Designing and pricing menus of extended warranty contracts

Extended warranties provide “piece of mind” to a consumer in that product failures which occur after the base warranty expires are rectified at little or no cost. They also provide an additional source of revenue for manufacturers or third‐party providers, such as retailers or insurance providers, and help cultivate consumer loyalty. In this article, we analyze a number of extended warranty contracts which differ in design, including restrictions on deferrals and renewals. With the use of dynamic programming, we compute the optimal strategy for a consumer with perfect information and determine the optimal pricing policy for the provider given the consumer's risk characterization. We also provide insight into when different contracts should be issued. Finally, we illustrate how profits can be dramatically increased by offering menus of warranty contracts, as opposed to stand alone contracts, with the use of integer programming. Surprisingly, risk‐taking consumers provide the greatest benefit to offering menus. These insights can help a company develop a comprehensive warranty planning strategy for given products or product lines. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Warranty claims modeling

A company wishes to estimate or predict its financial exposure in a reporting period of length T (typically one quarter) because of warranty claims. We propose a fairly general random measure model which allows computation of the Laplace transform of the total claim made against the company in the reporting interval due to warranty claims. When specialized to a Poisson process of both sales and warranty claims, statistical estimation of relevant quantities is possible. The methodology is illustrated by analyzing automobile sales and warranty claims data from a large car manufacturer for a single car model and model year. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Warranty costs: An age‐dependent failure/repair model

An age‐dependent repair model is proposed. The notion of the “calendar age” of the product and the degree of repair are used to define the virtual age of the product. The virtual failure rate function and the virtual hazard function related to the lifetime of the product are discussed. Under a nonhomogeneous Poisson process scenario the expected warranty costs for repairable products associated with linear pro‐rata, nonrenewing free replacement and renewing free replacement warranties are evaluated. Illustration of the results is given by numerical and graphical examples. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Stochastic modeling for computational warranty analysis

We examine two key stochastic processes of interest for warranty modeling: (1) remaining total warranty coverage time exposure and (2) warranty load (total items under warranty at time t). Integral equations suitable for numerical computation are developed to yield probability law for these warranty measures. These two warranty measures permit warranty managers to better understand time‐dependent warranty behavior, and thus better manage warranty cash reserves. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Some aspects in estimating warranty and post‐warranty repair demands

When customers buy a product, they are often eligible for free repairs for a certain warranty period. In this article, we study some important aspects, which are often overlooked in the literature but are of interest to the manufacturer, in estimating both warranty and post‐warranty repair demands. We consider that the installed base of the product (i.e., the number of units of the product actually in use) varies with time due to both new sales and units being taken out of service. When estimating warranty and post‐warranty repair demands, we explicitly address the fact that customers may not always request repairs for failed units. For the case where the product failure time distribution is exponential, we derive the closed‐form expressions for both types of repair demands of a single unit and of the time‐varying installed base. The insights into some risk‐related quantities are also presented. Furthermore, the proposed model is extended by considering delayed warranty claims that are frequently seen in practice. Numerical examples illustrate that understanding both types of repair demands and the related decision variables is important for managing the obligatory and profitable repair services. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 499–511, 2013     

高新装备复合式预防性保修风险模型

结合高新装备保修需求,引入复合式预防性保修策略,以"定期更换周期内辅以功能检测"这种典型复合维修工作为例,从安全性影响的角度分析了装备的故障发生情况,并建立了其故障风险数学模型。在此基础上,通过算例给出了所建模型的应用方法,研究了该策略下决策变量对故障风险的影响,并分析了模型的通用性。     

Outsourcing warranty repairs: Dynamic allocation

In this paper we consider the problem of minimizing the costs of outsourcing warranty repairs when failed items are dynamically routed to one of several service vendors. In our model, the manufacturer incurs a repair cost each time an item needs repair and also incurs a goodwill cost while an item is awaiting and undergoing repair. For a large manufacturer with annual warranty costs in the tens of millions of dollars, even a small relative cost reduction from the use of dynamic (rather than static) allocation may be practically significant. However, due to the size of the state space, the resulting dynamic programming problem is not exactly solvable in practice. Furthermore, standard routing heuristics, such as join‐the‐shortest‐queue, are simply not good enough to identify potential cost savings of any significance. We use two different approaches to develop effective, simply structured index policies for the dynamic allocation problem. The first uses dynamic programming policy improvement while the second deploys Whittle's proposal for restless bandits. The closed form indices concerned are new and the policies sufficiently close to optimal to provide cost savings over static allocation. All results of this paper are demonstrated using a simulation study. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

不完全维修策略的产品保修期研究

以保修期内的保修费用和可用度2个目标作为优化决策依据,权衡厂家和顾客的利益及需求,建立基于改善因子的不完全预防性维修模型,并通过实例确定厂家和顾客共同达到最大满意度的最佳维修间隔期及保修期,验证了模型的实用性。     

军民融合条件下新型军械装备保修模式研究

针对如何引入承制方优质技术力量支援部队维修保障能力建设这一问题,分析我军现役军械装备维修保障力量、保障模式存在的不足和地方装备维修保障力量的能力特点,明确承制方在军民融合条件下装备维修保障力量中的重要地位.在借鉴国外研究成果的基础上,深入分析和系统设计了我军军械装备的保修模式.结合部队巡检机制,建立了一维免费-按比例收费组合保修的费效模型来验证采购合同中保修条款的合理性.最后进行了案例分析,证明了模型的有效性和实用性.     

新型光电装备延伸保修决策方法研究

延伸保修是开展军民融合式装备保障的重要技术手段之一,通过合理选择延伸保修策略,可以在有限的经济条件下较好地完成维修保障任务,提高装备维修保障效益.针对新型光电装备特点,在考虑安全性、任务性和经济性因素的背景下,提出一种由逻辑决断分析法和模糊层次分析法相结合的延伸保修决策方法.通过逻辑决断分析从定性角度选择合理的延伸保修策略,采用模糊层次分析法对逻辑决断得到的结果进行定量补充分析,为类似装备的延伸保修决策提供决策参考.