动态供应链网络均衡模型构建与分析

基于单一商品流,考虑了时间变量和库存问题,建立了三层动态供应链网络结构模型.对制造商、零售商和需求市场的多期独立决策行为及其相互作用进行了分析,应用变分不等式构建了各层均衡模型和整个供应链网络均衡模型.最后与相关文献的模型进行了比较.     

随机需求下供应链协调优化模型

考虑了由一个供应商和多个零售商构成的两级供应链系统,在随机需求下,通过共同补给期进行协调的问题.作为Stackelberg博弈的领导者,供应商给出共同补给期策略,零售商作为跟随者以最优库存策略响应,建立了确定共同补给期和相应价格折扣模型.通过数值实例对该模型进行分析,得出Stackelberg均衡解,达到Pareto最优.     

具过度自信零售商的双渠道供应链网络均衡研究

将零售商的过度自信行为纳入双渠道供应链网络均衡模型,研究了由供应商、分销商以及具过度自信行为的零售商构成双渠道供应链网络均衡问题。借助变分不等式以及互补理论,刻画了制造商、分销商以及过度自信零售商的最优行为,并构建了双渠道供应链网络均衡条件。解析分析了市场出现有利信息和不利信息两种情形下,零售商的过度自信行为对其订购决策的影响。最后,数值算例验证上述结论,并借助数值结果分析了零售商的过度自信行为对双渠道网络均衡的影响。     

供应链协调中供应商的价格歧视策略

分析了包含一个供应商和两个不同零售商的供应链网络的协调问题.将这一问题构建为一个两层次的博弈模型:零售商之间的非合作博弈以及供应商与零售商之间的Stackelberg博弈.博弈的均衡表明,通过简单的价格歧视,供应商就能够实现整个供应链网络的协调,而且价格歧视的水平与零售商之间的市场容量差异、产品需求的价格敏感系数以及产品的边际生产成本有关.在合理的参数范围内,市场容量更大的零售商所收取的零售价格较低,从供应商那里取货的成本也较低.这样的结论是比较符合现实情形的,这也就说明该模型为现实世界中的价格差异提供了另一种解释.此外,还分析了当供应商无法实施价格歧视时,由此导致的供应链的损失.     

由零售商负责回收的多期闭环供应链网络均衡

本文研究了零售商回收模式下多期闭环供应链网络均衡问题。制造商通过零售渠道将产品销售给消费者,以满足消费市场需求,同时消费产生的废旧品由零售商回收返回制造商处进行再制造,通过产品库存和回收废旧品连接相邻规划期。运用变分不等式理论和互补理论,分别刻画了制造市场、零售市场和消费市场的均衡,接着构建了多期闭环供应链网络均衡模型。利用变分不等式的投影收缩算法,对模型进行求解。算例着重分析了废旧品利用率对网络均衡状态和供应链成员利润的影响。结果表明:当制造商的废旧品利用率逐渐增加时,回收量逐渐增加,制造商的利润先减后增,零售商利润一直增加,而供应链总利润一直增加,供应链网络中的最优决策变量主要受到回收量约束的影响。     

下游风险约束下的供应链博弈与合作研究

考虑了由风险中立的单供应商和风险规避的单零售商组成的二级供应链,分别建立了分散决策下和回购契约下供应商占主导地位的Stackelberg博弈模型,求得了均衡解.并研究了零售商下游风险参数值对博弈决策的影响,研究发现当零售商期望目标利润较大时,风险约束下的回购契约机制将无效,且期望目标利润越大则供应商和零售商利润越小,最后用算例对这一结论进行了说明.     

随机需求下供应商管理库存的供应链模型

以一个供应商和一个零售商的两阶段供应链为背景,利用报童模型给出了供应商管理库存(VMI)的供应链模型,在需求服从均匀分布的条件下得出解析解,并与传统的零售商管理库存(RMI)系统作了比较,分析了这两种情况下批发价和订货量的变化.数值结果表明VMI导致了批发价的缩减,但提高了订货量,VMI减轻了双重边际效应,系统利润多于传统的RMI系统.     

双渠道双目标的多期供应链网络均衡问题研究

以变分不等式为工具建立双渠道双目标的多期供应链网络均衡模型.在传统实体交易和电子网上交易的双渠道环境下,考虑时间因素与库存变量的影响,提出由制造商、零售商和需求市场组成的三层多期供应链网络均衡问题,其中制造商和零售商均追求经济利润最大化与风险最小化的双重目标.分别对各系统成员的独立决策行为及其相互作用进行分析,得到各层决策成员的均衡条件并给出相应经济解释,推导与双渠道双目标的多期供应链网络均衡问题等价的有限维变分不等式模型.在证明其解在一定的假设条件下存在的基础上,构造数值算例以验证模型的正确性与合理性.     

具有服务水平的差异产品供应链网络均衡模型研究

顾客服务水平已成为当今企业获取较高市场占有率的重要手段。本文考虑了由多个供应商和多个零售商组成的供应链网络模型,通过制造商和零售商提供的服务水平,零售商的订货满足率以及零售价格等因素较为贴切的刻画消费者的选择偏好,利用变分不等式方法分析了制造商、零售商,需求市场以及整个供应链网络均衡条件,并给出了经济解释。最后,通过算例验证了模型的合理性。     

考虑RFID应用的资金约束供应链订购决策研究

RFID技术的应用在有效降低商品库存损耗率的同时,也增加了供应链企业的运营成本,尤其是具有资金压力的供应链中小企业。在零售商具有资金约束的二级供应链下分析RFID技术的应用对资金约束供应链绩效的影响,通过构建贸易信贷下基于批发价合同的Stackelberg博弈模型,对比采用RFID前后资金约束供应链成员的均衡决策及期望收益,探讨了该供应链采用RFID的必要条件。结果显示当RFID标签成本低于某个阈值,或RFID库存损耗恢复率高于某个阈值时,供应链成员会选择采用RFID。此外,当RFID单位标签成本或零售商标签成本分摊系数较低,或RFID库存损耗恢复率较高时,制造商会提供比不采用RFID时更高的批发价;在采用RFID的条件下,零售商订购数量低于不采用RFID时的数量。通过设计收益分享契约实现了采用RFID时资金约束供应链的协调。     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].