Optimal maintenance policy and length of extended warranty within the life cycle of products

This paper investigates maintenance policy and length of extended warranty for repairable products from the seller’s viewpoint. When the product failed within the base and extended warranty periods, product failures are rectified using minimal repair. To reduce the number of product failures, the seller performs imperfect preventive maintenance (PM) actions when the age of the product reaches a controlled-limit within the base and extended warranty periods. After the base warranty period expires, the seller gives a discount of purchasing extended warranty expense if the consumer purchases the extended warranty for products. Under this maintenance scheme, the mathematical model of profit is constructed and then the optimal controlled-limit, the number and degree of PM and the length of extended warranty are obtained such that the expected total profit is maximized for the seller. Finally, numerical examples are given to illustrate the influences of the optimal length of the extended warranty and the maintenance policy for profit model.     

Preventive-maintenance policy for leased products under various maintenance costs

This paper investigates the effects of preventive-maintenance cost functions on the optimal preventive-maintenance policy for a leased product with Weibull life-time distribution. During the lease period, any product failures are rectified by minimal repairs and may incur a penalty to the lessor, if the time duration for performing a minimal repair exceeds a pre-specified time limit. To reduce repair costs and possible penalty, preventive-maintenance actions are scheduled in the lease contract. The objective of this paper is to derive the optimal preventive-maintenance schedule and maintenance degrees such that the expected total cost is minimized. Some structural properties of the optimal policy are obtained and an efficient algorithm is provided to search for the optimal policy. For the cases where the preventive maintenance cost is a constant or a linearly increasing function, the effects of the preventive-maintenance cost function on the optimal policy are investigated in detail both theoretically and numerically.     

Ordering,wholesale pricing and lead-time decisions in a three-stage supply chain under demand uncertainty

This paper develops a game theoretic model of a three-stage supply chain consisting of one retailer, one manufacturer and one subcontractor to study ordering, wholesale pricing and lead-time decisions, where the manufacturer produces a seasonal/perishable product. We explicitly model the effects of the lead-time and the length of selling season on both demand uncertainty and inventory-holding costs. We present the equilibrium outcome of the decentralized supply chain. When the lead-time increases, we find that the retailer increases the order quantity, the manufacturer offers a lower unit-wholesale price and the subcontractor decreases its unit-wholesale price if the manufacturer subcontracts part of the retailer’s order. In the endogenous lead-time setting, we illustrate the effects of some factors such as unit holding cost and capacity on the equilibrium outcome. We find that a higher unit holding cost implies a lower optimal lead-time and order quantity while higher unit-wholesale prices; the basic demand uncertainty increases the optimal lead-time and order quantity while decreases the unit-wholesale prices. The effects of distribution form on equilibrium outcome/profits are investigated by employing a numerical example. The profit loss of decentralization decreases (increases) with the basic demand uncertainty and manufacturer’s capacity (mean demand).     

Optimal maintenance policies for systems subject to a Markovian operating environment

Many stochastic models of repairable equipment deterioration have been proposed based on the physics of failure and the characteristics of the operating environment, but they often lead to time to failure and residual life distributions that are quite complex mathematically. The first objective of our study is to investigate the potential for approximating these distributions with traditional time to failure distribution. We consider a single-component system subject to a Markovian operating environment such that the system’s instantaneous deterioration rate depends on the state of the environment. The system fails when its cumulative degradation crosses some random threshold. Using a simulation-based approach, we approximate the time to first failure distribution for this system with a Weibull distribution and assess the quality of this approximation. The second objective of our study is to investigate the cost benefit of applying a condition-based maintenance paradigm (as opposite to a scheduled maintenance paradigm) to the repairable system of interest. Using our simulation model, we assess the cost benefits resulting from condition-based maintenance policy, and also the impact of the random prognostic error in estimating system condition (health) on the cost benefits of the condition-based maintenance policy.     

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example.     

