Two-stage stochastic variational inequalities: an ERM-solution procedure

We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample average approximation are established. Examples of this model are given, including the optimality conditions for stochastic programs, a Walras equilibrium problem and Wardrop flow equilibrium. We also formulate stochastic traffic assignments on arcs flow as a two-stage stochastic variational inequality based on Wardrop flow equilibrium and present numerical results of the Douglas–Rachford splitting method for the corresponding two-stage stochastic programming with recourse.     

Stochastic Survivable Network Design Problems

In this paper we introduce survivable network design problems under a two-stage stochastic model with fixed recourse and finitely many scenarios. We propose a new cut-based formulation based on orientation properties which is stronger than the undirected cut-based model. We use a two-stage branch&cut algorithm for solving the decomposed model to provable optimality. In order to accelerate the computations, we suggest a new cut strengthening technique for the decomposed L-shaped optimality cuts that is computationally fast and easy to implement.     

基于可信性理论的两阶段生产计划模型

为了准确有效地处理农业生产中的不确定性因素,基于可信性理论和两阶段模糊优化方法提出一类新的带有最小风险准则的两阶段模糊农业生产计划模型.然后,讨论可信性函数的逼近方法并且设计一个基于逼近方法、神经网络和模拟退火的启发式算法来求解这个两阶段模糊农业生产计划最小风险模型.最后,给出一个数值例子来表明所设计算法的可行性和有效性.     

两阶段模糊运输期望值模型及其逼近方法

基于可信性理论和两阶段模糊优化方法,提出一类带有模糊参数的两阶段运输期望值模型.由于提出运输问题包含带有无限支撑的模糊变量系数,因此它是一个无限堆的优化问题.然后,讨论两阶段模糊运输期望值问题的逼近方法并且将逼近方法嵌套到遗传算法中产生一个基于遗传算法的逼近方法求解提出的两阶段模糊运输期望值问题.最后,给出一个数值例子...     

两个半相依模型回归系数的改进估计

对于两个半相依回归系统的未知回归系数,本文首先借鉴文献中给出的两步协方差改进估计的方法给出两种两步协方差改进估计序列,并给出其与两步估计等价的条件和均方误差意义下的优良性; 其次,我们对文献中给出的一种两步估计作简单改进,使得改进后的估计在更大的参数空间内优于最小二乘估计. 再次,本文另辟蹊径, 构造了一种新的估计,同样地,此估计也具有更好的小样本性质.本文最后一节讨论了Pitman准则下两步估计的优良性.     

Valuing interdependent multi-stage IT investments: A real options approach

In this paper, we use the market asset disclaimer assumption and develop a binomial lattice based real options model to include cash flow interdependencies between multi-stage information technology (IT) investments. Using a simple two-stage IT investment problem with interdependent cash flows, we apply the binomial lattice based real options model to obtain combined valuation of the two-stage IT investment. In addition to investment valuation, our experience with the two-stage IT investment valuation suggests that the binomial lattice based real options model provides a powerful decision aid tool for appropriate timing, delaying and abandoning of the second-stage IT investment.     

交通网络下的多厂商两阶段随机非合作博弈问题——基于随机变分不等式

研究集生产、运输和销售为一体的多个制造商在随机市场环境下的两阶段随机非合作博弈问题.首先,建立了该两阶段随机非合作博弈问题的模型,然后将其转化为两阶段随机变分不等式(Stochastic Variational Inequality,简称SVI).在温和的假设条件下,证明了该问题存在均衡解,并通过Progressive Hedging Method(简称PHM)进行求解.最后,通过改变模型中随机变量的分布和成本参数,分析与研究厂商的市场行为.     

