchical multi-objective decision systems for general resource allocation problems[J].Journal of Optimization Theory and Applications,1981,35(4):517-533.
[3]仲伟俊,徐南荣.具有合作关系的多人递阶资资源分配问题研究[J].系统工程理论与实践,1993,13(2):11-16.
[4]刘新旺,达庆利.一种多人递阶资源分配问题的模糊满意解[J].系统工程理论与实践,2000,22(4):51-56.
[5]曾玲,高金伍.带模糊参数的递阶资源分配问题[J].系统工程理论与实践,2004,11:10-19.
[6]Arora S R,Ritu Gupta.Interactive fuzzy goal programming approach for bilevel programming problem[J].European Journal of Operational Research,2009,194(2):368-376.
[7]Gang J,Tu Y.A multi-objective bi-level location planning problem for stone industrial parks[J].Computers&Operations Research,2015,56:8-21.
[8]Asaduzzaman S,Maheswaran M.Decentralized management of bi-modal network resources in a distributed stream processing platform[J].Journal of Parallel and Distributed Computing,2011,71(6):774-787.
[9]邓胜岳,周立前,汪新凡.上层含约束条件且具有模糊决策变量的二层多随从线性规划[J].控制与决策,2014,29(10):1803-1808.
[10]Xu J,Yao L.Random-like multiple objective decision making[J].Springer,2011.
[11]Xu J,Zhou X.Fuzzy-like multiple objective decision making[J].Springer,2011.