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.     

Design of Extended Warranties in Supply Chains under Additive Demand

We study the design of extended warranties in a supply chain consisting of a manufacturer and an independent retailer. The manufacturer produces a single product and sells it exclusively through the retailer. The extended warranty can be offered either by the manufacturer or by the retailer. The party offering the extended warranty decides on the terms of the policy in its best interest and incurs the repair costs of product failures. We use game theoretic models to answer the following questions. Which scenario leads to a higher supply‐chain profit, the retailer offering the extended warranty or the manufacturer? How do the optimum price and extended warranty length vary under different scenarios? We find that, depending on the parameters, either party may provide better extended warranty policies and generate more system profit. We also compare these two decentralized models with a centralized system where a single party manufactures the product, sells it to the consumer, and offers the extended warranty. We also consider an extension of our basic model where either the manufacturer or the retailer resells the extended warranty policies of a third party (e.g., an independent insurance company), instead of offering its own policy.     

Retail Strategies for Extended Warranty Sales and Impact on Manufacturer Base Warranties

Consider two competing manufacturers selling their products through the same retailer. If this retailer derives profits from extended warranty sales, the manufacturers face a dilemma in setting their base warranties. Although they have incentive to increase their warranties to make their products attractive to consumers, the retailer might prefer selling lower‐warranty products to enhance extended warranties sales. We develop a stylized model to determine and analyze optimal manufacturer and retailer strategies in this setting. Consistent with the ongoing decline in warranties for products that are sold through independent retailers, we show that these interactions exert downward pressure on manufacturer warranties. Rather than pitching the extended warranty at the checkout after customers have selected a certain product, we find that retailers can often benefit from inducing simultaneous consideration of product and extended warranty characteristics, for example by posting extended warranty information right on the product shelf.     

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。     

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。     

Simultaneous Determination of Joint Product Cost Allocations and Cost-Plus Prices*

Use of the net realizable value approach for joint manufacturing cost allocations requires knowledge of selling prices of joint products. However, joint product selling prices themselves are functions of the allocated costs under a cost-plus pricing policy. In this case, it is necessary to determine joint cost allocations and joint product prices simultaneously. This paper applies a nonlinear programming (NLP) approach to simultaneously determine the optimal joint production decision, joint product cost-plus prices, and joint cost allocations using the net realizable value method. The NLP solution provides not only the optimal joint production and pricing decisions, but also the necessary conditions for such optimal decisions.     

带保修期的寿命型产品多属性招标采购机制设计——以大型医疗设备为例

产品的期望寿命是重要的质量属性之一,事前不可观察且不可验证,直接对该质量属性进行投标没有意义。针对此问题,以大型寿命型医疗设备招标采购为例,利用拍卖机制设计理论建立了一类具有信号传递功能的多属性招标采购模型。模型确定了最优投标规则,包括设备最优期望寿命投标、最优保修期投标与最优价格支付。模型确立了甄别投标企业技术类型与传递产品质量可靠性信息的机制。研究结果表明:首先该机制满足参与约束与激励相容约束,投标企业分别按自身期望利润最大化进行投标;其次该最优机制能保证企业承诺的保修期与期望寿命正相关,能保证技术类型最高、所提供产品期望寿命最大(保修期最长)的企业中标,并且中标企业创造相对来说最高的社会福利。构造一个算例说明新的多属性招标采购机制在实践中易于操作,是可实施的。当质量指标存在不可观察和不可验证的维度时,相关研究为解决多属性招标采购问题提供了一个新思路。     

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.     

