【作者】 徐斌；

【导师】 李南；

【作者基本信息】 南京航空航天大学 ， 管理科学与工程， 2008， 博士

【摘要】 多层规划是为了研究系统层次性问题而产生的,它是以递阶决策问题为研究对象的量化方法。目前对多层规划建模方法和求解算法的研究依然存在许多不完善的方面,尤其是对带有区间灰数的不确定性多层规划的研究基本上还是处于起步阶段,这将不利于解决具有灰色信息的递阶层次系统规划问题,所以,迫切需要对多层规划展开深入研究。同时,实际的产品分销系统是一个递阶层次系统,具有阶层性,因此,采用多层规划方法解决产品分销网络规划问题更合理。本文首先对确定性多层规划建模及求解方法,进行了总结和拓展。根据上下层决策者之间的结构关系和决策者目标数的多少,总结和介绍了确定性多层单目标规划、确定性多层多目标规划、确定性离散多层规划模型,其中,对已有的双层多目标规划模型进行了拓展,建立了确定性多层多目标规划的一般模型;同时,介绍了前人提出的求解多层规划模型的一种有效算法——交互式模糊算法。本文接着介绍和研究了不确定多层规划模型及其求解算法,其中包括随机、模糊和灰色多层规划。根据刘宝碇教授提出的期望值模型、机会约束规划和相关机会规划等三大类随机和模糊规划模型[56],并且基于对单目标、多目标和离散条件的考虑,首先建立了随机条件下的单目标和多目标期望值、机会约束、相关机会多层规划模型,来描述随机条件下的单目标和多目标多层决策问题;介绍了文献[1]中提出的随机离散双层规划模型,来描述随机条件下的离散双层决策问题;接着建立了模糊条件下的期望值、机会约束、相关机会多层单目标规划模型,来描述模糊条件下的单目标多层决策问题;最后提出灰色多层规划的建模方法,建立灰色双层漂移型和灰色离散双层漂移型线性规划模型,用来描述含有区间灰数的双层和离散双层决策问题,不仅符合阶层系统的决策机理,而且能够反映其递阶层次特性;并提出求解灰色双层漂移型线性规划模型的白化交互式模糊算法、将灰色线性规划转化为确定性非线性规划的算法、改进的交互式模糊算法和提出求解灰色离散双层漂移型线性规划模型的白化交互式模糊算法、交互式补偿模糊算法等算法,这些算法使系统中的区间灰数能够得到妥善处理,有效地解决含有区间灰数的阶层系统正确决策问题,是求解灰色多层规划模型简单、有效的算法。其中,改进的交互式模糊算法和交互式补偿模糊算法将区间灰数带入优化过程,在决策过程中反映出灰色信息,使得灰色递阶决策系统中的灰色信息能够尽可能地得到利用,同时补偿算法中通过引入补偿算子,可以使处于独立决策状态下的下层决策者的目标更容易达成一致。通过算例分析得到的结果验证了,本文提出的求解算法克服了区间灰数处理和一般多层规划求解的复杂性和困难性,同时,提高各方的满意度,更容易得到各决策者都满意的解,使得求解过程简单、结果有效。本文最后研究了多层规划理论和方法在产品分销网络规划问题中的应用。首先将多层规划方法应用到确定条件下分销网络规划问题中,分别采用双层规划方法解决产品分销中心选址规划问题、竞争环境下的产品分销网络规划问题,同时也采用离散双层规划方法解决离散条件下的二级分销网络规划问题。模拟算例计算结果验证了采用基于分层建模和求解的双层规划方法来解决分销网络规划问题,能够充分考虑分销系统的递阶层次性和客户的选择行为,并能反映实际分销网络的决策机制,计算结果更优。接着将灰色离散双层规划方法应用到解决具有区间灰数的二级分销网络规划问题中,建立了灰色离散双层线性规划模型,充分考虑了网络决策部门及客户双方的利益、客户间决策的独立性,最后通过算例验证了采用基于分层建模和求解的灰色离散双层规划方法来解决具有区间灰参数的分销网络规划问题,能够充分考虑分销系统的递阶层次性和客户的选择行为,并能反映实际分销网络的决策机制,计算结果更优。本文的研究丰富和完善了多层规划建模方法及其求解算法,并将其应用到解决产品分销网络的规划问题中。本文的创新点主要有以下几点:(1)提出了灰色多层规划的建模方法,建立灰色双层漂移型和灰色离散双层漂移型线性规划模型。(2)提出了求解灰色双层漂移型线性规划模型的白化交互式模糊算法、将灰色线性规划转化为确定性非线性规划的算法、改进的交互式模糊算法。(3)提出了求解灰色离散双层漂移型线性规划模型的白化交互式模糊算法和交互式补偿模糊算法。(4)将灰色离散双层规划方法应用到解决具有区间灰数的二级分销网络规划问题中。更多还原

