A One-Time Excess Inventory Disposal Decision Under a Stationary Base-Stock Policy

We consider a stochastic inventory system that has been operated under a policy different from the one that will be implemented in the future. Such a situation may arise as a result of changes in model assumptions leading to the implementation of a different policy. Before the new policy is implemented, there may be some units on hand which may exceed the optimal order-up-to level. Hence, one needs to evaluate a one-time inventory disposal decision immediately before the new policy replaces the policy in use. For this purpose, we develop three models under different assumptions that describe the demand during the disposal period and present analytical results characterizing their optimal solutions.     

Optimality of Base-Stock and (s, S) Policies for Inventory Problems with Information Delays

Information delays exist when the most recent inventory information available to the inventory manager (IM) is dated; namely, the IM observes only the inventory level of an earlier period. We introduce information delays into the standard multiperiod stochastic inventory problem with backorders. We consider two types of information delays: (i) a constant delay and (ii) a random delay. We define an appropriate reference inventory position, which is a sufficient statistics for finding the optimal order quantity. We show that the optimal ordering policy is of base-stock type with respect to the reference inventory position and is of (s, S) type if there is also a fixed cost of ordering.All authors were supported in part by NSF Grant DMS-0509278.     

具有两类需求服务的随机库存系统控制策略研究

研究具有两类顾客排队需求服务的随机库存系统.系统采取(s,Q)补货策略且当库存水平下降到安全库存s时,到达的第二类顾客以概率P得到服务.首先,建立库存水平状态转移方程并通过递推算法求解获得库存水平稳态概率分布和系统稳态指标;接下来,构建库存成本函数;最后,采用数值试验的方法研究该库存系统的最优控制策略并考察系统参数的敏感性.     

求解硬时间窗约束下随机需求库存-路径问题的优化算法

随机需求库存-路径问题(Stochastic Demand Inventory Routing Problem, SDIRP)即考虑随机需求环境下供应链中库存与配送的协调优化问题,是实施供应商管理库存策略过程中的关键所在,也是典型的NP难题之一。文章以具有硬时间窗约束的随机需求库存-路径问题(Stochastic Demand Inventory Routing Problem with Hard Time Windows, SDIRPHTW)为研究对象,将SDIRPHTW分解为直接配送的随机库存-路径问题和具有硬时间窗约束的路径优化问题两个子问题,并以最小化系统运行成本和用车数量为目标,设计了一个基于(s,S)库存策略和修正C-W节约法的启发式算法。最后,通过相应的数值算例验证了算法的有效性。     

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 .     

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.     

Inventory control problem with freight cost and stochastic demand

This paper generalizes the standard newsboy model to the case including freight cost, in which the capacity of one container is the limit and the freight cost is proportional to the number of the containers used. We show that the optimal ordering quantity is either the newsboy solution or some multiple of the container’s capacity. We also propose an algorithm to compute the optimal policy. Furthermore, we generalize these results to the case in which the inventory and the price are determined jointly with emergency purchase.     

带客户协同分仓的动态车辆路径问题研究

随着互联网商业迭代的不断深化,越来越多的企业倾向于从商品前置视角解决配送距离与配送时效性的矛盾。为此,本文研究基于客户协同分仓备货的动态车辆调度问题(Dynamic Vehicle Routing Problem with Inventory Synergetic Customer, DVRP-ISC),设计考虑区域分异特征的协同分仓客户选择方法,建立多阶段动态配送网络优化模型。鉴于研究问题的特殊性,设计多阶段两级网络协同配送路径优化算法;最后,以仿真算例、自定义算例集和基准算例,验证所提模型和算法性能及其拓展性。     

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 Wiener Sequential Testing Problem with Finite Horizon

We present a solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of proof is based on reducing the initial optimal stopping problem to a parabolic free-boundary problem where the continuation region is determined by two continuous curved boundaries. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundaries can be characterized as a unique solution of the coupled system of two nonlinear integral equations.     

Finite Difference Approximations for Stochastic Control Systems with Delay

Abstract

This article considers the computation issues of the infinite dimensional HJB equation arising from the finite horizon optimal control problem of a general system of stochastic functional differential equations with a bounded memory treated in [2 Chang , M.H. , Pang , T. , and Pemy , M. accepted. Optimal control of functional stochastic differential equations with a bounded memory. Stochastics 80 ( 1 ): 69 – 96 . [Google Scholar]]. The finite difference scheme, using the result in [1 Barles , G. , and Souganidis , P.E. 1991 . Convergence of approximative schemes for fully nonlinear second order equations . J. Asymptotic Analysis 4 : 557 – 579 . [Google Scholar]], is obtained to approximate the viscosity solution of the infinite dimensional HJB equation. The convergence of the scheme is proved using the Banach fixed point theorem. The computational algorithm also is provided based on the scheme obtained.     

