Optimal order policy in response to announced price increase for deteriorating items with limited special order quantity

When a supplier announces an impending price increase due to take effect at a certain time in the future, it is important for each retailer to decide whether to purchase additional stock to take advantage of the present lower price. This study explores the possible effects of price increases on a retailer's replenishment policy when the special order quantity is limited and the rate of deterioration of the goods is assumed to be constant. The two situations discussed in this study are as follows: (1) when the special order time coincides with the retailer's replenishment time and (2) when the special order time occurs during the retailer's sales period. By analysing the total cost savings between special and regular orders during the depletion time of the special order quantity, the optimal order policy for each situation can be determined. We provide several numerical examples to illustrate the theories in practice. Additionally, we conduct a sensitivity analysis on the optimal solution with respect to the main parameters.     

考虑参照价格效应的易逝品定价与订购策略

在考虑消费者参照价格效应的基础上,构建一个易逝品的定价与订购联合决策模型,其中产品的需求不仅依赖于销售价格还与该产品在消费者心目中的参照价格相关,变质率为常数,系统不允许缺货.分别讨论了对称参照价格效应和非对称参照价格效应两种情况下零售商的最优定价与订购决策问题,证明并得到关于模型结构的一些性质,进而设计了问题的求解算法.通过数值方法分析了参照价格效应参数和变质率对系统最优解的影响,以及两种情况下最优解之间的关系.结果显示:当面对具有参照价格依赖的消费者时,采用适当的营销策略来提高消费者的参照价格对零售商总是有利的;对高变质率产品而言,零售商可保持一个较稳定的订购策略,更多地关注产品的定价策略;面对损失厌恶型消费者,随着消费者参照价格的逐渐提高,零售商的定价与订购策略均应缓慢地改变,而不宜急剧变化.     

An economic production quantity model for deteriorating items with preventive maintenance policy and random machine breakdown

In recent years, many researches on economic production quantity (EPQ) models with machine breakdown and preventive maintenance have been developed, but few of them have developed integrated models for deteriorating items. In this study, we develop EPQ models for deteriorating items with preventive maintenance, random machine breakdown and immediate corrective action. Corrective and preventive maintenance times are assumed to be stochastic and the unfulfilled demands are lost sales. Two EPQ models of uniform distribution and exponential distribution of corrective and maintenance times are developed. An example and sensitivity analysis is given to illustrate the models. For the exponential distribution model, it is shown that the corrective time parameter is one of the most sensitive parameters to the optimal total cost.     

Optimal dynamic pricing for deteriorating items with reference-price effects

In this paper, a dynamic pricing problem for deteriorating items with the consumers’ reference-price effect is studied. An optimal control model is established to maximise the total profit, where the demand not only depends on the current price, but also is sensitive to the historical price. The continuous-time dynamic optimal pricing strategy with reference-price effect is obtained through solving the optimal control model on the basis of Pontryagin's maximum principle. In addition, numerical simulations and sensitivity analysis are carried out. Finally, some managerial suggestions that firm may adopt to formulate its pricing policy are proposed.     

允许缺货待补的季节性商品二阶联合库存最优订购策略

针对季节性商品提出了二阶单周期缺货待补联合库存模型,其中假设零售商的库存策略采用报童模型且零售商的需求量服从正态分布。对制造商总利润函数的最优解,提出了充分与必要条件,以期可以简便迅速地获得制造商的最优生产批量以及最优订购周期。最后,通过数值算例及在管理上的含义对必要条件进行了充分的讨论。     

折损产品整合生产库存系统优化模型研究

在具有两个不同销售周期的销售市场情形下,当需求率、生产率和折损率为常数时,从供应链整合的角度对折损产品的库存系统进行了优化．通过对供应链中产品生产商和销售商库存系统的各自分析,建立了整合库存系统数学模型,给出了优化方法．     

Optimal order limit policy under cost effectiveness criterion

The reorder point/reorder quantity policies referred as (r, Q) policies are widely used in industry and extensively studied in the literature. It should be noted, however, that the shortage often occurs in practical situations even if the optimal reorder point and reorder quantity maximizing or minimizing any optimality criteria are rationally determined. In this paper, we present a mathematical model to adjust the shortage period by the emergency order. The problem is to choice the timing for the expedited order. Applying the concept on repair limit policy in the context of reliability theory, the optimal order limit policy maximizing an optimality criterion called cost effectiveness is analytically derived in the framework of (r, Q) inventory system. Finally, some examples for stochastic lead times are given to explain the numerical procedure to obtain the optimal policy.     