【Abstract】 Multi-level programming is put forward for the problems with hiberarchy, it is the method for solving the problems of multi-level decision-making. Up to now, there is much faultiness in the researches on multi-level programming problems and algorithms, especially for uncertain multi-level programming problems with Interval grey numbers. It is not good to solving the system programming problems with grey information. So it needs more researches on multi-level programming. Actual distribution networks are systems with hiberarchy, so it will be more reasonable to use multi-level programming to solve the problems of distribution network designs.Firstly, this thesis summarizes and develops certain multi-level programming models and algorithms. Based on the structural relationship between decision-makers and the number of object of decision-makers, this thesis introduces multi-level programming with single object, multi-level programming with multi-objects, and decentralized bi-level programming in certain circumstances. It also develops the existing bi-level multi-objects programming models, and makes the certain general model for multi-level multi-objects programming. It introduces the existing effective interactive fuzzy algorithm for multi-level programming.Secondly, this thesis introduces and researches uncertain multi-level programming models and algorithms, including stochastic, fuzzy and grey multi-level programming. According to Professor Liu’s three kinds of stochastic and fuzzy programming models which are Expectation programming, Chance-constrained programming and Dependent-chance programming models, and based on a single object, multi-object and decentralized conditions, this thesis makes stochastic one-object and multi-object Expectation programming, Chance-constrained programming and Dependent-chance programming models, introduces the stochastic decentralized bi-level programming models. It also makes fuzzy Expectation programming, Chance-constrained programming and Dependent-chance programming models. Finally it proposes multi-level grey programming modeling methods, makes grey bi-level drift-type linear programming and grey decentralized bi-level drift-type linear programming models to describe bi-level and decentralized bi-level decision making problems with interval grey numbers. These models not only accord with the decision-making mechanism of hiberarchy system, but also reflect its hierarchical characteristics. This thesis also gives the whiten interactive fuzzy algorithm, an algorithm of transforming programming models from grey linear to certain non-linear and an improved interactive fuzzy algorithm for grey bi-level drift-type linear programming models, and gives the whiten interactive fuzzy algorithm, interactive compensatory fuzzy algorithm for grey decentralized bi-level drift-type linear programming models. These algorithms are simple and effective for grey multi-level programming models, which can deal with the interval grey number in the systems properly. Improved interactive fuzzy algorithm and interactive compensatory fuzzy algorithm put interval grey numbers into the process of optimization, reflect the grey information in decision-making and utilize grey information in hierarchical decision-making system as much as possible. Compensation operator introduced can make the goal of independent decision-makers more easily to reach an agreement. The results of numerical analysis show that algorithms presented in this thesis overcomes the complexity and difficulty of the handling of interval grey numbers and multi-level programming and algorithms make the solution satisfied by all decision-makers to be get easily, the processes of getting results are simple and effective.Finally, multi-level programming is used to solve the problems of distribution network design. At first, it makes the bi-level programming models for the location of the distribution centers and distribution network design in competitive circumstances, and makes decentralized bi-level linear programming models for decentralized distribution network design. Simulation results show that use bi-level programming based on the hierarchical to solve the problem of distribution network design can take full account of the hierarchy and customer choice, and reflect the decision-making mechanism in distribution system. It can also get better results. And this thesis makes grey decentralized bi-level linear programming models for distribution network design with interval grey numbers. It gives full consideration about the interests to the network decision-making departments and customers, the independence of decision-making among customers. The results of numerical analysis show that decentralized bi-level programming based on the hierarchical to solve the problem of distribution network design can take full account of the hierarchy and customer choice, and reflect the decision-making mechanism in distribution system. It can also get better results.The researches in this thesis enriched and improved the methods for models and algorithms of multi-level programming and used them to solve the problems of distribution network design. There are several innovations in this thesis:(1)Present the modeling method for grey multi-level programming, make grey bi-level drift-type linear programming and grey decentralized bi-level drift-type linear programming models.(2)Present the whiten interactive fuzzy algorithm, an algorithm of transforming programming models from grey linear to certain non-linear and an improved interactive fuzzy algorithm for grey bi-level drift-type linear programming models.(3)Present the whiten interactive fuzzy algorithm, interactive compensatory fuzzy algorithm for grey decentralized bi-level drift-type linear programming models.(4)Apply grey decentralized bi-level programming into distribution network design with interval grey numbers.更多还原