一类关于不确定条件下鲁棒决策的研究

发布时间：2018-08-27 16:05

【摘要】：本文的主要贡献在于提出并应用一类鲁棒决策的方法,进而支持在不确定的环境下做出更优决策。具体而言,在理论贡献层面上,本文基于随机描述和多面体建模两种表达不确定性的逻辑,提出三类鲁棒优化的方法。其中随机描述是考虑不确定性的不同情境,以及相应的概率;而多面体建模是考虑不确定性分布于一个固定的多面体内。在实际应用贡献层面上,本文将提出的三类鲁棒优化的方法分别用于供应链管理和收益管理代表性问题的研究中。第一类鲁棒优化的方法整合了目标规划和不确定参数的情境分析,其原理是基于解的鲁棒性和模型鲁棒性之间的均衡。如果得到的一个解被称为解鲁棒,那么这个解在不确定参数属于任何情境中都始终距离最优解足够近;如果得到的一个解被称为模型鲁棒,那么这个解在不确定参数属于任何情境中都始终保持可行。本文提出用随机规划的方法来建立模型。考虑到在目标函数中存在绝对值表达式,本文亦提出一种线性化的方法。考虑到市场需求的不确定性,生产成本、资源消耗和产能的不确定性,此种鲁棒优化的方法被分别用于外包中供应商的选择以及瓶颈分配问题的研究中。第二类鲁棒优化的方法考虑两种不确定性的描述:有界限的不确定集和对称的不确定集,同时引入三个新的参数:不确定的水平,不可行的容忍度和可信赖度。针对线性规划问题参数的不确定存在于目标函数和约束条件中,本文提出一类新的鲁棒优化的方法,其优点在于保持线性和可以调节参数进行敏感性分析。考虑到市场订单数量的不确定性,此种鲁棒优化的方法被应用于研究海运舱位分配进而最大化收益管理的研究中。第三类鲁棒优化的方法是基于最小一最大后悔值的逻辑,运用多面体集合的概念描述不确定性,进而得到计算复杂度较低的鲁棒优化模型。此方法的优势在于并不需要关于不确定性的概率分布等信息,而仅仅需要知道其边界。考虑到生产过程中资源使用的不确定性,此种鲁棒优化的方法被运用在研究生产产能计划的研究。
[Abstract]:The main contribution of this paper is to propose and apply a class of robust decision making methods to support better decision making in uncertain environment. Specifically, on the theoretical contribution level, based on stochastic description and polyhedron modeling, we propose three kinds of robust optimization methods based on stochastic description and polyhedron modeling. The stochastic description considers the different situations of uncertainty and the corresponding probability, while the polyhedron modeling considers that the uncertainty is distributed in a fixed polyhedron. In the practical contribution level, the three classes of robust optimization methods proposed in this paper are applied to the representative problems of supply chain management and revenue management, respectively. The first kind of robust optimization method integrates the objective programming and the scenario analysis of uncertain parameters. The principle is based on the balance between the robustness of the solution and the robustness of the model. If the resulting solution is called solution robust, the solution is always close enough to the optimal solution in any case where the parameter is uncertain; if the resulting solution is called model robust, Then the solution is always feasible in any case where the parameter is uncertain. In this paper, a stochastic programming method is proposed to establish the model. Considering the existence of absolute expression in objective function, this paper also proposes a linearization method. Considering the uncertainty of market demand, production cost, resource consumption and capacity, this robust optimization method is applied to the selection of suppliers and bottleneck allocation in outsourcing. The second kind of robust optimization method considers two kinds of uncertain description: bounded uncertain set and symmetric uncertain set. At the same time, three new parameters are introduced: the level of uncertainty, the infeasible tolerance and the degree of trustworthiness. In view of the uncertainty of the parameters of linear programming problems in the objective functions and constraints, a new robust optimization method is proposed in this paper. The advantage of this method is to keep the linearity and adjust the parameters for sensitivity analysis. Considering the uncertainty of market order quantity, this robust optimization method is applied to the study of seaborne space allocation and maximization of revenue management. The third kind of robust optimization method is based on the logic of minimum and maximum regret value and uses the concept of polyhedron set to describe uncertainty and then obtains a robust optimization model with low computational complexity. The advantage of this method is that it does not need information such as probability distribution of uncertainty, but only needs to know its boundary. Considering the uncertainty of resource use in production process, this robust optimization method is applied to the study of production capacity planning.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：F274

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