Nash均衡、变分不等式和广义均衡问题的关系

主要讨论了Nash均衡问题(NE)与变分不等式(VI)和广义均衡问题(GEP)的关系.给出它们之间解的等价关系,以及与之相应的映射之间单调性的关系.研究结果为进一步研究Nash均衡、广义均衡问题理论及其算法提供了理论依据.     

O-D需求估计的双层规划模型及基于灵敏度分析的求解算法

本文在考虑三种交通模式 (一般机动车,公交车,自行车)的基础上,建立了一般拥挤网络多模式OD需求估计问题的双层规划模型,给出了一个基于灵敏度分析的启发式求解算法,并进行了数值试验。试验结果表明,本文所给的模型和算法不仅能较好地给出OD需求的估计值,而且同时还给出了各模式路段流量的估计值。     

基于出行时间可靠性的交通配流问题

提出一类由需求随机性所导致的基于出行时间可靠性的交通配流问题.由于每一天交通需求的随机变化,出行者的出行时间不是确定的,而是随机变量.假设出行者在过去经验的基础上能够得知出行时间的随机分布,提出一类新准则去刻画出行者在出行时间不确定情况下的路径选择行为.这种准则可以表示为一种以路径流量为变量的变分不等式模型.对于这类新的模型,给出了解的存在性证明,并且引入一个启发式的算法去求解该问题.数值算例展示了模型在应用上的特性和算法的有效性.     

多维动态用户最优出行选择的变分不等式模型

针对出行行为的出行模式,出发时间/路径选择三个方面,建立了基于路段的理想动态用户最优的变分不等式模型,该模型将用户的出行方案制定和实施作为一个整体进行考虑,表明了在满足动态用户最优选择条件下,交通流在出行模式、出发时间和出行路径上取得一致的动态均衡性,通过必要性和充分性的论证,得到了变分不等式模型和动态用户最优出行模式/出发时间/路径选择均衡条件的等价性,对模型解的存在惟一性成立需要满足的条件作了讨论,提出了求解的嵌套对角化算法,在此基础上,使用一个简单算例对模型进行了验证.     

电子商务环境下两阶段供应链网络均衡模型

研究了在电子商务环境下产品存在现货市场时,由供应商和制造商组成的两层供应链网络在两阶段交易情况下的均衡问题.假定制造商的需求具有不确定性,制造商和供应商有两次行动的机会,在初始时刻决定合同交易量,在需求到来时决定现货市场交易量.利用变分不等式方法建立了供应商和制造商的决策模型,考虑了同质的供应商/制造商之间存在竞争并且存在交易成本的情况,讨论了模型解的性质,给出了模型求解算法.     

考虑服务流的产品服务供应链网络均衡模型

产品服务供应链在向客户制造高质量产品的同时,也提供了产品全生命周期的专业服务,服务的嵌入增加了供应链协调的复杂性。考虑产品服务的双重需求,在分析各主体的运作行为的基础上,构建了包括多个制造商和多个销售商的多主体供应链网络;运用变分不等式刻画了制造商层、销售服务集成商层和需求市场的最优运作行为及其达成均衡的条件;最后,通过修正投影算法对数值算例进行了仿真。研究结果表明：产品服务供应链网络中的产品与服务均衡流相互影响,其中,服务水平直接影响到了产品需求;降低产品的售价将有利于服务价格和效益的提升。研究结论进一步印证了在产品服务供应链网络中承载于产品的服务将逐渐成为价值创造的主体。     

ATIS环境下交通配流的动态演化模型

考虑交通网络中实现用户均衡态的过程,引入决策出行费用的概念,提出一个 ATIS 环境下的交通配流动态演化模型,模型中的 OD 需求是可变内生的.利用稳定性定理分析了该动态系统的稳定性,说明在一定条件下,系统的用户均衡态是稳定的.采用改进的欧拉法完成了模型的数值试验,结果表明该动态系统确实可以达到用户均衡态,同时也发现,某些模型参数的变化可能导致路径流量和 OD 费用演化轨迹的无规则摆动.     

