The Finite Horizon Trended Inventory Replenishment Problem With Shortages

A new type of replenishment policy is suggested for an inventory item having a finite shortage cost and linear trend in demand over a finite time horizon. The optimal solution of the suggested replenishment policy has a lower total cost as compared with the optimal solution for the traditional replenishment policies.     

Optimal Consumption in a Brownian Model with Absorption and Finite Time Horizon

We construct ?-optimal strategies for the following control problem: Maximize $\mathbb {E}[ \int_{[0,\tau)}e^{-\beta s}\,dC_{s}+e^{-\beta\tau}X_{\tau}]$ , where X _t =x+μt+σW _t ?C _t , τ≡inf{t>0|X _t =0}∧T, T>0 is a fixed finite time horizon, W _t is standard Brownian motion, μ, σ are constants, and C _t describes accumulated consumption until time t. It is shown that ?-optimal strategies are given by barrier strategies with time-dependent barriers.     

需求依赖销售努力和销售价格的库存模型

在假定在确定性需求的前提下,提出了一种需求同时依赖销售价格和销售努力的决策模型.然后通过与没有增加销售努力手段时的最优平均利润函数的比较,显示了该分析方法的优越性.最后通过数值实例验证了模型的可行性,得出相关启示.     

Computing a Stationary Base-Stock Policy for a Finite Horizon Stochastic Inventory Problem with Non-linear Shortage Costs

Abstract

We consider a periodic-review stochastic inventory problem in which demands for a single product in each of a finite number of periods are independent and identically distributed random variables. We analyze the case where shortages (stockouts) are penalized via fixed and proportional costs simultaneously. For this problem, due to the finiteness of the planning horizon and non-linearity of the shortage costs, computing the optimal inventory policy requires a substantial effort as noted in the previous literature. Hence, our paper is aimed at reducing this computational burden. As a resolution, we propose to compute “the best stationary policy.” To this end, we restrict our attention to the class of stationary base-stock policies, and show that the multi-period, stochastic, dynamic problem at hand can be reduced to a deterministic, static equivalent. Using this important result, we introduce a model for computing an optimal stationary base-stock policy for the finite horizon problem under consideration. Fundamental analytic conclusions, some numerical examples, and related research findings are also discussed.     

A Finite Horizon Production Model with Variable Production Rates and Constant Demand Rate

In this paper we present a finite horizon single product single machine production problem. Demand rate and all the cost patterns do not change over time. However, end of horizon effects may require production rate adjustments at the beginning of each cycle. It is found that no such adjustments are required. The machine should be operated either at minimum speed (i.e. production rate = demand rate; shortage is not allowed), avoiding the buildup of any inventory, or at maximum speed, building up maximum inventories that are controlled by the optimal production lot size.     

存货质押融资质押物价格变化MRS-GRACH模型研究

针对质押物价格收益序列存在的结构转换特征,对常系数ARCH模型进行改进,引入一个变化服从马尔科夫过程的状态随机变量反映价格收益不同的波动状况,从而构建了质押物价格收益MRS-GARCH模型.实例研究表明MRS-GARCH模型能够刻画现实中质押物价格收益波动结构动态变化过程,同时能够识别外界不可见因素对收益波动的影响力度,MRS-GARCH模型较GARCH模型在拟合及预测价格收益波动方面具有更准确的效果.     

An Inventory Model with Two-Component Demand Rate and Shortages

The article investigates a deterministic inventory system with two-component demand rate. The demand rate is stock-dependent down to a certain level and then constant. Shortages are allowed and are fully backlogged. The storage space is assumed to be limited. A flowchart is provided to solve a general system. To study the effects of changes in the system parameters on the average net profit a sensitivity analysis has been performed.     

允许缺货且带数量折扣的腐烂物质库存模型

在短缺量拖后率是等待时间的负指数函数、订购成本是批量的线性函数的条件下,建立了带数量折扣的腐烂物质库存模型,目标是优化总平均利润.在给定销售价格的情况下,证明了库存系统的最优补货策略存在且唯一;且若采用最优补货策略,平均利润函数是销售价格的凹函数;最后给出了模型的算法,并用数值例子说明了模型和算法的有效性.     

带有提前购买价格折扣的易逝品库存模型

经典Newsboy模型是在购买价格不变的情形下去确定最优进货批量．然而,对于一些具有特定的消费时间的商品（如中秋节的月饼等）,生产厂家为了更好地安排生产,通常提供提前购买价格折扣．这样确定何时进货、进多少货的问题对经销商来说就显得非常重要．本文研究了该问题,并建立了带有提前购买价格折扣的易逝品的一个库存模型,同时也给出了应用实例与参数的灵敏度分析．     

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.     

可替代产品库存模型的研究

以零售商的角度,讨论了在允许进货的情况下可替代产品的库存问题,建立了这类问题利润最大化的库存模型,讨论了各参数对利润和库存的影响.然后证明了问题的解是存在的,利润函数是子模的,并给出了最优解的一阶必要性条件,同时探讨了目标函数的凹性问题.通过理论分析和数值试验证明了在一定条件下替代和重新进货都能提高利润,并能降低总的库存水平.     

Optimal Stopping Time on Semi-Markov Processes with Finite Horizon

Journal of Optimization Theory and Applications - In this paper, we consider the optimal stopping problems on semi-Markov processes (sMPs) with finite horizon and aim to establish the existence and...     

An Inventory Model with an Inventory-Level-Dependent Demand Rate and Relaxed Terminal Conditions

This paper investigates an inventory system with an inventory-level-dependent demand rate followed by a constant demand rate. The analysis previously conducted on this model imposed a terminal condition of zero inventory at the end of the order cycle. This condition is not warranted for systems with inventory-level-dependent demand rates, even for deterministic models. This paper relaxes this restriction, and an appropriate model is developed.     

随机补货间隔且需求依赖库存水平的库存控制模型

定期补货库存模型在实践中被广泛使用,尤其是在单一供应商中购买多种不同产品的库存系统中更为常见.然而,大多数定期补货库存模型都假设补货的时间间隔是恒定不变的.但在实践中,补货的时间间隔也可能是一个随机的时间长度.提出了一个随机补货时间间隔和需求依赖于当前展示库存水平的库存控制模型,且补货间隔服从指数分布和均匀分布,同时允许短缺发生并且短缺量部分延期供给,并研究了模型最优解的存在性与唯一性.最后,给出了数值算例来说明模型在实际中的应用.     

易变质产品的可替代库存模型的最优订购策略研究

研究了易变质产品的可替代库存模型.在有限计划期内,供应商面临两种不同产品的需求,当一种产品发生短缺时,另一种产品可以以一定的替代率代替短缺产品.通过分析系统的总成本函数的性质,提出了最优订购策略.最后通过算例验证了算法的最优性.     

有限时区上的最优转换和停止问题

讨论了有限时区上的最优转换和停止问题,它是一类同时具备脉冲控制和最优停止特征的最优控制问题.问题的最优值以及最优转换和停止决策可以由具有混合障碍的多维反射倒向随机微分方程的解来刻画.接着考虑了形式更一般的反射倒向随机微分方程并证明了方程解的存在唯一性.