Box-Cox变换用于分位数回归曲线相交问题的研究

将Box-Cox变换与分位数回归模型相结合(两阶段法),是分位数回归研究领域的一大进步。该法虽然两步都与分位数回归的检验函数紧密结合,但是由于没有利用分位数回归的优良性质,而是引入了中间参变量,因此增加了模型的累进误差,降低了模型精度。更重要的是,两阶段法没有对于分位数回归领域中普遍出现的分位数回归曲线的相交问题给出解决方法。针对这些问题,经研究应该首先确定Box-Cox变换的参数,避免模型中不确定因素的引入,然后对数据进行整体变换并结合分位数检验函数,直接利用分位数回归的优良性质,最终确定分位数回归模型的参数。实例证明,该方法提高了模型的精度,可以有效地解决分位数回归曲线的相交问题。     

基于在险价值的物流网络规划模糊两阶段模型与精确求解方法

针对物流网络规划问题中顾客需求和运输成本的不确定性,使用在险价值量化投资风险,建立了以投资损失的在险价值最小化为目标的模糊两阶段物流网络规划模型。对于模型中不确定参数均为规则模糊数的这一类模糊两阶段规划模型,本文通过理论分析和证明将其转化为等价的确定一阶段规划模型进行求解,从而将无穷维的优化问题转化为有限维的经典优化问题,降低了计算难度且得到了模型的精确解。不同规模的数值实验证实了所提出模型及其求解方法的有效性。     

基于复合式团队两阶段道德风险模型的担保企业评委激励机制

学术界将团队道德风险与两阶段道德风险模型结合构建复合式模型成为激励理论新研究的趋势.然而,这种复合式模型对团队成员间协作,业务两阶段间努力的影响以及代理人的行为因素考虑不足.以担保企业的评委团队在评议会和评审会两阶段的道德风险为研究对象,运用经济学激励理论和最优理论与算法,构造了团队两阶段道德风险复合模型,并通过数值仿真揭示了评委团队在不同规模人数下,团队成员的业务两阶段的努力影响因子,评委团队协作度、两阶段评委道德敏感度与激励强度的关系.主要研究结果表明:在业务评议会阶段,评委团队为3~5人规模,且两阶段努力影响因子偏小或评委道德敏感度偏大时,对该阶段评委团队应施加高激励;而当评委间的协作度为中等或高水平时,随着评委间协作度的增加,对该阶段评委团队的激励强度应递减.在业务评审会阶段,随着评委人数的增加且评委两阶段的努力影响因子减小,对该阶段评委团队应施以较强的正激励;随着评委道德敏感度的减小或评委的协作度增加,对该阶段评委应强化正激励.     

飞机维修短期计划模型及其算法研究

目前对于飞机维修计划的研究,大都通过精确算法一次性完成周期内所有飞机的排班优化。本文在分析传统数学规划模型的基础上,以最大化利用两次维修之间的可用飞行时间为目标,构造了飞机维修计划优化模型。然后提出了求解此模型的启发式两阶段分解算法,第一阶段优先完成需维修飞机的任务指派,第二阶段再完成余下飞机的任务指派。利用航空公司真实数据进行的数值试验表明,两阶段分解算法能够显著提高模型的求解效率和质量,可以有效求解大规模飞机维修计划制定问题。     

Reverse logistics network design and planning utilizing conditional value at risk

Nowadays, due to some social, legal, and economical reasons, dealing with reverse supply chain is an unavoidable issue in many industries. Besides, regarding real-world volatile parameters, lead us to use stochastic optimization techniques. In location–allocation type of problems (such as the presented design and planning one), two-stage stochastic optimization techniques are the most appropriate and popular approaches. Nevertheless, traditional two-stage stochastic programming is risk neutral, which considers the expectation of random variables in its objective function. In this paper, a risk-averse two-stage stochastic programming approach is considered in order to design and planning a reverse supply chain network. We specify the conditional value at risk (CVaR) as a risk evaluator, which is a linear, convex, and mathematically well-behaved type of risk measure. We first consider return amounts and prices of second products as two stochastic parameters. Then, the optimum point is achieved in a two-stage stochastic structure regarding a mean-risk (mean-CVaR) objective function. Appropriate numerical examples are designed, and solved in order to compare the classical versus the proposed approach. We comprehensively discuss about the effectiveness of incorporating a risk measure in a two-stage stochastic model. The results prove the capabilities and acceptability of the developed risk-averse approach and the affects of risk parameters in the model behavior.     

Group decision-making based on heterogeneous preference relations with self-confidence

Preference relations are very useful to express decision makers’ preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing preference relations. In this study, we define the preference relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the preference relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective preference vector for the group decision-making based on heterogeneous preference relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results.     