Competitive and Collaborative Quality and Warranty Management in Supply Chains

Product quality and product warranty coverage are two important and closely related operational decisions. A longer warranty protection period can boost sales, but it may also result in dramatically increased warranty cost, if product quality is poor. To investigate how these two decisions interact with each other and influence supply chain performance, we develop a single‐period model with a supplier that provides a product to an original equipment manufacturer, which in turn sells it to customers. Customer demand is random and affected by the length of the product warranty period. Warranty costs are incurred by both the supplier and the manufacturer. We analyze two different scenarios based on which party sets the warranty period: manufacturer warranty and supplier warranty. Product quality is controlled by the supplier, and the manufacturer determines the ordering quantity. We analyze these decentralized systems and provide the structural properties of the equilibrium strategies. We also compare the results of centralized and decentralized systems and identify the conditions under which one system provides a longer warranty and better product quality than the other. Our numerical study further shows that, in decentralized settings, when the warranty period is determined by the firm sharing the larger proportion of total warranty costs, the supply chain can achieve greater system‐wide profit. Both parties can therefore benefit from properly delegating the warranty decision and sharing the resulting additional profit. We further design a supplier‐development and buy‐back contract for coordinating decentralized supply chains. Several extensions are also discussed.     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

Economic Lot Scheduling Problem with Returns

Motivated by a case study of a company that produces car parts, we study the multi‐product economic lot scheduling problem for a hybrid production line with manufacturing of new products and remanufacturing of returned products. For this economic lot scheduling problem with returns (ELSPR), we consider policies with a common cycle time for all products, and with one manufacturing lot and one remanufacturing lot for each product during a cycle. For a given cycle time, the problem is formulated as a mixed integer linear programming (MIP) problem, which provides the basis for an exact solution. The application of this model for one of the core products of the case study company indicates a 16% reduction in cost compared to the current lot scheduling policy.     

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.     

Promoting Seismic Retrofit Implementation Through “Nudge”: Using Warranty as a Driver

This article proposes a new type of warranty policy that applies the “nudge” concept developed by Thaler and Sunstein to encourage homeowners in Japan to implement seismic retrofitting. Homeowner adaptation to natural disasters through loss reduction measures is known to be inadequate. To encourage proactive risk management, the “nudge” approach capitalizes on how choice architecture can influence human decision‐making tendencies. For example, people tend to place more value on a warranty for consumer goods than on actuarial value. This article proposes a “warranty for seismic retrofitting” as a “nudge” policy that gives homeowners the incentive to adopt loss reduction measures. Under such a contract, the government guarantees all repair costs in the event of earthquake damage to the house if the homeowner implements seismic retrofitting. To estimate the degree to which a warranty will increase the perceived value of seismic retrofitting, we use field survey data from 1,200 homeowners. Our results show that a warranty increases the perceived value of seismic retrofitting by an average of 33%, and an approximate cost‐benefit analysis indicates that such a warranty can be more economically efficient than an ex ante subsidy. Furthermore, we address the failure of the standard expected utility model to explain homeowners’ decisions based on warranty evaluation, and explore the significant influence of ambiguity aversion on the efficacy of seismic retrofitting and nonanalytical factors such as feelings or trust.     

基于消费者情绪效用下劣势耐用品企业的延保服务策略有效性研究

基于消费者情绪效用对耐用品企业延保服务策略有效性的影响，构建双寡头微分博弈模型，研究耐用品企业的延保服务策略对产品均衡价格的影响特征，并进一步讨论了劣势耐用品企业延保服务策略的有效性。结论表明：服务投入在不同范围内，产品均衡价格随着服务投入的增加而变化的特征不同；高质量企业的延保最优价格与服务投入成递增关系变化，而低质量企业的延保最优价格随服务投入增加的变化特征还与其故障率、延保期等因素有关。低质量耐用品企业的服务投入满足大于1时，采取增加服务投入缩小与高质量产品的价格差是有效的；只有在一定条件下，采取延长质保期、延保期策略缩小价格差才是有效的。最后，利用数值分析法进一步验证了结论的合理性。研究可为耐用品企业有效实施延保服务策略提供决策支持。     

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.     

