Distribution Free Procedures for Some Inventory Models

Stochastic inventory models, such as continuous review models and periodic review models, require information on the lead time demand. However, information about the form of the probability distribution of the lead time demand is often limited in practice. We relax the assumption that the cumulative distribution function, say F, of the lead time demand is completely known and merely assume that the first two moments of F are known and finte. The minmax distribution free approach for the inventory model consists of finding the most unfavourable distribution for each decision variable and then minimizing over the decision variable. We solve both the continuous review model and the periodic review model with a mixture of backorders and lost sales using the minmax distribution free approach.     

基于MCMC的随机库存系统中提前期需求分布的计算

在需求和提前期均是随机的库存系统中,提前期需求的分布是由提前期分布与需求分布复合而成的,这个复合分布的计算通常是困难的。本文采用基于Gibbs抽样的马尔科夫链蒙特卡洛(MCMC,Markov chain Monte Carlo)方法,抽取条件分布样本作为提前期需求分布的样本,通过样本来计算提前期需求分布密度、服务水平和损失函数。这种方法避免了直接求解复杂积分计算上的困难,也克服了近似分布拟合偏差过大的问题,有效地解决了随机需求与随机提前期的复杂库存系统中提前期需求确定问题。理论与数值分析结果表明:与现有方法相比较,基于MCMC的方法具有计算简便、拟合精度高、通用性好等特点。     

Gompertz分布顺序统计量的一些随机比较

考虑两组相互独立的来自非齐次总体Gompertz分布的样本,给出了最小顺序统计量的反向失效率序、散度序以及凸变换序之间的比较和最大顺序统计量的普通随机序的比较.     

库存控制的随机优化(英文)

本文将随机扰动引入企业库存控制系统,并重点讨论了扰动引入后,库存投资与市场需求的相互作用,及对未来折现利润的相关影响.文章建立了关于库存控制管理的最优跨时决策模型.不同于其它文献中将市场需求及库存投资看作具有具体分布的随机变量,文章将两者设置为随机过程并分别服从不同的It型SDE.文章得出了三个命题及一些有意义的结果.     

随机提前期随机需求条件下的二级库存模型

考虑由一个分销中心和若干零售商组成的两级分销系统 ,假设分销中心和零售商实行连续性盘点、( R,Q) 订货策略 ,分销中心的交货时间是常量 ,而零售商处的提前期为随机变量 ,且需求服从独立的复合泊松过程 .以整个系统平均成本最小为目标函数 ,由此得到最优的订货策略 ,并且给出数值例子及敏感性分析 .     

The Gamma Distribution and Inventory Control

The paper aims to justify the applicability of the gamma distribution to inventory control and to collect under one heading the properties of the distribution and associated formulae arising from inventory control theory. Algorithms for computer calculation are given.     

The Use of Divided Differences in Finite Element Calculations

Divided differences are used to calculate gradients of functionscomputed by finite element methods. On regular elements it isshown that for quite general difference formulae and commonfinite element methods this retains the full order of accuracyof the methods. Examples are given together with the resultsof numerical trials. Applicability to irregular meshes is consideredand a practical test with encouraging results is given.     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

The Single-Period Inventory Problem with Triangular Demand Distribution

A simple method is presented for determining ‘closed-form’ solutions for an optimum (s, S) ordering policy for the single-period inventory problem with a set-up cost of ordering and the uncertain total demand over the period represented by a triangular probability density function. The distribution reflecting the decision maker's degree of belief that all values of total demand outside of two (possibly ‘soft’) limits are barely credible and all values within the limits have uniform increasing probability density towards a (possibly ‘soft’) modal value. The importance of the closed form solutions obtained is that they remove the need for enumeration over alternative values of s in determining the optimum (s, S) ordering policy, also they can be encoded in an algorithm simple to implement and they allow easy sensitivity analysis of the results to perturbations in the estimates of the problem parameters. A numerical example is presented to illustrate the essential features of the method.     

The Fractional Calculus for Some Stochastic Processes

Abstract

The integration and differentiation of fractional orders are well known concepts for deterministic functions (see Miller, K.S.; Ross, B. An Introduction to Fractional Calculus and Fractional Differential Equations; John Wiley: New York, 1993; I. Podlubny and Ahmed M.A. El-Sayed, On two definitions of fractional calculus Slovak Academy of Sciences Institute of experimental Phys. UEF-03-96 ISBN 80-7099-252-2, 1996; Podlubny, I. Fractional Differential Equations; Acad. Press: San Diego – New York, London etc. 1999; Samko, S.G.; Kilbas, A.A.; Marichev, O. Integral and derivatives of the fractional orders and some of their applications. Nauka i Teknika Minisk 1983). In earlier work, we have studied the fractional calculus for mean square continuous stochastic processes. In this work, we shall study the mean square (m.s.) fractional calculus for stochastic processes which are m.s. Riemann-integrable and prove some its properties.     

