A simple integrated production policy of an imperfect item for vendor and buyer

This article develops a simple approach for determining an optimal integrated vendor–buyer inventory policy for an item with imperfect quality. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. This model is assumed to produce a certain number of defective items during the production process. Items of poor quality detected in the screening process of a lot are sold at a discounted price. The expected annual integrated total cost function is derived and a solution procedure is proposed to determine the optimal policy. Finally, a numerical example is also given to illustrate the solution procedure presented in this article.     

Exact closed-form solutions for “optimal inventory model for items with imperfect quality and shortage backordering”

Wee et al. [Optimal inventory model for items with imperfect quality and shortage backordering. Omega 2007;35(1):7–11] recently contributed an optimal inventory model for items with imperfect quality and shortage backordering. This article revisits their study and applies the well-known renewal-reward theorem to obtain a new expected net profit per unit time. We derive the exact closed-form solutions to determine the optimal lot size, backordering quantity and maximum expected net profit per unit time, specifically without differential calculus. We also solve the same model algebraically from another direction, which has been mentioned, but the process has not been finished yet. The problem parameter effects upon the optimal solutions are examined analytically and numerically.     

航空公司机上周转品多基地库存优化模型

在民航业日益激烈的市场竞争环境下，航空公司对成本控制的精细化管理显得尤为重要。本文基于航空公司的实际背景，针对为旅客提供的机上周转品，建立了一个多基地库存系统的库存优化模型。该模型以系统的总库存成本最小为目标，在考虑需求、回收、调运、安全库存等因素下，决策一个订货周期内的订货及调运方案。基于最优解的分析，在成本参数满足一定条件下，可以得到系统最优的期初订货量；在此基础上，可以将该模型转化为一个网络流模型，参考最小费用最大流算法，设计了一个多项式求解算法来求解该网络流模型，进而得到各基地之间的最优调运量，并证明该算法的最优性；此外，根据期初订货量可行解的范围，设计了一个求解原库存模型的启发式算法。通过实例分析，验证了该模型与两种算法的有效性。     

The effects of the warranty cost on the imperfect EMQ model with general discrete shift distribution

In this paper, we investigate the effect of the warranty cost on optimization of the economic manufacturing quality (EMQ). This is done for a deteriorating process where the production process shifts from the in-control state to the out-of-control state following a general discrete probability distribution. Once the production process goes out of control, the production process produces some defective items. The defective item cost includes reworking and warranty costs. Thus, in order to economically operate a production-inventory system with products sold under warranty, the tradeoffs among the production setup, inventory, and defective item cost, including the reworked cost before sale and the warranty cost after sale, needed to be analysed. This objective in this paper is to determine the production lot size while minimizing the total cost per unit of time per unit of time. Various special cases are presented. Two of them are extensions of results obtained previously in the literature. Finally, a numerical example is given which uses a discrete Weibull probability distribution. Sensitivity analysis of the model with respect to cost and time parameters is also performed.     

An inventory model with lot-size dependent ordering cost

The classical Harris - Wilson inventory model assumes that the ordering cost is constant and does not depend on the quantity ordered. There are, however, many practical situations where this is not true. This paper considers an inventory model where the ordering cost depends on the size of the lot and increases in steps as the lot size increases. An algorithm is developed to determine the economic order quantity and is illustrated by a numerical example.     

An EOQ model with deteriorating items in response to a temporary sale price

In economic order quantity models, it is often assumed that the unit purchase cost is constant. Such an assumption is usually not fulfilled in many practical situations. In practice, it is observed that suppliers sometimes offer temporary price discounts to stimulate demand, boost market share or decrease inventories of certain items. In this paper, a deteriorating inventory model with a temporary sale price has been developed. We shall be concerned with finding the optimal total cost saving for deteriorating items during the special replenishment period. Numerical examples are presented to illustrate the proposed model.     

