【作者】 王英楠；

【导师】 韩继业；

【作者基本信息】 河南大学 ， 运筹学与控制论， 2007， 硕士

【摘要】 鲁棒优化(RO)作为数学规划的一个新分支最近才发展起来,它是解决不确定规划问题的一种强有力工具。由于测量误差或模型本身的缺陷,或者决策阶段缺乏信息等原因,实际中许多优化问题的数据是受到干扰的或是不确定的,并且概率分布也无法预知。鲁棒优化通过“集合”形式描述数据的不确定性(而不是概率分布),使得约束条件在不确定数据取值于已知集合中所有可能值的情况下都满足,并以此建立最坏情况下最优化目标函数的鲁棒对应模型(RC),从而得到问题的鲁棒最优解。不同的“集合”形式得到不同类型的鲁棒对应模型,其复杂程度也不相同,但对同一个问题使用不同的不确定集合对鲁棒最优解和目标值有什么影响,它们之间存在什么联系,本文将对此进行初步的研究。另一方面,供应链中需求信息的多变和价格波动的频繁造成供应商和零售商诸多决策问题的困难,所以本文选取供应链管理中零售商-供应商柔性合同RSFC问题为应用背景,从鲁棒优化理论的两种鲁棒模型Ben-Tal & Nemirovski鲁棒模型和Bertsimas & Sim鲁棒模型入手,以不确定线性规划为研究对象,研究两种鲁棒模型的本质区别和内在联系。通过对两种模型中保守度参数的选取,给出两种模型在一定条件下存在相同最优解的必要条件和充分条件,并且结论是“逐条”的,即对每条约束可以独立使用而互不影响。根据上述性质建立混合鲁棒模型,并通过RSFC问题的算例实验分析说明保守度的选取对RSFC模型决策的影响以及为此所付出的鲁棒代价,以及混合模型的可行性和有效性。本文的主要贡献如下:(1)对使用单一保守度的Ben-Tal & Nemirovski鲁棒模型进行局部调整,每条含有不确定数据的约束引入不同的保守度,在不影响约束违反概率的情况下使得模型的保守度降低,从而改进了目标最优值。(2)研究最优解相同的情况下两种模型保守度参数的选取问题,在一定假设下给出其充分条件和必要条件,并通过算例验证结论的正确性。(3)建立价格和需求均不确定的RSFC问题的鲁棒对应模型,并利用(2)中结论和其“逐条”性质,建立同时使用两种不确定集合的混合型鲁棒模型。更多还原

【Abstract】 Robust optimization (RO) is a relatively recent technique as a new branch of maths programming, and it is a powerful methodology used to solve uncertain program problems. Many real-world optimization problems involve input data that are perturbed or uncertain, and the probability distributions of the uncertain data are unknown or unavailable due to measurement or modelling errors, or the unavailability of the information at the time of the decision. RO is based on a description of uncertainty via sets, as opposed to probability distributions. The uncertain parameters are only known to belong to known sets, and one associates with the uncertain problem its robust counterpart (RC) where the constraints are enforced for every possible value of the parameters within their prescribed sets; under such constraints, the worst-case value of the cost function is then minimized to obtain a“robust”solution of the problem. Different type of sets gets different type of robust counterparts, which have different complexities. What are the effects on robust solution and its optimal value when using different type of sets, and what are the relations between them, we’ll try to study these problems.In this paper we take the retailer-supplier flexible commitment (RSFC) problem in supply chain management as applied background, because in RSFC there are decision problems caused by changefully demand information and fluctuant price.We study two RC of uncertain RSFC problems: Ben-Tal & Nemirovski RC and Bertsimas & Sim RC, and their essential difference and internal relations. Via the conservativeness parameters of the two RC, we derive the sufficient condition and necessary condition when they have the same solution under some premise. Furthermore, the propositions are“consrtaintwise”: can be used independently in different constraint.Through case study, the RC is found to provide effective protect from the disruption of uncertain data and the robust price paid at the same time. Comparing two tests’results, it validates the sufficient and necessary conditions.The contributions of this paper are as follows:1) We introduce each contaminated constraint of Ben-Tal & Nemirovski RC a proper conservativeness parameters not only a single one, and this modifying improves optimal value without change the probability of constraint violate.2) After studying the relation between the two RC’s conservativeness parameters when there are existing the same solutions, we derive the sufficient condition and necessary condition under some premise, and they are all testified by case study.3) The RC of RSFC problems with both uncertain demand and uncertain price is formulated, and by the propositions (2) above, we formulate the mixed-RC model using both two types RC.更多还原