随机局部弹性及在库存管理中的应用

提出随机局部弹性的概念，讨论了相应的运算法则，研究了不允许缺货的存贮模型中，总费用对采购量与采购周期的局部弹性。给出了总费用联合概率密度的一般表达式。通过实例说明，当采购量与采购周期的分布特性已知时，总费用的弹性变化范围就完全被确定。     

Dynamic Control and Optimization of Capital-Constrained Stochastic Inventory Systems

For most firms,especially the small-and medium-sized ones,the operational decisions are affected by their internal capital and ability to obtain external capital.However,the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely.An important question that arises is:what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital?In this paper,we review some of the latest developments in this area.After a brief review of single period models,we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth.Two cases are discussed in detail:self-finance and short term finance.In the first case,the firm has to rely on its own capital for all ordering decisions,while in the second,the firm can borrow short term loan from lenders.A detailed characterization of the optimal policy is presented and its managerial insights are discussed.Several possible extensions are suggested.     

某些三维流形不变量的计算

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Devaney混沌的随机性质

讨论了Devaney混沌的随机性质,证明了如果度量空间上的连续变换f是弱混合的,那么f是拓扑传递的,并且若f的周期点稠密,则f还是初值敏感的.     

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??This review article introduces two recent advances in stochasticsimulation: the construction of efficient algorithms for estimatingrare events and the generation of samples from a stationarydistribution that has no closed form. Estimating a very smallquantity requires extreme accuracy to form a useful confidenceinterval. This makes the slowly convergent rare-event simulation achallenge task in both efficiency and accuracy. In this report, weintroduce the examples of rare events of interest and thedifficulties in estimating them. Various approaches to pursue robustand efficient estimators along the development are discussed andevaluated. Numerical experiments on estimating ruin probability areprovided to show the quality of these approaches.In steady-statesimulation, how to generate samples from a stationary stochasticprocess has long been the key subject. The common practice is todiscard the data gathered during the initial transient period.However, how long the warm-up period must be raises another problemthat has no satisfactory answer. Fortunately, by the development inthe past two decades, exact simulation has become possible forcertain stochastic models. In this report, we will introduce twoimportant methods and related applications.     

Applications of the Weibull Distribution in Inventory Control

This paper is intended to show that the Weibull distribution can effectively be used to approximate the lead time demand in several cases of distributed demands coupled with distributed lead times. With this approximation, the computations involved are shown to be very simple, requiring no numerical or iterative procedures for determining the re-order levels or protection levels. Some pertinent properties of the Weibull distribution are summarized, and necessary tables for estimating the parameters of the Weibull distribution are given. Numerical examples are given in three cases of distributed demands and lead times and, in each case, the Weibull approximation results are compared with exact and/or other approximate results.     

The Stochastic Control Model for Use Conversion of Land

In this paper, the authors investigate the optimal conversion rate at which land use is irreversibly converted from biodiversity conservation to agricultural production. This problem is formulated as a stochastic control model, then transformed into a HJB equation involving free boundary. Since the state equation has singularity, it is difficult to directly derive the boundary value condition for the HJB equation. They provide a new method to overcome the difficulty via constructing another auxi...     

传统分销系统的经销商的库存管理

目前我国快速消费品行业中的中小企业的分销系统大都是传统的分销系统,在它之中经销商是处于核心地位.本文通过对经销商的库存进行重点分析,以了解产生经销商跨区冲货的原因及如何有效控制经销商合理库存的方法.作者认为分销系统是一个典型的系统工程.     

Some Aspects of Stability in Stochastic Programming

Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measures as a backbone we discuss qualitative and quantitative stability of recourse models that possibly involve integer variables. We sketch stability in chance constrained stochastic programming and provide some applications in statistical estimation. Finally, an outlook is devoted to issues that were not discussed in detail and to some open problems.     

Evaluation of Some Integrals Encountered in Calculations in Many-fermion Systems

The integrals and (l(x)=3j₁(x)/x) and j₁(x) the spherical Bessel function of thefirst order) are evaluated analytically