Optimal inventory model for items with imperfect quality and shortage backordering

In this study, we develop an optimal inventory model for items with imperfect quality and shortage backordering. Such implicit assumption is reasonable in view of the fact that poor-quality items do exist during production. They are usually picked up during the screening process and are withdrawn from stock instantaneously. It is assumed that all customers are willing to wait for new supply when there is a shortage. The analysis shows that our model is a generalization of the models in current literatures. An algorithm and numerical analysis developed show that our model always results in better performance.     

A note on an economic production quantity model and just-in-time production

In this paper an economic production quantity (EPQ) model in which the production rate is variable is studied. An analysis is presented of the impact of a variable production rate on the optimal production quantity and the total relevant cost. It is observed that this EPQ production and inventory system, in which the production rate is close to the demand rate, possesses many characteristics that are similar to a just-in-time (JIT) production system. It is shown that the normal prerequisites and benefits of JIT production can be identified from an analysis of such an EPQ system.     

SETUP REDUCTION AND MACHINE AVAILABILITY

This paper is an extension of Billington, who used the framework of the economic production quantity (EPQ) to model setup cost reduction. In the present paper, we use the EPQ model as a starting point to investigate the nature of setup costs and the effect of setup time reduction on the increase in available capacity. Reducing setup is vital to a company's success because a lengthy changeover of machinery is expensive: it demands long production runs to justify its cost, and these, in turn, lead to excessive inventory and to a slow response to customer needs. As in Billington, setup reduction is modeled as a function of an annual amortized investment. The paper examines the behavior of the setup time, the inventory cost, the lot size, and the freeing up of machine time in the face of a capacity constraint. A solution algorithm is provided to find setup times that minimize the sum of setup and holding cost, subject to a constraint on machine availability. The analysis sheds light on the true nature of setup cost and on the opportunity cost of not reducing setups. In the constrained optimization, the Lagrangian multiplier gives an estimate of the marginal value of adding one time unit of machine capacity, or, alternatively, of reducing one unit of setup time.     

Multi-item production lot-size inventory model with varying order cost under a restriction: A geometric programming approach

In this paper we present a geometric programming approach for determining the inventory policy for multiple items having varying order cost, which is a continuous function of the order quantity, and a limit on the total average inventory of all items. Our model is a generalization of that of Gupta and Gupta for unrestricted single-item order quantity model with varying order cost and assumes the same order cost function. This cost function relates well to real-life situations since it increases as the order quantity increases and, at the same time, it is easy to handle when deducing previous work as special cases of our model since it is easily reducible to a constant. An example is solved to illustrate the method.     

An integrated vendor-buyer cooperative inventory model for items with imperfect quality

This article develops a model to determine an optimal integrated vendor-buyer inventory policy for flawed items in a just-in-time (JIT) manufacturing environment. The aim is to minimize the total joint annual costs incurred by the vendor and the buyer. The proposed model extends the integrated vendor-buyer inventory model by accounting for imperfect quality items. The expected annual integrated total cost function is derived and an analytic solution procedure is proposed to determine the optimal policy. Finally, numerical examples are also given to illustrate the solution procedure presented in this article.     

考虑质量相关性需求与完全预防性维修的EPQ决策

在经典EPQ模型基础上，考虑质量相关性需求和周期性完全预防性维修策略，以单位时间利润最大化为目标，构建经济生产批量的决策模型。在企业单位时间利润模型的构建中，结合质量相关性需求以及设备退化这一实际问题，进行动态预防性维修成本、恢复成本、次品修复成本以及产品需求率的构建。考虑目标函数的复杂性，本文采用遗传算法对模型进行数值求解，并通过与不考虑质量相关性需求的EPQ决策的比较分析，验证其合理性。     

Note on: An integrated vendor–buyer cooperative inventory model for items with imperfect quality

Huang [Huang, C., 2002. An integrated vendor–buyer cooperative inventory model for items with imperfect quality. Production Planning and Control, 13 (4), 355–361] proposes an integrated inventory model which allows a vendor and a buyer to minimise their expected integrated total cost function when the vendor's production process is not perfect. This note identifies two errors in the paper and provides a reformulation of the model.     