An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate

In this paper, we formulate a deteriorating inventory model with stock-dependent demand by allowing preservation technology cost as a decision variable in conjunction with replacement policy. Moreover, it is assumed that the shortages are allowed and partially backlogged, depending on the length of the waiting time for the next replenishment. The objective is to find the optimal replenishment and preservation technology investment strategies while maximizing the total profit per unit time. For any given preservation technology cost, we first prove that the optimal replenishment schedule not only exists but is unique. Next, we show that the total profit per unit time is a concave function of preservation technology cost when the replenishment schedule is given. We then provide a simple algorithm to find the optimal preservation technology cost and replenishment schedule for the proposed model. Finally, we use some numerical examples to illustrate the model.     

Lease-based consistency schemes in the web environment

There are many methods to maintain consistency in the distributed computing environment. Ideally, efficient schemes for maintaining consistency should take into account the following factors: lease duration of replicated data, data access pattern and system parameters. One method used to supply strong consistency in the web environment is the lease method. During the proxy’s lease time from a web server, the web server can notify the modification to the proxy by invalidation or update. In this paper, we analyze lease protocol performance by the varying update/invalidation scheme, lease duration and read rates. By using these analyses, we can choose the adaptive lease time and proper protocol (invalidation or update scheme of the modification for each proxy in the web environment). As the number of proxies for web caching increases exponentially, a more efficient method for maintaining consistency needs to be designed. We also present three-tier hierarchies on which each group and node independently and adaptively choose the proper lease time and protocol for each proxy cache. These classifications of the scheme make proxy caching adaptive to client access pattern and system parameters.     

Optimal control of investments for quality of supply improvement in electrical energy distribution networks

This paper considers the problem of deciding multi-period investments for maintenance and upgrade of electrical energy distribution networks. After describing the network as a constrained hybrid dynamical system, optimal control theory is applied to optimize profit under a complex incentive/penalty mechanism imposed by public authorities. The dynamics of the system and the cost function are translated into a mixed integer optimization model, whose solution gives the optimal investment policy over the multi-period horizon. While for a reduced-size test problem the pure mixed-integer approach provides the best optimal control policy, for real-life large-scale scenarios a heuristic solution is also introduced. Finally, the uncertainty associated with the dynamical model of the network is taken care of by adopting ideas from stochastic programming.     

基于序贯博弈的装备制造业复杂产品研发补贴和关税决策

增大国内装备制造业的研发投入和引入国外产品带来的研发溢出可提升国内装备制造业科技水平,但同时带来了企业的研发成本负担和国外产品抢占国内市场的问题,因此政府在其中的研发补贴和关税政策调控显得尤为迫切.探究政府研发补贴和关税政策对存在研发溢出的国外装备制造商和国内装备制造商进行序贯博弈时的市场份额、利润和研发水平的影响问题.进一步分析政府以社会福利最大为目标时,政府的最优决策并对关键因素进行敏感性分析.最后通过数值扩展验证结论的稳健性.研究发现:研发补贴系数或关税增大都会提高(降低)国内制造商(国外制造商)的产量、利润和研发水平;政府以社会福利最大进行决策时,随着两种产品竞争强度的增大,总的研发补贴会减小,而单位研发补贴先减后增,关税先增后减.研发成本系数越高,关税和单位研发补贴会越高,但总的研发补贴会减少.     

