顾客需求量不确定时生产商的在线数量折扣策略

针对顾客需求量不确定时,生产商为节省库存成本而采用数量折扣策略鼓励零售商提高单次订货量的决策问题,从在线问题与竞争分析的角度出发,设计了平衡策略,并证明了该策略是最优在线数量折扣策略.然后给出了算例,算例表明了无论顾客的需求量如何变化,平衡策略确定出的数量折扣,总能使生产商的成本接近于顾客需求量确定时的最小成本;同时与传统的数量折扣模型进行了对比,说明了在传统的数量折扣模型中做出的决策,往往不是我们所提出的新的评价准则(竞争比)下的最优策略.     

社会责任情境资金约束生产商的供应链融资

考虑社会责任情境下,资金短缺的生产商和零售商之间进行Stackelberg博弈,建立无资金约束、提前支付和银行贷款三种供应链融资模型,分析社会责任因子和初始资金如何影响供应链成员的最优决策和利润,以及生产商选择何种融资方式.结果表明:一旦生产商有资金约束时,其社会责任水平会降低.当供应链外部融资(银行)利率大于提前支付折扣时,生产商选择银行贷款融资策略,社会责任因子超过临界值后,生产商选择提前支付融资策略;当供应链外部融资(银行)利率小于提前支付折扣时,生产商先选择提前支付融资策略,社会责任因子超过临界值后,生产商选择银行贷款融资策略.此研究可为履行社会责任的企业提供融资参考及借鉴意义.     

数量折扣契约下制造商与零售商库存合作联盟的稳定性

针对实际中存在的不同形式合作联盟,研究了零售商库存合作联盟,以及制造商与零售商库存合作联盟所形成混合合作联盟的稳定性。在随机需求情况下,制造商通过自身中心仓库向多个零售商提供数量折扣契约,首先证明了两个合作联盟的最优运作决策都存在且唯一,并给出了制造商向零售商库存合作联盟提供数量折扣契约的形式,然后分析了两种合作联盟的稳定性,并得出混合合作联盟的总期望利润要高于零售商库存合作联盟的结论。     

广告分担、价格折扣与供应链的纵向合作广告

研究了生产商和零售商的纵向合作广告问题。分别在广告分担和价格折扣策略下，探讨了双方的均衡结果和利润。当生产商的边际利润较小时，生产商的最优决策是不采取任何一种策略。当生产商的边际利润达到一定范围时，广告分担策略是双方共同的最优选择。而无论在什么样的条件内，价格折扣策略都不会使双方同时满意。为了增加双方的收益，供应链成员应该在广告上集成决策。最后给出了系统集成的可行最优解的范围和Nash讨价还价解。     

不同情形下供应链优化决策模型的比较分析

本文提出三种不同情形（制造商与零售商追求各自利润最大化，并且没有价格折扣策略；制造商与零售商共同追求总利润最大化，不实施价格折扣策略；制造商与零售商共同追求总利润最大化，并实施价格折扣策略）下供应链价格和库存补充策略的优化决策模型，并通过具体数例进行比较分析，结果表明，供应链合作并实施价格折扣策略时的供应链总利润最高，而供应链双方利润分配系数的变化对基于供应链总利润最大化的供应链优化决策没有影响．     

模糊随机需求报童问题的Stackelberg-Nash均衡策略

针对模糊随机需求下的分布控制型报童问题,建立了无数量折扣和有数量折扣情况下的利润最大化两层规划模型,并结合模糊随机模拟技术和遗传算法设计了模型求解的混合智能算法.解决了上层制造商制定包括折扣区间和折扣价格的最优数量折扣策略,以及下层多零售商确定各自的最优订货量的Stackelberg-Nash均衡策略问题.     

模糊随机需求下多产品报童问题的均衡策略

针对模糊随机需求下单制造商多零售商的分布控制型多产品报童问题, 建立了含资金约束的期望利润最大化两层规划模型.结合模糊随机模拟技术与遗传算法, 设计了求解模型的混合智能算法.该算法不仅可获得上层制造商的最优折扣批发价及下层零售商的最优订购量,亦可求得该折扣形式的起始折扣点(折扣区间).算例分析表明,当制造商采取最优数量折扣策略时:1)促使零售商订货量增加至资金约束上限;2)部分产品订货量可达模糊随机市场需求的最大可能值:3)零售商和制造商的利润均增加.     

基于多个供应商和多个零售商组成的经济批量问题研究

本文考虑了由两个供应商和两个零售商组成的经济批量问题,当在每个供应商处的进货费用函数为数量折扣费用函数时,我们分析了该问题最优解的性质,并设计了一个计算复杂性为的动态规划算法,进而说明该问题是多项式可解的.     

时间约束下鲜活农产品供应链应急协调数量折扣契约研究

本文的目的就是针对一个由生产商和一个零售商构成的鲜活农产品供应链,在考虑损耗和新鲜度的影响下,研究数量折扣契约如何协调供应链应对突发事件。 首先,给出了正常情况下供应链协调模型;然后,在突发事件引起市场需求、零售商订货成本和产品运输时间同时扰动情况下,讨论了突发事件对集权、分权供应链的影响。 研究表明,集权供应链具有一定的鲁棒性,当突发事件造成市场需求、零售商订货成本和产品运输时间在一定范围内同时发生扰动时,其生产计划不需要调整,只需通过调整产品价格即可使集权供应链达到协调;对于分权供应链,根据三因素同时扰动的不同程度,通过调整数量折扣契约参数,可以实现对供应链的协调。 最后给出数值算例验证了相关结论。     

可替代产品环境下基于数量折扣的供应链协调研究

研究一个供应商和一个零售商基于数量折扣的两种可替代产品供应链协调问题,建立以供应商为主导的可替代产品数量折扣Stackelberg博弈模型,并将数量折扣模型与一体化和非一体化情形作对比,分析产品折扣率和替代率的变化对供应链的影响.研究结果表明虽然整个供应链利润随折扣率和产品可替代程度的增加而增加,但只是增加了处于主导地位供应商的利润,降低了零售商的利润;在实际运营中,供应商需要考虑销售返利或其它转移支付手段将利润一部分转移给零售商来实现基于数量折扣的供应链协调.     

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.     

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 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].