Lot sizing in case of defective items with investments to increase the speed of quality control

In many cases the quality of each item in a lot is checked. Speeding up the quality checking process increases the responsiveness of the system and saves cost. The percentage of defective items is a random variable and two models are proposed. In one of the models the system remains always at the same state, while in the other one after each order cycle, the state of the system may change, thus the percentage of defective items may be different in consecutive periods. In both cases the speed of the quality checking is a variable, and procedures are provided to find the optimal lot sizes and screening speed for general and specific investment cost functions. The characteristics of the two model settings will largely be different when the percentage of defective items is high. Among the important managerial insights gained is that a high unit backlogging cost, especially spurs the system to invest more intensively into improving the quality checking process.     

Case study: quality improvement model in a car seat assembly line

In this paper, we develop a quality improvement model based on the structure of classical economic production quantity (EPQ) model. The asymmetrical truncated loss function is used to evaluate the cost of poor quality in a production system. A practical quality improvement case which follows the 6-sigma DMAIC method in a car seat assembly line is discussed to verify the proposed model. Our model provides a fundamental structure for studying the cost of quality improvement in a production system. Based on this model, the management can evaluate the affect of quality investment to generate significant financial return in their production line.     

Multi-item EOQ inventory model with varying holding cost under two restrictions: A geometric programming approach

In this paper we provide a simple method to determine the inventory policy of multiple items having varying holding cost using a geometric programming approach. The varying holding cost is considered to be a continuous function of the order quantity. The EOQ inventory model with constant holding cost and the classical EOQ inventory model without constraints are derived.     

基于现金折扣和延期支付条件下变质产品的补货策略

针对变质产品,考虑产品非瞬时补货的情况下,在允许延期支付且如果零售商提前还款,供应商给予零售商现金折扣优惠的条件下,建立了相应的零售商库存决策模型。对模型进行求解,得出零售商的最优订货周期及最优付款时间。最后,通过具体算例,结合灵敏度分析方法,分析了模型中参数变化对最优订货策略的影响。     

WIP inventories in the simultaneous determination of optimal production and purchase lot sizes

This paper studies an integrated production and purchasing lot sizing model with work-in-process WIP inventory. In this model, the single product is made in a multiprocess manufacturing system. The raw materials are procured from outside sources and are converted gradually into the product. A solution procedure is developed to simultaneously find the optimal lot sizes for the product and its raw materials and the corresponding total relevant cost. It is shown that if the cost of WIP inventory is considered in the production lot size computation, the optimal lot sizes of the product as well as those of the raw materials could be altered significantly.     

A production model for deteriorating items with stochastic preventive maintenance time and rework process with FIFO rule

Due to unreliable production facility and stochastic preventive maintenance, deriving an optimal production inventory decision in practice is very complicated. In this paper, we develop a production model for deteriorating items with stochastic preventive maintenance time and rework using the first in first out (FIFO) rule. From our literature search, no study has been done on the above problem. The problem is solved using a simple search procedure; this makes it more practical for use by industries. Two case examples using uniform and exponential distribution preventive maintenance time are applied. Examples and sensitivity analysis are conducted for each case. The results show that rework and preventive maintenance time have significant affected the total cost and the optimal production time. This provides helpful managerial insights to help management in making smart decisions.     

基于数量折扣的改良品供应链协调策略

本文以改良品供应链为研究对象,采用数量折扣作为激励机制,研究了一个供应商和一个零售商构成的改良品二级供应链在批量对批量供应模式假设下的协调问题,以达到协调改良品供应链的目的。通过算例分析,发现基于数量折扣的改良品供应链协调策略有效地实现了改良品供应链的协调。最后对改良品供应链的改良率和市场需求率进行了敏感性分析,研究了它们对供应链的影响。