Cost optimization model following extended renewing two-phase warranty

In this paper, we study an extended warranty model under which the customer is offered an additional warranty period after the original two-phase warranty expires. Under the original two-phase warranty, the warranty period is divided into two non-overlapping subintervals, one of which is for replacement warranty, and the other is for minimal repair warranty. If the system failure occurs during the original warranty period, the failed system is either replaced or minimally repaired by the manufacturer, and if the failure occurs during the extended warranty period, only the minimal repair is conducted. For the system failure during the replacement warranty period, the failed system is replaced by a new one, and the warranty term is renewed anew. Following the expiration of extended warranty, the customer is solely responsible for maintaining the system for a fixed length of time period and replaces the system at the end of such a maintenance period. During the maintenance period, only the minimal repair is given for each system failure. Such a maintenance model can be considered as a generalization of several existing maintenance models which can be obtained as special cases. The main purpose of this article is to determine, from the customer’s perspective, the optimal length of maintenance period after the extended warranty expires. As the criterion to determine the optimal replacement strategy, we adopt the expected cost rate per unit time during the life cycle of the system. Given the cost structures incurred during the life cycle of the system, we formulate the expected cost and the expected length of life cycle to obtain the expected cost rate. The uniqueness of optimal solution for the decision variable is verified when the life distribution of the system shows an increasing failure rate. Numerical examples are provided to illustrate the proposed optimal replacement strategy.     

过度自信和需求不确定性对库存系统的影响

研究过度自信和需求不确定性对库存系统的影响。通过引入一个均值增加、方差缩小的变换来定量刻画决策者的过度自信水平,得到系统最优订货量和最优利润关于过度自信水平和单位缺货惩罚的单调性。证明随机大的需求会导致较高的最优订货批量,系统最优订货量在割准则序意义下具有随机单调性,并给出了比较系统最优订货量的充分或充分必要条件。进一步,运用标准化随机变量的变换证明了在高利润环境下系统利润将随着需求可变性的增加而减少。     

Preventive maintenance scheduling for repairable system with deterioration

Maintenance as an important part in manufacturing system can keep equipment in good condition. Many maintenance policies help to decrease the unexpected failures and reduce high operational cost such as conventional preventive maintenance. But these conventional preventive maintenance policies have the same time interval T that may easily neglect system’s reliability, because the system deteriorates with increased usage and age. Hence, this study has developed a reliability-centred sequential preventive maintenance model for monitored repairable deteriorating system. It is supposed that system’s reliability could be monitored continuously and perfectly, whenever it reaches the threshold R, the imperfect repair must be performed to restore the system. In this model, system’s failure rate function and operational cost are both considered by the effect of system’s corresponding condition, which helps to decide the optimal reliability threshold R and preventive maintenance cycle number. Finally, through case study, the simulation results show that the improved sequential preventive maintenance policy is more practical and efficient.     

可用度约束条件下的设备不完美预防维修策略

针对2M1B生产系统,基于设备实际维修情况,提出了故障设备不完美预防维修策略。首先,考虑设备随时间不断劣化的情况,基于准更新过程,建立了生产周期内设备随机故障次数的表达式,计算了设备维修总费用。其次,通过分析缓冲区内库存的变化轨迹,以生产周期内设备随机故障次数为基础,计算了缓冲区库存费用,综合设备维修费用和缓冲区库存费用,构建了周期内生产总成本模型。以满足系统最低要求的可用度水平为约束条件,以预防维修周期和缓冲区库存量为决策变量,以生产周期内单位时间总成本为目标函数,通过离散迭代算法获得最优预防维修周期和此周期下的最佳缓冲区库存量。最后,通过数值分析验证了模型的有效性,为制定最佳维修策略提供了有效依据。     

基于二阶段时间延迟的多产品生产系统生产与维修联合优化研究

针对多产品生产部件串联系统的生产和维修问题进行了研究,提出了基于二阶段时间延迟的联合优化模型。首先,基于生产周期分段理论,将整个周期等分成若干单位时间段,生产与维修共用每段时间,且若干时间段后采取一次预防维修。其次,考虑生产系统的实际生产时间、可用生产时间和维修耗费时间,建立了生产计划与维修计划总成本模型。其中,维修计划考虑缺陷和故障维修费用、维修检查费用,以及非正常状态下设备运行可能产生的不合格产品损失费用;生产计划考虑生产成本、库存成本、延期未交货成本和维修停机后恢复生产的设备启动成本。最后,通过算例分析,计算最优预防维修周期和各单位时间段各产品产量,验证了模型的有效性。     