考虑交易安全风险控制投入的在线旅游供应链网络均衡模型

基于包括供应商、平台和消费市场的三层供应链网络结构,利用变分不等式刻画均衡态时在线旅游供应链网络各成员的最优经济行为,以及平台交易安全风险控制投入对供应链平台企业、供应链整体的风险水平和期望收益的影响。研究发现,在平台企业风险控制投入相同情况下,平台和消费市场的产品交易数量和价格大致相同,验证了模型的合理性和有效性。其次,随着交易安全风险控制投入的增加,平台自身交易安全风险下降,供应链网络整体的交易安全水平和交易数量上升,但平台自身的期望收益下降。最后,随着更多的平台加入,平台的期望收益下降,市场需求价格下降,消费者获利。但部分平台企业的搭便车行为,会导致供应链整体的交易安全风险水平上升。     

基于超网络的生态工业链动态均衡研究

通过分析生态工业链的结构,构建了将供应型企业、生产型企业、消费型企业及回收型企业耦合为一体的超网络模型。进而剖析了模型的影响因素,并通过量化这些因素和提出基本假设,运用变分不等式刻画了超网络模型中各层企业的行为和目标,得到了整个模型的动态均衡条件,给出了理论证明。在此基础上,结合动态均衡条件和KKT条件转换式,以贵港生态工业园的复合肥生态工业链为例,运用Lingo9.0和Matlab7.0进行模拟计算。结果表明,各层企业间契约履行率和操作技术参数与各层企业及整个生态工业链的利润率基本呈正比,而讨价还价能力值和交易损耗率与各层企业及整个生态工业链的利润率基本呈反比,计算结果与实际相符,验证了模型的有效性。     

考虑库存能力约束的多期闭环供应链网络均衡北大核心CSCDCSSCI

在多个规划期背景下,本文研究了由多个制造商、多个零售商和多个消费市场组成的闭环供应链网络的均衡问题,其中制造商存在库存能力约束并进行制造和再制造活动。特别地,对于再制造过程,考虑了产品寿命次数。利用规划期之间的库存转移和回收废旧品的再制造刻画规划期之间的联系,运用变分不等式、互补理论和对偶理论建立了各层成员和整个供应链网络的均衡条件。最后,结合固定步长的修正投影收缩算法对模型进行求解,并通过算例对有关参数进行了灵敏度分析。算例分析的结果表明:无论制造商是否具有库存能力约束,制造商和零售商的利润随着两次再制造转化率的变化均大致呈现线性关系;制造商的库存能力约束会改变制造商和零售商的利润,并使总利润有所增加但不会实现帕累托改进。本文的研究有望为闭环供应链及其网络均衡方面的研究提供一定的借鉴。     

Sensitivity Analysis for Computer Model Projections of Hurricane Losses

Projecting losses associated with hurricanes is a complex and difficult undertaking that is fraught with uncertainties. Hurricane Charley, which struck southwest Florida on August 13, 2004, illustrates the uncertainty of forecasting damages from these storms. Due to shifts in the track and the rapid intensification of the storm, real-time estimates grew from 2 billion dollars to 3 billion dollars in losses late on the 12th to a peak of 50 billion dollars for a brief time as the storm appeared to be headed for the Tampa Bay area. The storm struck the resort areas of Charlotte Harbor and moved across the densely populated central part of the state, with early poststorm estimates in the 28 dollars to 31 billion dollars range, and final estimates converging at 15 billion dollars as the actual intensity at landfall became apparent. The Florida Commission on Hurricane Loss Projection Methodology (FCHLPM) has a great appreciation for the role of computer models in projecting losses from hurricanes. The FCHLPM contracts with a professional team to perform onsite (confidential) audits of computer models developed by several different companies in the United States that seek to have their models approved for use in insurance rate filings in Florida. The team's members represent the fields of actuarial science, computer science, meteorology, statistics, and wind and structural engineering. An important part of the auditing process requires uncertainty and sensitivity analyses to be performed with the applicant's proprietary model. To influence future such analyses, an uncertainty and sensitivity analysis has been completed for loss projections arising from use of a sophisticated computer model based on the Holland wind field. Sensitivity analyses presented in this article utilize standardized regression coefficients to quantify the contribution of the computer input variables to the magnitude of the wind speed.     

多供应商条件下制造商最优订货批量分配模型

研究了多供应商条件下制造商的订货批量及其在不同供应商之间的分配问题,建立了相应的非线性规划模型,给出了模型的K-T条件及订货批量的一般表达式;提出了基于最低总成本的供应商的粗选方法及确定订货批量及其分配的算法步骤,并用实例加以说明.     

新产品开发的最优战略均衡模型

在分析了产品开发时间、产品开发成本、单位产品成本和产品质量这4个战略因素之间权衡关糸的基础上,运用最优控制理论,建立了关于成本、质量、时间的最优战略均新模型,通过对该最优控制问题的求解,揭示了4个战略因素之间的最优均衡关系     

Sensitivity Analysis for Importance Assessment

We review briefly some examples that would support an extended role for quantitative sensitivity analysis in the context of model-based analysis (Section 1). We then review what features a quantitative sensitivity analysis needs to have to play such a role (Section 2). The methods that meet these requirements are described in Section 3; an example is provided in Section 4. Some pointers to further research are set out in Section 5.     

