随机需求下直销多商品流供应链网络均衡模型

建立了随机需求下直销多商品流供应链网络均衡模型,导出了供应链网络达到均衡的条件,它等价于一个有限维变分不等式.通过构建修改拟牛顿法,获得了随机需求下直销多商品流供应链网络均衡模型的解(变分不等式的解),并给出了1个算例,验证了模型的正确性和算法的可行性.     

多目标供应链网络平衡模型

针对生产商、零售商和消费群三层决策者问题建立了一个多目标供应链网络均衡模型.给出此模型的均衡条件,并讨论了(弱)均衡解和标量化解之间的关系.最后,给出具体的例子说明此模型.     

基于微分变分不等式的多商品流网络动态模型

针对由多个制造商和多个零售商构成并且具有多商品流的供应链网络,建立了制造商、零售商之间从事微分Nash博弈的供应链网络动态模型.首先,在介绍微分变分不等式定义的基础上,利用微分变分不等式的方法建立了制造商、零售商以及供应链网络的均衡条件.然后,在正则条件下分析了供应链网络动态模型解的存在性条件.最后,利用数值算例验证了模型的合理性.     

带多阈值的两类索赔风险模型中的期望折现罚函数

本文考虑了带多阈值两类索赔到达风险模型,在假定两类索赔到达过程均为phase-type 分布时,建立了期望折现罚函数所满足的积分-微分方程.并通过拉普拉斯变换讨论了方程的解.     

一个局部带优先权的最大多物资网络流问题

给出一个局部带优先权的最大多物资网络流问题(MMFP-LPRI),证明它的解存在,并给出其η-松弛解的定义.通过做辅助网络,并运用程丛电等根据Korte和Vygen于2000年在Young,Garg和K(o|¨)nemann等工作的基础上给出的求最大多种物资网络流问题的ε-近似解的多项式方案设计的一个算法作为子程序进行二分收索建立了一个求所给问题的η-松弛解的拟多项式算法.最后,进行算法分析,证明了所设计的算法的输出结果确实是MMFP-LPRT的一个η-松弛解.     

片面追求"一题多解"的背后

一题多解,是指对同一个题目从不同角度来审视,探求出不同的解决方案,它对开阔学生的视野,提高学生分析问题解决问题的能力,培养学生的创新意识和创新精神无疑是十分必要的,尤其是高三复习课不像讲授新课那样受教材内容的限制,在内容和方法上给师生提供了更为广阔的自由空间,因此一题多解在高三复习课的教学中倍受师生们亲睐,然而教师在教学过程中往往只注重了方法多样性的展示和挖掘,而忽视了一题多解的教学价值,这种刻意追求一题多解的背后隐藏着令人担忧的浮躁,更存在着对一题多解教学功能理解上的偏离,本文从两节高三教学案例出发,谈一谈本人在一题多解教学方面的几点思考.……     

具有全局性公平满意度的最大多物资网络流问题

我们研究-个具有全局性公平满意度的最大多物资网络流问题(MMFP-GFMR).该项工作不仅丰富了最大多物资网络流问题的内容,而且可用于研究某些实际优化决策问题,例如运输过程中的一些资源分配问题.文中主要内容如下:(A)定义问题MMFP-GFMR并证明其解的存在性.(B)设计-个求解MMFP-GFMR的拟多项式逼近算法.(C)研究算法的复杂性与逼近程度.(D)最后通过模拟计算验证了我们的工作.     

基于再制造的多周期闭环供应链网络均衡模型

针对单周期模型在刻画废旧产品回收和再制造过程中的局限性,以多周期的再制造闭环供应链网络为研究对象,利用均衡理论和变分不等式的方法构建了基于再制造的多周期闭环供应链网络均衡模型,得到了制造商和零售商及整个供应链网络的均衡条件及其经济解释,并分析了均衡解的唯一性条件。针对所建立的模型,利用Euler算法进行了算例分析,说明了潜在市场份额对供应链成员决策的影响。     

多物种无穷维反应扩散过程的存在性

本文利用鞅方法研究多物种无穷维反应扩散过程的存在性，证明了一簇鞅解就是一个Ｆｅｌｌｅｒ过程．     

对一题多解的辩证理解

1 一题多解的优点“一题多解”之所以深受数学教师的重视,就是因为在解题过程中能够引导学生多层次、多角度的思考问题,全面地应用知识来分析问题与解决问题.例如人教版第二册(下B)的习题9.8的第4题:如图,已知正方体ABCD-A′B′ C′D′的棱长为1,求直线DA′与AC的距离.教师可以引导学生从不同的入口,挖掘不同的解法.解法1 ∵AC∥平面A′DC′,∴点A到平面A′DC′的距离h就等于异面直线AC与DA′的距离,从而转化为点面距.     

