销售问题的分解算法

销售问题:一家商店经销某种商品,有一个容量为w件的仓库,每月初订货一次,订货提前时间为0,第i月的订货单价为a_i,售货单价为b_i,a_i>0,b_i>0,i=1,…,n;第1月订货前已有存货c件;0≤c≤w,w>0;第n月末不须存货,试制订出一个从第1月到第n月的购销方案,使总收益最大。为讨论方便,如果某个月售货就假定把当月的总售货量在月底一次售完。     

一道中考销售类试题蕴含模型思想的探究

模型思想是中学数学学习中涉及的重要思想.本文通过对一道中考销售类试题进行分析,解析其中蕴含的模型思想及建模思路,并给出教学中培养学生模型思想的三点建议.     

排队论在销售管理中的应用

销售性企业如何才能降低销售时的综合成本是一个值得研究的问题.以排队论为基础对这一问题展开讨论,分析了顾客到达企业时的排队方式,得出了单队多服务通道要比多队多服务通道排队方式要优;分析了系统的服务规则及评价指标,并建立了一个输入率可变、服务率可变且先到先服务的、有不耐烦顾客的销售模型,以及一个输入率可变、服务率可变且有非强占优先权的销售模型,分别得出了系统的平均服务率及顾客在系统中的平均等待时间,从而建立了企业销售时的综合成本函数,并结合实例给出了求综合成本函数最小值的方法.     

生产与销售的库存模型

本对工厂生产所需原材料的库存和生产的产品的库存问题进行了研究,给出了生产和销售速率一般意义下的库存模型和计算最佳生产周期的地,并对两种生产和销售速率的特殊情况,分析进行了讨论。     

带有二次订购和二次销售的报童问题

本文提出二次进货二次销售的报童模型 ,并分析了新模型与经典报童问题和带有反馈生产模型的最优订购量及收益关系 ,分析了模型的灵敏度 ,服务水平等 .     

奖惩机制下考虑销售努力的闭环供应链协调

以一个制造商和一个零售商组成的闭环供应链为研究对象,考虑在政府的奖惩机制下需求同时受销售价格和销售努力影响的供应链协调问题.首先,在集中决策下,研究了供应链系统的最优决策,并给出了均衡解存在的条件和奖惩力度所满足的范围;在分散决策下,重点分析了奖惩力度以及销售努力对供应链双方决策的影响.其次,使用特许经营契约能够使供应链达到协调.最后,给出了数值算例和仿真分析.     

基于遗传算法的汽车整车销售物流配送路径优化

为了优化汽车整车销售物流配送网络,提高配送服务质量,构建了以配送费用最小为目标的带时间窗的整车配送路径优化模型,采用改进遗传算法对模型进行求解,结合上汽通用五菱公司的配送实例,对其整车销售物流配送路径进行研究,并将改进遗传算法所确定的优化路径、节约里程法的优化路径、企业实际的配送路径进行比较,改进遗传算法确定的最优路径其配送费用比其它两种路径的配送费用降低了5.5%和8.9%,研究结果可以为企业确定经济、合理的配送路径提供参考.     

Hanoi塔问题的一个公式解

Hanoi塔问题自提出以来已有一百多年的历史.其间,这一问题吸引了许多的研究者.正如H.A.Simon所指出的,Hanoi塔问题对于认知科学就象大肠杆菌对现代基因学那样,是一个无价的研究标本.事实上,它已成为组合数学,人工智能,计算机科学以及规划等中的递归问题的典型例子,并由此产生了各种各样成熟的算法.回顾这些结果,我们提出一个基本问题能否对Hanoi塔问题给出一个公式解?本文就此给出了一个肯定的回答.在我们的研究中,图论将是一个有力的工具     

碳税政策下生产和销售的选址问题

本文考虑碳税政策下一个生产型企业生产和销售的选址问题。消费者分布在一条直线上,运输成本是线性的,企业除承担自身产品的运输费用外还承担消费者的运输成本。本文建立了利润最大化模型,分析了利润函数的性质,给出了求解方法。通过数值实验证明了求解方法的有效性,同时得出,即使消费者分布是中心对称的,最优的选址也不一定中心对称,这纠正了人们的错觉。增加碳税可使销售点靠近自己的消费者,增加企业的费用,但不一定起到减排的作用,只有通过灵活的碳税政策才有可能达到减排的目的。     

一种新的正则化方法求解热传导方程的侧边值问题

考虑了四分之一平面内的热传导方程的侧边值问题,这类问题是严重不适定的.采用传统拟逆方法得到该问题的一个近似解,但发现它并不是一个正则化解.有趣的是,对解的分母项加以修正便可以得到侧边值问题的一个正则化解,进而提出了一种新的正则化方法,并分别给出先验和后验两种正则化参数选取规则下的Hlder型误差估计.数值实验验证了所提方法的可行性和有效性.     