评标专家均衡随机抽取模型

在分析原有评标专家抽取模型不足的基础上,本文提出了评标专家均衡随机抽取模型.这种新的抽取模型不仅可以保证抽取过程的随机性,还能改善一段时间内专家被抽取状况的均衡性.本文介绍了新模型的构建思路和算法步骤,并利用实际数据进行仿真实验,验证了新模型的优势.评标专家均衡随机抽取模型的提出对提高招投标工作的公平性和公正性具有重要的现实意义.     

Sensitivity Analysis of a Two-Dimensional Probabilistic Risk Assessment Model Using Analysis of Variance

This article demonstrates application of sensitivity analysis to risk assessment models with two-dimensional probabilistic frameworks that distinguish between variability and uncertainty. A microbial food safety process risk (MFSPR) model is used as a test bed. The process of identifying key controllable inputs and key sources of uncertainty using sensitivity analysis is challenged by typical characteristics of MFSPR models such as nonlinearity, thresholds, interactions, and categorical inputs. Among many available sensitivity analysis methods, analysis of variance (ANOVA) is evaluated in comparison to commonly used methods based on correlation coefficients. In a two-dimensional risk model, the identification of key controllable inputs that can be prioritized with respect to risk management is confounded by uncertainty. However, as shown here, ANOVA provided robust insights regarding controllable inputs most likely to lead to effective risk reduction despite uncertainty. ANOVA appropriately selected the top six important inputs, while correlation-based methods provided misleading insights. Bootstrap simulation is used to quantify uncertainty in ranks of inputs due to sampling error. For the selected sample size, differences in F values of 60% or more were associated with clear differences in rank order between inputs. Sensitivity analysis results identified inputs related to the storage of ground beef servings at home as the most important. Risk management recommendations are suggested in the form of a consumer advisory for better handling and storage practices.     

Sensitivity Analysis of Model Output with Input Constraints: A Generalized Rationale for Local Methods

In this work, we introduce a generalized rationale for local sensitivity analysis (SA) methods that allows to solve the problems connected with input constraints. Several models in use in the risk analysis field are characterized by the presence of deterministic relationships among the input parameters. However, SA issues related to the presence of constraints have been mainly dealt with in a heuristic fashion. We start with a systematic analysis of the effects of constraints. The findings can be summarized in the following three effects. (i) Constraints make it impossible to vary one parameter while keeping all others fixed. (ii) The model output becomes insensitive to a parameter if a constraint is solved for that parameter. (iii) Sensitivity analysis results depend on which parameter is selected as dependent. The explanation of these effects is found by proposing a result that leads to a natural extension of the local SA rationale introduced in Helton (1993) . We then extend the definitions of the Birnbaum, criticality, and the differential importance measures to the constrained case. In addition, a procedure is introduced that allows to obtain constrained sensitivity results at the same cost as in the absence of constraints. The application to a nonbinary event tree concludes the article, providing a numerical illustration of the above findings.     

Sensitivity Analysis for Dependent Variables*

Decision analysts use sensitivity analysis to identify influential variables, to determine which input variables to model stochastically, and to characterize scenarios that could affect a change in the rank ordering of the alternatives. A frequently recommended sensitivity analysis technique is “one‐way” sensitivity analysis, which determines a variable's influence by the degree to which the objective function changes as that variable is varied while all other variables are held fixed. Disadvantages of one‐way analysis are that it measures the influence of only one variable at a time and it assumes independence among the input variables. Clearly, however, there are situations when dependencies exist among the input variables that could possibly affect the sensitivity analysis results. This research develops a strategy that incorporates dependence relations among the input variables into the sensitivity analysis using rank correlations. Only decision problems with a finite number of alternatives and continuous state variables are considered.     

多模式交通条件下合理制定旅客票价的优化模型及算法

在本文中,充分考虑了旅客和交通管理部门两方面的利益,提出了一个双层规划模型来描述城市间多种交通方式竞争条件下合理制定旅客票价问题。在此模型中,既保障了旅客使自己的广义出行费用最小,又使得交通管理部门在客运市场的竞争中取得最大的经济效益。然后给出了求解该模型的基于灵敏度分析的启发式算法 (SAB)。最后用一个实际算例说明了该模型及算法的应用。