WARRANTY COST ESTIMATION: A GOAL PROGRAMMING APPROACH

This paper proposes a goal programming approach to the warranty cost estimation problem. Past research on this topic has mostly dealt with a single objective—the minimization of the warranty reserve cost or the maximization of profit. A more realistic approach to warranty cost problems could, however, involve several goals, some of which might be conflicting to others. In this paper, three goals are prioritized. The goals considered are minimization of warranty reserve cost per unit, offering a minimum level of warranty time based on an allowable proportion of failures within the warranty period, and capturing a minimum specified market share of the product. An example is illustrated using the proposed formulation, and goal achievements are discussed.     

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.     

Optimal policy for imperfect inspection in discrete time

Abstract

The problem of finding the optimal inspection interval for a fallible system that operates in discrete time when inspection is subject to errors was addressed. A Markov chain model of the system state was developed to formulate the objective function, which is the minimum expected total cost per lime unit. A numerical search procedure was used to find local minima for a representative range of parameter values. The objective function turned out to be quite insensitive to deviations in the inspection interval in the neighbourhood of the minimum, so an approximate method based on curve fitting was developed and tested, yielding good results in the representative range.     

静态市场下考虑重复购买的价格和质保期联合决策

本文研究静态市场下的以质保期和价格为决策变量的最优控制决策问题。考虑了初次购买和重复购买两个过程以及重复购买过程是否受价格影响两种情况。模型中的生产成本考虑了产品生产过程中的学习效应, 质保成本使用了免费维修质保策略并假设产品两次故障之间的时间服从韦伯分布。在完整建模的基础上, 应用最大化原理对基本模型进行了求解, 之后本文给出了一种基本模型的具体应用场景, 并运用Lingo11软件进行了数值试验。最后对主要研究结论进行了应用讨论。     

A decomposition technique for quantifying real process performance

A decomposition technique for quantifying the impacts of changes in product mix and process performance on aggregate process-related indicators is presented. Through application of the technique, the real performance of a process can be quantified. Changes in real performance over time can be monitored to provide useful information for process evaluation and production planning. Two case studies, one related to the aggregate defective rate for an assembly line of an integrated circuit fabrication plant and the other to the aggregate inventory turnover for a tyre distribution company, are presented to illustrate the application of the technique.     

A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.     

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。     

End‐of‐Life Inventory Decisions for Consumer Electronics Service Parts

We consider a consumer electronics manufacturer's problem of controlling the inventory of spare parts in the final phase of the service life cycle. The final phase starts when the part production is terminated and continues until the last service contract or warranty period expires. Placing final orders for service parts is considered to be a popular tactic to satisfy demand during this period and to mitigate the effect of part obsolescence at the end of the service life cycle. Previous research focuses on repairing defective products by replacing the defective parts with properly functioning spare ones. However, for consumer electronic products there typically is considerable price erosion while repair costs stay steady over time. As a consequence, there might be a point in time at which the unit price of the product drops below the repair costs. If so, it is more cost effective to adopt an alternative policy to meet service demands toward the end of the final phase, such as offering customers a new product of the similar type or a discount on a next generation product. This study examines the cost trade‐offs of implementing alternative policies for the repair policy and develops an exact expression for the expected total cost function. Using this expression, the optimal final order quantity and switching time from repair to an alternative policy can be determined simultaneously. Numerical analysis of a real world case sheds light on the cost benefits of these policies and also yields insights into the quantitative importance of the various cost parameters.     

Optimal control of an accelerated drifting process

This paper considers a production process in which product quality follows a stochastic drifting process during production. The drift time is assumed to be dependent on the process state and the deterioration rate increases when the process state deviates from its target. The discrete geometric jump model is studied first and then continuous approximation is examined for the drifting process. Optimal adjustment level is derived from a cost model.     

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.     

考虑信用销售的改良品联合采购决策

信用销售能够提升生产企业竞争力、扩大经营规模,帮助销售企业缓解资金压力,对供应链的运作效率有较大影响,成为供应链管理研究的重要课题之一。考虑在单一供应商和多个零售商组成的二级改良品供应链中,供应商提供延迟支付作为信用销售手段,分别建立零售商独立采购和联合采购的最小单位时间总成本函数,通过比较最小单位时间总成本函数得到联合采购优于独立采购的条件。将改良品联合采购的成本分配问题构造为改良品联合采购博弈,给出博弈具有的基本性质,并设计一种基于博弈核心的成本分配方法。通过数值算例和敏感性分析验证了文中所构建模型的正确性。     

生产性企业组织学习最优控制模型及其理论分析

运用最优控制理论研究生产性企业组织学习活动的动态最优决策问题.以企业的概念性学习投资率和操作性学习投资率为决策变量,累积知识量、生产率、单位成本和废品率等为状态变量,计划期内的总利润为指标函数,建立了一个最优控制模型,其特点在于规范地描绘概念性学习和操作性学习对企业累积知识量、生产率、单位成本、质量以及企业利润的动态影响.根据生产性企业组织学习和生产经营的实际情况,提出了一些定量化表达的假设和定义.在假设和定义的基础上利用最大值原理分析了所建立的模型,获得了关于动态最优概念性学习投资策略和操作性学习投资策略性质的一些结论,将这些结论与实际问题相结合,指出了在生产性企业组织学习实践上的含义.     

Optimal price,warranty length and production rate for free replacement policy in the static demand market

In the present paper, a decision model is developed for producers in the static demand market to determine the optimal price, warranty length and production rate of a product to maximize profit based on the pre-determined life cycle. The free renewal warranty policy is considered under which failed products are renewed before the end of warranty length at no cost to consumers. The expected number of renewals based on warranty length is derived for Weibull life distributed products. The objective function includes both demand and cost functions, where production cost, warranty cost and inventory cost are involved. A solution approach using the maximum principle is described, and is applied to two specific cases of markets. The first case of market considers positive discount rate, and the second case of market considers zero discount rate. The economic sensitivity analysis is conducted to evaluate the effect of model parameters on the optimal solution. Some conclusions are drawn based on the sensitivity analysis.     