Managing dual warehouses with an incentive policy for deteriorating items

Distributors in a supply chain usually limit their own warehouse in finite capacity for cost reduction and excess stock is held in a rent warehouse. In this study, we examine inventory control for deteriorating items in a two-warehouse setting. Assuming that there is an incentive offered by a rent warehouse that allows the rental fee to decrease over time, the objective of this study is to maximise the joint profit of the manufacturer and the distributor. An optimisation procedure is developed to derive the optimal joint economic lot size policy. Several criteria are identified to select the most appropriate warehouse configuration and inventory policy on the basis of storage duration of materials in a rent warehouse. Sensitivity analysis is done to examine the results of model robustness. The proposed model enables a manufacturer with a channel distributor to coordinate the use of alternative warehouses, and to maximise the joint profit of the manufacturer and the distributor.     

Optimal control of the production–inventory system with deteriorating items and tradable emission permits

Using the well-known Arrow and Karlin (1958) Arrow, K.J., and Karlin, S. (1958), ‘Production over Time with Increasing Marginal Costs’, in Studies in the Mathematical Theory of Inventory and Production, eds. K.J. Arrow and S. Karlin, Stanford: Stanford University Press, pp. 61–69. [Google Scholar] dynamic production–inventory model and the model with tradable emission permits which was presented by Dobos (2005 Dobos, I. (2005), ‘The Effects of Emission Trading on Production and Inventories in the Arrow–Karlin Model’, International Journal of Production Economics, 93–94, 301–308.[Crossref], [Web of Science ®] , [Google Scholar], 2007) Dobos I. (2007), ‘Tradable Emission Permits and Production-inventory Strategies of the Firm’, International Journal of Production Economics, 108, 329–333.[Crossref], [Web of Science ®] , [Google Scholar], we develop a model of the production–inventory system with deteriorating items and tradable emission permits. The objective of this paper is to apply the optimal control theory to solve the production–inventory problem with deteriorating items and tradable emission permits, and derive the optimal inventory level and the optimal production rate that minimise the total cost. The results are discussed with a numerical example and a sensitivity analysis of the optimal solution with respect to the parameters of the production–inventory system is carried out.     

Algebraic multilevel iterative preconditioning methods for h-matrices

A purely algebraic method is presented to construct preconditioned for symmetric positive definite H-matrices. The main technique is H-compatible splitting and diagonal compensation reduction. Associated with some special matrix polynomials, under certain condition, this method is optimal with respect to the rate of convergence and computational complexity. Numerical results that illustrate these properties are provided.     

有租借仓库并允许缺货的随机存贮模型

库存管理中已经存在的EOQ、(S,s)等经典模型,尚无法解决“有租借仓库”、“允许缺货”和“随机交货”并存的存贮管理问题。本文提出了针对上述三个条件并存情况下的存贮模型,将统计意义下单位时间损失费用作为指标函数来评价该方案,并将单品种固定库存总量随机存贮管理模型推广到多品种固定库存总量随机存贮管理模型中,给出了非线性规划模型。最后给出实例,采用优化算法在MATLAB下对模型求解。     

需求依赖于变质时间的非立即变质品联合补货优化

基于产品非立即变质的特征,构建需求依赖于变质时间的多品种联合补货库存模型,目标是使单位时间内的总成本最小.由于联合补货问题是NP难题,且考虑变质使问题变得更加复杂,针对这一难点,采用一种截断泰勒级数的方法对目标函数的指数项进行简化,提出一种基于定界的启发式算法求解模型,并通过数值案例验证算法的有效性和实用性.最后对主要参数的敏感性进行分析,为非立即变质品的零售商在实施联合补货时提供有益的管理建议.     

不确定环境下的一种动态响应库存优化方法

针对随机需求提前期环境下的库存管理问题,提出一种启发式动态响应算法求取最优订货策略。建立最优订货策略的动态非线性优化模型,并设定客户需求和订货提前期分别为线性和高斯随机变量,通过变化形式、步长和变化频率的不同模拟实际经济运营过程;在微粒群寻优过程中引入柔性变异概率及动态更新响应方式,使微粒具有感知外界环境变化及对变化的响应能力,提高算法对复杂动态系统环境变化的适应性。实证分析结果证明了所提方法对最优订货量实时变化的动态响应能力。