战略性新兴产业创新金融支持机理及两阶段演化博弈分析

为了研究金融支持如何影响战略性新兴产业创新主体培育的问题,在剖析金融支持主体间双螺旋耦合机理基础上,构建了战略性新兴产业金融支持两阶段演化博弈模型,运用动态系统的相平面理论求取两阶段ESS近似解析解,并借助MATLAB实现两阶段演化博弈模型的数值仿真,分析不同参数赋值对两阶段ESS演进的影响。研究发现:(1)存在机会主义(补贴创新利润率T₁<创新外活动利润率T₂)和非机会主义行为(k>T₂)两种对立占优情境;(2)机会主义行为(或非机会主义)占优情境下,金融支持主体的期望社会效用越小(或越大)、适度减小(或增加)补贴金额,越有利于提升战略性新兴产业创新主体接受补贴的积极性;(3)战略性新兴产业创新主体的自有资金R对其积极性影响不大,而补贴资金利率a越稳定越有利于提高其积极性。基于上述结论,本文最后构建了战略性新兴产业金融支持两阶段ESS演进实现框架,并探究其“累积式”、“悖论式”、“累积—悖论式”递进功能路径,为政府制定提升创新主体培育金融支持效率的相关政策提供了理论支持。     

融合两阶段过程模型和改进Bass模型的网络社交平台上产品信息扩散研究

提出并验证了融合两阶段过程模型和改进Bass模型的网络社交平台上产品信息扩散模型。考虑用户转发动机构建产品信息扩散两阶段过程模型;考虑用户兴趣衰减效应改进Bass模型;融合这两个模型,考虑产品信息发布者明星效应、产品信息质量对产品信息扩散的影响,提出了产品信息扩散模型。以2019年11~12月新浪电影发布的电影预告片转发数据验证了所提模型,并与Bass模型进行了比较。结果表明,用户转发动机和用户兴趣衰减效应对产品信息扩散均有显著影响,所提模型的预测精度和拟合效果均优于Bass模型。所提模型可用于存在不同转发动机及具有衰减效应的其他信息转发量预测,尤其适合于在产品信息投放前期和早期对转发量的预测,是对信息扩散模型的补充。     

多元t分布下相依回归模型参数的两步估计

本文把文献中关于正态分布下相依回归模型参数Zellner估计的有限样本均方误差结果和效率结果以及两步协方差改进估计的一般均方误差结果推广到多元t分布情况,在该分布下两种估计的统计优效性质均不变.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

二阶段加法DEA模型的生产可能集与生产前沿面

针对二阶段加法DEA模型的中间要素的特殊性,构造生产可能集及其公理体系,由此定义生产前沿面,并建立DEA有效和生产前沿面之间的等价关系.通过构造一个多目标规划模型,建立该问题的Pareto有效解与DEA有效之间的等价关系.     

小样本下两阶段MCMC参数估计方法——基于信用风险强度模型的研究

应用我国金融市场数据估计信用风险强度模型参数时,常遇到由小样本而导致的偏差问题,对此本文提出了两阶段MCMC参数估计方法:第一阶段用Lee和Mykland的跳辨识方法估计跳跃项参数;第二阶段用MC-MC方法估计扩散和漂移项参数。误差分析的结果表明两阶段MCMC方法小样本下信用风险模型参数估计的效果要明显好于单纯的MCMC方法。作为应用,采用我国第一支个人住房抵押贷款支持证券"建元2005-1"的违约和提前还款数据,估计了信用风险强度模型的参数。     

考虑消费动机和动态竞争的电影日需求预测模型

提出并验证考虑消费动机和动态竞争的电影日需求预测模型。考虑非粉丝及粉丝型的消费动机,构建电影消费两阶段过程模型;融合该模型和Bass模型,考虑竞争导致市场潜量的动态性,考虑映前被关注度、口碑、节假日对票房的影响,提出电影日需求预测模型。利用2016~2017年上映的电影数据验证该模型,并与Bass模型对比分析。结果显示,该模型预测效果优于Bass模型。因考虑竞争导致的动态市场潜量,考虑粉丝型消费者由续集效应及改编效应导致的动态市场潜量提升,该模型能显著提高预测准确度。利用映前被关注度和电影口碑数据,该模型能实现映前及上映早期的预测。该模型可推广至存在消费动机不同、市场动态竞争的其它短生命周期体验品的需求预测,是对Bass模型的改进。