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.     

需求依赖库存且有时变短缺拖后率的非立即变质物品库存模型

研究了时变短缺部分拖后条件下非立即变质性物品的库存补给模型,其中物品的变质率随时间变化而变化。当库存水平为正值时,市场需求受销售价格影响;当库存为负值时,不能满足的需求被部分拖后,拖后率与在缺货期间已经发生的缺货量有关。通过考虑短缺拖后率和变质率同时随时间变化对库存补给策略的影响,建立具有短缺量部分拖后的非立即变质性物品的库存模型,并且给出模型最优解存在的必要条件,得到一类更加符合实际情形的库存模型。最后,用数值算例说明模型的实际应用。     

一类允许缺货的易变质物品的随机非线性存贮模型

研究了货物存贮问题．考虑到在仓库出空期间一般人们有耐烦与不耐烦两种反应,研究中假设仓库出空期丢失顾客量服从正态分布,据此建立允许缺货的易变质物品的非线性存贮模型,使模型更接近于实际．并给出数值例子,运用Matlab软件求解最优存贮控制策略,得到近似的最佳进货量和最佳出空期长度．     

An integrated production-inventory deteriorating model for pricing policy considering imperfect production,inspection planning and warranty-period- and stock-level-dependant demand

In marketing, enterprises try all motivated selling strategies to stimulate customers to buy a product. One of these selling strategies is a warranty policy that provides a return promise of free replacement. The buyer may place more orders because of the display of the product. An increasing demand resulting from these motivated factors influences the replenishment planning. In operational process, quality level resulting in relevant activities may cause changes of operational planning. The purpose of this study is to investigate an integrated production inventory deteriorating model considering the pricing policy, the imperfect production, the inspection planning, the warranty-period and the stock-level-dependant demand with the Weibull deterioration, partial backorder and inflation. We incorporate a single-retailer single-manufacturer cooperation from the perspectives of both the manufacturer and the retailer. The classical optimisation technique and the heuristic method are used to derive the optimum solutions. A numerical example and sensitivity analysis are presented.     

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．     

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 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.     

可延迟供货的冷轧生产库存问题之建模与优化

本文针对可延迟供货的冷轧生产系统,建立了以最小化库存成本、拖期惩罚和启动成本为目标的多阶段生产库存模型,模型中充分考虑了工序不允许停机的情况以及计划与调度之间的一致性问题.同时开发了基于变量分离的有效拉格朗日松弛求解算法,并使用120个基于实际生产数据的算例进行了仿真实验,计算结果显示该算法能够在合理的时间内得到高质量的解.     

基于提前支付的非瞬时变质产品批量订货定价策略

当供应商处于供应链节点的买方市场时,通常要求零售商提前支付一定比例购置成本作为订金.针对该问题研究零售商促销努力下存在随机需求的非瞬时变质产品批量订货定价策略,考虑零售商提前支付策略,允许部分缺货.在一定条件下可得零售商最优补货周期和局部最优定价策略,随之提出相应的求解算法.数值计算结果表明:若提前支付购置成本占比或利率增大,则零售商利润将显著减少;提前支付期限和期数均对最优利润产生消极影响;零售商采取积极促销策略可有效提升自身利润.     

EPQ model with learning consideration,imperfect production and partial backlogging in fuzzy random environment

The article scrutinises the learning effect of the unit production time on optimal lot size for the uncertain and imprecise imperfect production process, wherein shortages are permissible and partially backlogged. Contextually, we contemplate the fuzzy chance of production process shifting from an ‘in-control’ state to an ‘out-of-control’ state and re-work facility of imperfect quality of produced items. The elapsed time until the process shifts is considered as a fuzzy random variable, and consequently, fuzzy random total cost per unit time is derived. Fuzzy expectation and signed distance method are used to transform the fuzzy random cost function into an equivalent crisp function. The results are illustrated with the help of numerical example. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out.     

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 production run length with imperfect production processes and backorder in fuzzy random environment

This article considers the economic production run time problem with imperfect production processes and allowable shortages. The elapsed time until the production process shifts is assumed to be a fuzzy random variable, and fuzzy random total cost per unit time model is constructed. The expectation theory and signed distance are employed to transform the fuzzy random model into crisp model. An effective approximate algorithm is developed to search for the optimal production run length. Furthermore, numerical examples are provided to illustrate the results of proposed model.