Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.     

Ordering Cost Depletion in Inventory Policy with Imperfect Products and Backorder Rebate

This study presents an inventory model for imperfect products with depletion in ordering costs and constant lead time where the price discount in the backorder is permitted. The imperfect products are refused or modified or if they reached to the customer, returned and thus some extra costs are experienced. Lately some of the researchers explicitly present on the significant association between size of lot and quality imperfection. In practical situations, the unsatisfied demands increase the period of lead time and decrease the backorders. To control customers' problems and losses, the supplier provides a price discount in backorders during shortages. Also, an order’s policies may result in including some imperfect products in arrival lots. A discount on price may be offered by the supplier on the out-of-stock products to manage the backorder problems. The study aims to develop a model with imperfect products by permitting the price discount in backorders, and the cost of ordering is considered a decision variable. First, it is assumed that the demand for lead time is followed by a normal distribution and then stops it and assumed that the first two moments of demand for lead time are known. Further, the minimax distribution method is used to solve this model, and a separate algorithm is designed. In this study, two models are discussed with and without a normally distributed rate of demand. The current study verified with the help of some numerical examples over various model parameters.     

Computational procedure of optimal inventory model involving controllable backorder rate and variable lead time with defective units

This article considers that the number of defective units in an arrival order is a binominal random variable. We derive a modified mixture inventory model with backorders and lost sales, in which the order quantity and lead time are decision variables. In our studies, we also assume that the backorder rate is dependent on the length of lead time through the amount of shortages and let the backorder rate be a control variable. In addition, we assume that the lead time demand follows a mixture of normal distributions, and then relax the assumption about the form of the mixture of distribution functions of the lead time demand and apply the minimax distribution free procedure to solve the problem. Furthermore, we develop an algorithm procedure to obtain the optimal ordering strategy for each case. Finally, three numerical examples are also given to illustrate the results.     

Optimal economic production quantity policy for randomly failing process with minimal repair,backorder and preventive maintenance

This study examines the feasibility of using an economic production quantity (EPQ) model incorporating maintenance and production programs to model an imperfect process involving a deteriorating production system. In response to failure, defective parts were produced and minimal repairs performed to create an in-control state. The conditions are studied in the case of the EPQ model undergoing a backorder owing to rejection of defective parts after a failure. Following production run period, two types of periodic preventive maintenance (PM) exist: imperfect and perfect. The probability of perfect PM being performed depends on the number of imperfect PM performed since the last renewal cycle. For the EPQ model, the optimal run time for minimising the total cost is discussed. Various special cases are considered, including the PM learning effect. Finally, this investigation presents a numerical example to illustrate the effects of PM ability, repair cost and defect number on total costs and production period. This study finds that enhancing maintenance ability reduces production related costs. The product system can be produced more efficiently using a PM program.     

基于METRIC的民机初始备件数量确定及配置模型

针对航空公司备件保障中如何以合理备件费用最大化机队可用度问题,根据维修组织结构及备件送修过程在建模过程中的影响,建立了基于METRIC(multi-echelon technology for recoverable item control)理论的多级库存优化模型。首先,分析了两级库存系统中备件的状态转移流程;其次,根据波音模型的求解过程,对比给出多级库存模型;再次,以备件短缺总量为目标、费用为约束,利用边际分析法进行多级库存优化求解;最后,以某航空公司购买的波音737-800的初始备件为对象,运用METRIC理论对其数量进行优化,并分别以相同费用或相同的总短缺量为条件进行对比,结果证明了METRIC模型的优越性。     

Economic production quantity (EPQ) models under an imperfect production process with shortages backordered

In this paper, we develop economic production quantity (EPQ) models to determine the optimal production lot size and backorder quantity for a manufacturer under an imperfect production process. The imperfect production process is characterised by the fraction of defective items at the time of production γ. The paper considers different cases of the EPQ model depending on (1) whether γ is known with certainty or is a random variable, and (2) whether imperfect items are drawn from inventory (a) as they are detected, (b) at the end of each production period or (c) at the end of each production cycle. Straightforward convexity results are shown and closed-form solutions are provided for the optimal order and backorder quantities for each of the cases we considered. We provide two numerical examples: one in which the defective probability follows a uniform distribution and the second which we assume follows a beta distribution, to illustrate the effects of yield variability and timing of the withdrawal of defectives on the optimal solutions. We obtain similar results for both numerical examples, which show that both the yield variability and the withdrawal timing are not critical factors.     

A production quantity model for imperfect quality items with shortage and screening constraint

This study develops an economic production quantity (EPQ) model and solution procedure for imperfect items with shortage and screening constraint. The Renewal Reward Theorem (RRT) is applied to formulate the exact expected total profit per unit time. We have shown the robustness of our model using time interval as decision variable rather than the traditional order size and backorder quantity. A solution procedure is provided to derive the optimal policy. Special cases of the EOQ/EPQ models can be obtained by taking the parameter limiting values. Numerical examples and sensitivity analysis are presented to verify our results.     

含缺货且缺陷产品可修复的模糊生产库存模型

当生产的产品含有缺陷时,经典的经济生产批量模型不再适用.为更好地解决现实生活问题,提出了一些新的模型.基于检验速度的不同,建立了两种含LR模糊缺陷率、模糊废品率、修复成本且允许缺货的经济生产批量模型.运用符号距离和简单代数方法,确定了模糊模型的最优生产策略.通过理论分析揭示了模型1和模型2的关系.结合算例,分析了产品缺陷率、废品率的模糊性和检验速率对最优生产量和最小成本的影响.     

BASS预测模型与库存控制集成研究

根据短生命周期产品的特征调整BASS扩散模型,并将其应用于短生命周期产品的需求预测,同时考虑产品需求对无形变质和短缺拖后量的影响,进而建立短生命周期产品多周期订货模型。通过算例分析获得短生命周期产品的成熟期开始时间和持续时间,进而求订货次数和订货量,给出多周期最优订货策略。数据实验结果显示基于BASS需求函数的库存控制模型可以提高需求预测精确度,有效降低库存成本,对企业库存控制具有指导意义。     

基于多部件迟单模型的制造企业库存控制策略

针对大型机械制造企业装配阶段物料衔接不畅导致产品延期交货现象,综合考虑服务水平与部门职能限制,建立多部件迟单库存控制模型,并根据企业实际情况确定关键零部件经济批量与再订购点;制定降低缺货率的库存策略,经验证明该策略能将关键零部件缺货率降低至5％以内。