Stochastic leadtimes in a one-warehouse,N-retailer inventory system with the warehouse not carrying stock

This study extends upon a multi-echelon inventory model developed by Graves, introducing in the one-warehouse, N-retailer case—as Graves suggested—stochastic leadtimes between the warehouse and the retail sites in place of the original deterministic leadtimes. Effects of stochastic leadtimes on required base stock levels at the retail sites in the case where the warehouse carries no stock (e.g., serves as a cross-dock point) were investigated analytically. Two alternative treatments of stochastic leadtime distributions were considered. Using as a baseline Graves’ computational study under deterministic leadtimes, results of the current study suggest that it may be better to use the deterministic model with an accurately estimated mean leadtime than a stochastic model with a poorly estimated mean leadtime.     

带批次和临时库存的越库配送车辆路径问题研究

从零售业供应链整合入手,构建供应商、配送中心和零售点构成的协同配送网络,研究带批次和临时库存的越库配送车辆路径问题.将越库过程分为取货、分拣和配货三个阶段,考虑配送中心分拣能力,分批次设置车辆协同到达配送中心的服务时刻,据此建立以最小化车辆运输成本、临时库存成本和固定成本为目标的数学模型.考虑问题特征,设计一种混合变邻...     

带奇异系数的有限维与无穷维随机微分方程

本文对具非Lipschitz系数的随机微分方程给出解的存在唯一性与非爆炸性的新判别条件,少许改进了文\cite{4}的有关结果. 通过控制交互作用, 该结果还被推广到无穷维情形.     

Stochastic Theta Method for a Reflected Stochastic Differential Equation

In this article, a stochastic theta method for a reflected stochastic differential equation is proposed. When the parameter θ = 0, this method coincides with the projection Euler scheme; while when the parameter θ = 1, it is called an implicit projection Euler scheme which is first proposed in this article. Under some conditions, the strong convergence and the A-stability of this numerical scheme are proved.     

模糊随机需求的连续盘点存储策略研究

考虑到需求的模糊随机性,建立模糊随机需求情况下连续盘点存储策略的模糊随机成本模型。利用模糊随机变量的期望值理论,推导出了其成本期望值模型的解析表达式,进而给出了最优再订货点所属区间的判别条件以及最优再订货点和经济订货量的计算式;基于此,设计了一模糊随机需求的连续盘点最优存储策略算法。最后结合数值算例,分析了模糊随机需求概率分布及缺货成本对最优存储策略的影响。     

一类跳扩散需求存贮系统(s,S)库存控制策略研究

考虑的是连续检查库存,需求为一个常时间函数和-个复合Poison跳扩散随机过程的和的存贮系统最优库存控制问题.基于期望折扣成本最小建立了无穷时间区间具有固定订购成本的最优库存模型,确定可采用(s,S)策略进行库存控制,给出了最优(s,S)策略的充要条件--HJB方程Ⅰ、Ⅱ.我们采用猜测的方法确定了最优(s,S)策略对应的值函数形式,建立了确定库存参数的最优化模型.     

Stochastic optimization models for a single-sink transportation problem

In this paper, we study a single-sink transportation problem in which the production capacity of the suppliers and the demand of the single customer are stochastic. Shipments are performed by capacitated vehicles, which have to be booked in advance, before the realization of the production capacity and the demand. Once the production capacity and the demand are revealed, there is an option to cancel some of the booked vehicles against a cancellation fee; if the quantity shipped from the suppliers using the booked vehicles is not enough to satisfy the demand, the residual quantity is purchased from an external company. The problem is to determine the number of vehicles to book in order to minimize the total cost. We formulate a two-stage and a multistage stochastic mixed integer linear programming models to solve this problem and test them on a real case provided by Italcementi, the primary Italian cement producer and the fifth largest cement producer in the world. We test the influence of different scenario-tree structures on the solutions of the problem, as well as sensitivity of the results with respect to the cancellation fee.     

基于随机提前期的二级库存系统的优化方法

针对需求和提前期均是随机的情况下,考察了一个简单的二级库存系统,即单个供应商、单个零售商的优化问题,两者均采用s,Q策略进行库存管理,他们的订货数量Qr,Qs都是已知常数,以每计划周期内系统运行期望总费用最小建立了目标函数,寻求系统的决策变量sr,ss,最后给出了求解算法与数值算例.     

需求依赖于展示区库存水平的易腐品订购和转运策略

本文主要研究易腐品零售商的订货和转运策略。零售商的库存分为两部分,即展示区/货架库存和仓库库存。零售商定期向供应商订货,零售商收到订购的商品首先将其中一部分商品存放在展示区中,余下的部分储存在仓库。展示区的空间是有限的,并且需求依赖于展示区商品的库存量。本文首先建立了以平均利润最大化为目标的库存优化模型并对模型最优解的存在性进行了分析,然后得到了求解最优订购量、转运量、转运时间间隔以及再订购点的算法,最后给出了不同参数条件下的算例。