Ordering,Pricing, and Lead‐Time Quotation Under Lead‐Time and Demand Uncertainty

In this article, we study the newsvendor problem with endogenous setting of price and quoted lead‐time. This problem can be observed in situations where a firm orders semi‐finished product prior to the selling season and customizes the product in response to customer orders during the selling season. The total demand during the selling season and the lead‐time required for customization are uncertain. The demand for the product depends not only on the selling price but also on the quoted lead‐time. To set the quoted lead‐time, the firm has to carefully balance the benefit of increasing demand as the quoted lead‐time is reduced against the cost of increased tardiness. Our model enables the firm to determine the optimal selling price, quoted lead‐time, and order quantity simultaneously, and provides a new set of insights to managers.     

不同市场能力下的“电商—平台—物流”在线销售系统的决策研究

近年来,随着互联网的快速发展,市场上衍生出了一些在线销售网站。考虑了一个包含电商卖家、电商平台和物流公司的在线销售系统模型,其中需求依赖于产品价格、平台和物流服务水平。研究了当物流、平台同时决策时,在线销售系统中电商卖家和平台、物流之间的不同市场能力结构问题。考虑了3种不同市场能力的分散决策模型:(1)物流-平台Stackelberg模型;(2)电商Stackelberg模型;(3)Nash模型。相关的均衡解和最优利润被得到。研究结果表明,在不同的市场能力结构下,当物流公司和平台同时决策时,即使他们的服务投入不相同,但最优收费相同。市场能力结构对在线销售成员和消费者有重要的影响。对电商而言,当市场能力较高时,会制定较低的零售价格,并获得最多的利润,同时能够提升消费者购买的积极性;当市场能力较低时,电商会制定较高的零售价格,并获得最少的利润。对平台和物流公司而言,当市场能力较高时,会制定比较高的收费,同时付出较少的努力,但并不能获得最高利润,同时会打击消费者的积极性;但是,当市场能力较低时,他们一定获得最少的利润。在Nash模型中,平台和物流公司会付出最大的努力,同时获得最大的利润,而整个在线销售系统的总利润也是最多。在物流-平台Stackelberg模型中,平台和物流公司付出的努力最少,而整个在线销售系统的总利润也最少。     

竞争市场上保修期与价格的联合质量信号传递作用

虽然顾客重视产品的质量（可靠性），但其在做出购买决策时往往不能完全掌握产品的质量信息。不同质量的产品可能具有不同生产和保修成本，因此保修期和销售价格可以成为传递产品质量的有效信号。考虑市场上存在相互竞争的两个生产商：在位者和新进者，顾客了解在位者的产品质量信息但不了解新进者的质量状况。研究并比较了仅保修期作为单质量信号、保修期和价格同时作为质量信号时，市场实现分离均衡的条件，以及新进者的保修期设计与定价决策。研究表明：在保修期作为单质量信号时，只要高质量新进者的单位时间保修成本小于低质量新进者，即可实现分离均衡；在保修期和价格同时作为质量信号时，当满足某些条件时也可实现分离均衡。相对于保修期作单质量信号的情形，当保修期和价格同作质量信号时，高质量新进者实现分离均衡所需提供的保修期更短、价格更低（信息租金更少），且能获得更高的市场份额和利润。最后，数值分析表明保修期和价格同作质量信号时所需满足的条件是比较宽松的，比保修期单独作质量信号时更容易实现分离均衡。     

动态竞争环境下的产品保证管理最优控制策略研究

产品保证与产品质量和价格密切相关,在动态变化的市场环境中,如何通过产品保证优化管理实现保证政策与产品质量和价格三者的均衡,对扩大产品市场占有率、提高企业利润有重要作用.对国内外关于产品保证优化管理的研究进行总结,着重分析当前研究存在的问题,在此基础上提出动态市场竞争环境下企业保证管理的最优控制模型,通过引入市场竞争变量构建产品销售率函数,综合考虑市场竞争环境下产品保证与产品质量和价格的动态变化关系;采用极大值原理对该模型进行求解,并对最优解的参数和变化规律进行详细的分析讨论;应用灵敏度分析验证相关的分析结论,评估时间、市场变量和成本结构等参数对最优解的影响,并有针对性地提出具有指导性的管理建议.     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.