“报童问题”中风险偏好下的条件风险值及其优化

建立了报童随机利润的分布函数,得到任意风险水平下的VaR解析表达式或应满足的条件。考虑缺货成本,针对风险规避和风险偏爱两种情况,分别建立不同订购量和风险水平下的条件风险值模型,并将模型中对利润变量的积分转换为对随机需求变量的积分,解决了模型中因包含VaR变量而求解困难的问题。分析了给定风险水平下的最优决策,讨论了缺货成本为0的特殊情形。风险中性报童的期望利润与最优决策可由风险规避或风险偏爱的相应公式推导。最后对下一步的研究方向进行了展望。     

基于价格折扣的有条件延期支付策略

在延期支付及价格折扣策略下,建立以供货商为主导的主从斯坦伯格模型,从供货商的角度研究基于价格折扣的有条件延期支付策略设置问题.通过对模型的理论分析和模型求解,给出了各情形下供货商的延期支付策略、零售商的最佳订单量和货款的最佳支付时间.数值结果表明,此策略在激励零售商加大订单量的同时,还能吸引其尽早交付货款,从而加快供货商的资金周转,实现双赢.     

动态定价策略下的精确库存成本建模与优化

提出一种更接近实际的需求率公式,在式中同时考虑了价格和出厂时间对客户需求率的影响.基于新的需求率公式,建立了动态定价策略下的精确库存持有成本模型和库存商品的利润函数.注意到利润函数的复杂性,使用遗传算法分析了利润函数的性质,得出最优定价时间、定价价格和最大利润的关系,并分析了库存持有成本变化和消费者购买欲望变化对各定价参数的影响.     

Determination of production run time and warranty length under system maintenance and trade credits

Manufacturers offer a warranty period within which they will fix failed products at no cost to customers. Manufacturers also perform system maintenance when a system is in an out-of-control state. Suppliers provide a credit period to settle the payment to manufacturers. This study considers manufacturer's production and warranty decisions for an imperfect production system under system maintenance and trade credit. Specifically, this study uses the economic production quantity to model the decisions under system maintenance and trade credit. These decisions involve how long the production run time and warranty length should be to maximise total profit. This study provides lemmas for the conditions of optimality and develops a theorem and an algorithm for solving the problems described. Numerical examples illustrate the solution procedures and provide a variety of managerial implications. Results show that simultaneously determining production and warranty decisions is superior to only determining production. This study also discusses the effects of the related parameters on manufacturer's decisions and profits. The results of this study are a useful reference for managerial decision-making and administration.     

A neural network approach for optimal software testing and maintenance

In this paper, we propose a neural network-based model for optimal software testing and maintenance policy, where the software testing environment and the operational environment are characterized by an environmental factor. We also present a systematic study for defect detection and correction processes. In our proposed approach, we consider the logistic growth curve model and the constant correction time for defect prediction. Then, we estimate the jointly optimal software testing period and maintenance limit via minimization of a software cost function that takes into account the environmental factor and the imperfect fault removal. More precisely, the total expected cost is formulated via a discrete-type software reliability model based on the difference between operational environments, imperfect defect removal, and defect correction process. Experimental results on a real software data set are presented to demonstrate the effectiveness of the proposed approach in defect prediction as well as in determining the jointly optimal testing period and planned maintenance limit.     

The value of modeling with reference effects in stochastic inventory and pricing problems

We analyze a periodic review inventory system in which the random demand is contingent on the current price and the reference price. The reference price captures the price history and acts as a benchmark against which the current price is compared. The randomness is due to additive and multiplicative random terms. The objective is to maximize the discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We study three key issues using numerical computation and simulation. First, we study the effects of reference price mechanism on the total expected profit. It is shown that high dependence on a good history increases the profit. Second, we investigate the value of dynamic programming and show that the firm that ignores the dynamic structure suffers from the revenue. Third, we analyze the value of estimating the correct demand model with reference effects. We observe that this value is significant when the inventory related costs are low.