Analysis of nonlinear BVPs motivated by fluid film flow over a surface

We study a coupled nonlinear boundary value problem which has been shown to have applications to fluid flow and heat transfer in a fluid film over a stretching surface for set values of the model parameters (one of which determines the size of the problem domain). For arbitrary values of these parameters we are able to establish the existence and uniqueness of a class of monotone solutions. Perturbation solutions are then constructed and used to approximate certain invariants for the solutions. We then study a related boundary value problem formed by imposing an additional boundary condition on one of the governing equations (which results in an ill-posed problem), and we arrive at conditions allowing for solutions to this four-parameter problem to agree with the solutions to the three-parameter problem.     

Weak solutions for a class of generalized nonlinear parabolic equations related to image analysis

In this paper, we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a class of generalized nonlinear parabolic partial differential equations, which are related to the Malik-Perona model in image analysis.     

基于Riemann-Hilbert问题建模求解孤立子解

基于矩阵谱问题构造了一种实用的方法来对一类实轴上的可积方程的Riemann-Hilbert问题进行建模。当跳跃矩阵是单位矩阵时,孤立子解通过特殊约化的Riemann-Hilbert问题显性表示。作为一个范例,对于具有任意阶矩阵谱问题的多分量非线性薛定谔方程,给出了该方法的具体应用。     

Mixed boundary value problems with a shift for a pair of metaanalytic and analytic functions

In this article, we reconsider the mixed boundary value problem on the unit circle for a pair of metaanalytic and analytic functions as in Du and Wang (2008) [9]. By adopting appropriate transformations, we convert the problem into two independent boundary value problems for analytic functions. We then obtain expressions of solution and condition of solvability for the mixed boundary value problem. The forms of the solutions and the condition of solvability here are rather dissimilar to those in Du and Wang (2008) [9]. But the equivalence is established at the end of this article.     

A modified quasi-boundary value method for ill-posed problems

In this paper, we study a final value problem for first order abstract differential equation with positive self-adjoint unbounded operator coefficient. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions converge if and only if the original problem has a classical solution. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.     

三种不同需求分布条件下报童问题期望费用的计算

报童问题是运筹学中典型的随机性存贮模型.目前很多运筹学和管理科学教科书一般只给出报童问题最优订购量应该满足的条件,而没有给出具体的期望费用的表达式,这对于报童问题模型在实际中的应用造成不便.研究了三种不同需求分布条件下报童问题期望费用计算问题,所得出的关于期望费用计算公式具有简洁和便于实际应用的特点.     

Stability and Hopf bifurcations in a business cycle model with delay

In this paper, a business cycle model with discrete delay is considered. We first investigate the stability of the equilibrium and the existence of Hopf bifurcations, and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. This research has an important theoretical value as well as practical meaning.     

Fractional model and solution for the Black‐Scholes equation

This work presents a new model of the fractional Black‐Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation. Then the problem is solved by using the Fourier‐Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case.     

Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors

We consider a one-dimensional bipolar hydrodynamic model of semiconductors. Although some results exist for the bipolar case, almost their conditions (the boundary condition, the doping profile, etc.) are far from practical application. In the present paper, under a condition appropriate for engineering, we shall prove the existence and the uniqueness of classical solutions for the stationary problem. The most difficult point is to obtain the bounded estimate and the energy estimate.     

On a New Approach to Frequency Sounding of Layered Media

Frequency sounding of layered media is modeled by a hyperbolic problem. Within the framework of this model, we formulate an inverse problem. Applying the Laplace transform and introducing the impedance function, the latter is first reduced to the inverse boundary value problem for the Riccati equation and then to the Cauchy problem for a first-order quadratic equation. The advantage of such transformations is that the quadratic equation does not contain an unknown coefficient. For a specific class of data, it is shown that the Cauchy problem is uniquely solvable. Based on the asymptotic behavior of solutions to both the Riccati and quadratic equations, a stable reconstruction algorithm is constructed. Its feasibility is demonstrated in computational experiments.