Discrete Sequential Search with Group Activities*

Equipment failures can have significant implications in terms of cost and customer satisfaction. Reducing the time required to find the cause of a failure can provide large cost savings and help preserve customer goodwill. Single‐item discrete sequential search models can be used to sequence the tasks in diagnostic search to minimize the expected time required to find the cause of the failure. We increase the utility of the single‐item discrete sequential search model by developing a formulation that includes simple precedence relationships as well as sequence dependent relationships defined by group activities. This formulation can be applied to a number of other problems including determining the sequence for multiple quality control tests on an item, scheduling oil well workovers to maximize the expected increase in oil production, and sequencing tasks in a research project where there is a technological risk associated with each task.     

劣势耐用品厂商的产品质保期与质保服务投入策略研究

在实际中，消费者购买耐用品时均同时获得厂商提供的质保服务，由于产品质保服务影响着消费者的产品使用效用，因此耐用品定价、质保期和产品质保服务投入是影响厂商利润的主要因素。考虑双寡头市场环境下，建立微分博弈模型讨论单位产品质保服务投入和产品质保期对双寡头厂商均衡价格的影响。结论表明双寡头厂商的单位产品质保服务投入越高、质保期越长，均衡价格越高；但单位产品保服务投入与质保服务对消费者效用影响系数的关系影响着竞争对手在均衡价格的变化趋势；劣势的低质量厂商可以通过增加单位产品质保服务投入策略或延长质保期的策略实现在均衡下与高质量厂商以同等价格销售耐用品，但劣势厂商增加单位产品质保服务投入策略要优于延长质保期策略。最后，利用数值分析进一步验证了所得结论的有效性。     

Burn-in Time and Estimation of Change-Point with Weibull-Exponential Mixture Distribution*

Many industrial products have three phases in their product lives: infant-mortality, normal, and wear-out phases. In the infant-mortality phase, the failure rate is high, but decreasing; in the normal phase, the failure rate remains constant; and in the wear-out phase, the failure rate is increasing. A burn-in procedure may be used to reduce early failures before shipping a product to consumers. A cost model is formulated to find the optimal burn-in time, which minimizes the expected sum of manufacturing cost, burn-in cost, and warranty cost incurred by failed items found during the warranty period. A mixture of Weibull hyperexponential distribution with shape parameter less than one and exponential distribution is used to describe the infant-mortality and the normal phases of the product life. The product under consideration can be either repairable or non-repairable. When the change-point of the product life distribution is unknown, it is estimated by using the maximum-likelihood estimation method. The effects of sample size on estimation error and the performance of the model are studied, and a sensitivity analysis is performed to study the effects of several parameters of the W-E distribution and costs on the optimal burn-in time.     

An optimal set-up policy for control charts

A model of a production process, using an unscheduled set-up policy and utilizing fraction-defective control charts to control current production is developed taking into consideration all the costs; namely cost of sampling, cost of not detecting a change in the process, cost of a false indication of change, and the cost of re-adjusting detected changes. The model is based on the concept of the expected time between detection of changes calling for set-ups. It is shown that the combination of unscheduled set-ups and control charts can be utilized in an optimal way if those combinations of sample size, sampling interval and extent of control limits from process average will be used that provide the minimum expected total cost per unit of time. The costs when a production process with unscheduled set-up is controlled by using the appropriate optimal control charts is compared to the cost of a production process using scheduled set-ups at optimum intervals in conjunction with its appropriate control charts. This comparison indicates the criteria for selecting production processes with scheduled set-ups using optimal set-up intervals over unscheduled set-ups. Suggestions are made to evaluate the optimal process set-up strategy and the accompanying decision parameters, for any specific cost data, by use of computer enumeration.     

The effects of learning and forgetting on the optimal lot size quantity of intermittent production runs

This paper studies the effects of learning and forgetting on the production lot size problem with infinite and finite planning horizons. It is assumed that the determination of the economic manufactured quantity (EMQ) in the succeeding production run is dependent on: (1) the maximum inventory accumulated prior to interruption; (2) the length of the interruption period which incurs total forgetting; and (3) the level of experience in equivalent units remembered at the start-up of the next production run. The optimum operating inventory doctrines is obtained by trading off procurement cost per unit time and the inventory carrying cost per unit time, so that their sum will be a minimum. A numerical example is presented to demonstrate the application of learning and forgetting to the determination of the EMQ.     

An optimal replenishment model for inventory items with normally distributed deterioration

This paper deals with the inventory replenishment problem for deteriorating items with normally distributed shelf life, continuous time-varying demand, and shortages under the inflationary and time discounting environment. The reasons of choosing normal are twofold: it is one of the most important probability phenomena in the real world due to the classical central limit theorem, and it is also one of the most commonly used lifetime distributions in reliability contexts. The problem is formulated as a dynamic programming model and solved by numerical search techniques. The solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of the future costs associated with the system is minimized. In the extensive experiments, we validate the model, demonstrate the optimal replenishment schedule and lot-size, and carry out a comparative study to ascertain its contribution. In addition, sensitivity analysis was provided to help identify the most crucial factors that affect system performance. The experimental result shows that the deteriorating problem solved by an appropriate model (i.e. the proposed normal model) can save the total cost up to 2% approximately. It also identifies that the magnitudes of purchase cost per unit and demand rate are the most significant parameters that affect the replenishment decisions and cost.