多服务台服务同一顾客的M/M/m+k/N可修排队系统

研究带有备用服务台的可修排队系统,假设多个服务台可同时服务同一顾客,利用马尔可夫过程理论建立了系统稳态方程组,然后利用分块矩阵的解法求出系统稳态概率的矩阵解,在此基础上建立系统的费用模型,并利用Matlab软件进行数值实例分析.     

On Multiple Criteria Decision Support for Suppliers on the Competitive Electric Power Market

As an active participant of a competitive energy market, the generator (the energy supplier) challenges new management decisions being exposed to the financial risk environment. There is a strong need for the decision support models and tools for energy market participants. This paper shows that the stochastic short-term planning model can be effectively used as a key analytical tool within the decision support process for relatively small energy suppliers (price-takers). A self-scheduling method for the thermal units on the energy market is addressed. A schedule acquired for given preferences can be used as a desired pattern for bidding process. The uncertainty of the market prices is modeled by a set of possible scenarios with assigned probabilities. Several risk criteria are introduced leading to a multiple criteria optimization problem. The risk criteria are well appealing and easily computable (by means of linear programming) but they meet the formal risk aversion standards. The aspiration/reservation based interactive analysis applied to the multiple criteria problem allows us to find an efficient solution (generation scheme) well adjusted to the generator preferences (risk attitude).     

IMOST: Interactive Multiple Objective System Technique

An interactive multiple objective system technique (IMOST) is investigated to improve the flexibility and robustness of multiple objective decision making (MODM) methodologies. The interactive concept provides a learning process about the system, whereby the decision maker can learn to recognize good solutions, the relative importance of factors in the system, and then design a high-productivity and zero-buffer system instead of optimizing a given system. This interactive technique provides integration-oriented, adaptation and dynamic learning features by considering all possibilities of a specific domain of MODM problems which are integrated in logical order. It encompasses the decision-making processes of formulating problems, constructing a model, solving the model, testing/examining its solution, and improving/reshaping the model and its solution in a specific problem domain. Although IMOST deals with multiple objective programming problems, it also provides some valuable orientation of integrated system methodologies.     

延误休假且修理延迟的可修系统的更换策略

研究了修理工多重延误休假且修理延迟的可修系统,假设系统故障后均不能"修复如新",系统在准备休假期间故障的概率为q,系统延迟修理的概率为1-P,以系统故障次数为更换策略,运用更新过程和几何过程理论,得出系统长期运行单位时间内平均停机时间的表达式,并通过数值例子验证了存在最优策略,使得平均停机时间最短.     

Mean-Variance Hedging Under Multiple Defaults Risk

We solve a mean-variance hedging problem in an incomplete market where multiple defaults can occur. For this purpose, we use a default-density modeling approach. The global market information is formulated as a progressive enlargement of a default-free Brownian filtration, and the dependence of the default times is modelled using a conditional density hypothesis. We prove the quadratic form of each value process between consecutive default times and recursively solve systems of coupled quadratic backward stochastic differential equations (BSDEs). We demonstrate the existence of these solutions using BSDE techniques. Then, using a verification theorem, we prove that the solutions of each subcontrol problem are related to the solution of our global mean-variance hedging problem. As a byproduct, we obtain an explicit formula for the optimal trading strategy. Finally, we illustrate our results for certain specific cases and for a multiple defaults case in particular.     

多重极限点解分支的数值逼近

对N阶分歧问题多重极限点解分支的数值逼近问题进行了研究,给出了解分支的结构,构造了求解分支的扩充系统,证明了扩充系统解的存在性,讨论了解分支的数目,并给出了解的误差估计.     

On a Class of Multiple Integrals

A multiple integral encountered in the theory of Gauss--Markov processes is expressed in analytical form.     

Multiple voting location problems

The facility voting location problems arise from the application of criteria derived from the voting processes concerning the location of facilities. The multiple location problems are those location problems in which the alternative solutions are sets of points. This paper extends previous results and notions on single voting location problems to the location of a set of facility points. The application of linear programming techniques to solve multiple facility voting location problems is analyzed. We propose an algorithm to solve Simpson multiple location problems from which the solution procedures for other problems are derived.     

Integer Programming Duality in Multiple Objective Programming

The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.     

多险种场合的破产概率

本文将经典的破产模型由单险种推广到了多险种，分别讨论了各险种的索赔额均为复合Poisson过程和广义复合Poisson过程的情形，计算了两种情形下的破产概率．