Cost analysis of warranty policies

This article analyzes two general warranty policies involving an initial free replacement period, followed by a pro rata period. We examine the short-run total costs and longrun average costs under these policies. Formulas for both consumer costs and manufacturer profits under warranty are derived. We also study the expected number of purchases over the product life cycle under both policies. Bounds for the expected total costs and expected number of purchases are obtained for the case where the failure distribution of the item is new better than used.     

Distributions of manufacturer's and user's replacement costs under warranty

We derive and compute time-dependent distributions of replacement costs under warranty over the product life cycle, both for the manufacturer and the user, under conditional pro-rata and nonrenewing free-replacement warranty policies. For pro-rata warranties, the analysis is based on the joint distribution of the number of replacements and the user's cost over time. For free-replacement warranties, distribution of the user's cost follows from the observation that replacement points outside warranty periods form a renewal process. This property is also exploited to determine the distribution of the manufacturer's cost. We apply our findings to measure the impact of product conformance quality on warranty cost distributions and find that manufacturer's cost measures are more sensitive to changes in quality than user's cost measures. © 1995 John Wiley & Sons, Inc.     

Comparisons of renewable warranties

Two types of warranties are commonly applied. There are replacement‐free warranty and pro‐rata warranty. The third warranty is the mixing of the above two. That is it has a replacement‐free stage followed by a pro‐rata stage. In addition to the above classification, warranties can also be a renewable or nonrenewable. No matter which warranty is used, it always incurs certain cost to the manufacturer. Moreover, often manufacturers want to improve the quality of products by burn‐in before delivering them to consumers, and this incurs an extra cost. This article considers the random costs for both burn‐in and renewable warranty, and derives the mean warranty cost. Then the mean costs corresponding to pure replacement‐free warranty, mixing renewable warranty, and pure pro‐rata warranty are compared. Furthermore, the mean costs under the same warranty policy associated with different lifetime distributions of products are also compared. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 91–106, 1999     

Warranty reserves for nonstationary sales processes

Estimation of warranty costs, in the event of product failure within the warranty period, is of importance to the manufacturer. Costs associated with replacement or repair of the product are usually drawn from a warranty reserve fund created by the manufacturer. Considering a stochastic sales process, first and second moments (and thereby the variance) are derived for the manufacturer's total discounted warranty cost of a single sale for single‐component items under four different warranty policies from a manufacturer's point of view. These servicing strategies represent a renewable free‐replacement, nonrenewable free‐replacement, renewable pro‐rata, and a nonrenewable minimal‐repair warranty plans. The results are extended to determine the mean and variance of total discounted warranty costs for the total sales over the life cycle of the product. Furthermore, using a normal approximation, warranty reserves necessary for a certain protection level, so that reserves are not completely depleted, are found. Results and their managerial implications are studied through an extensive example. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 499–513, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10023     

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 policies and burn-in

Warranty is an important factor for consumer durable products in the marketplace. However, the warranty cost may drastically reduce profitability. Burn in is a common procedure to improve the quality of products after they have been produced, but it is also costly. By taking both the burn-in procedure and warranty policy into consideration, several cost functions can be formulated and optimized. Assuming that the failure-rate function of the product has a bathtub shape, it is shown that the optimal burn-in times that minimize the considered cost functions never exceed the first change point of the failure-rate function. The continuous dependence of the optimal burn-in times on the model parameters and the underlying distribution is also established. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 199–209, 1997     

Dynamic routing of prioritized warranty repairs

Recent years have seen a strong trend toward outsourcing warranty repair services to outside vendors. In this article we consider the problem of dynamically routing warranty repairs to service vendors when warranties have priority levels. Each time an item under warranty fails, it is sent to one of the vendors for repair. Items covered by higher priority warranty receive higher priority in repair service. The manufacturer pays a fixed fee per repair and incurs a linear holding cost while an item is undergoing or waiting for repair. The objective is to minimize the manufacturer's long‐run average cost. Because of the complexity of the problem, it is very unlikely that there exist tractable ways to find the optimal routing strategies. Therefore, we propose five heuristic routing procedures that are applicable to real‐life problems. We evaluate the heuristics using simulation. The simulation results show that the index‐based “generalized join the shortest queue” policy, which applies a single policy improvement step to an initial state‐independent policy, performs the best among all five heuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

基于费效分析的装备延伸保修购买决策

保修机制是部队引入承制方装备维修力量的重要途径,延伸保修对装备的寿命周期费用以及承制方保修费用有很大影响。针对军方延伸保修购买决策问题,在对维修策略分析的基础上,综合考虑装备维修费用和可用度,建立了延伸保修购买决策相关模型,结合装备承制方保修成本及军方装备维修费用——效能分析,得到了在不同价格区间内延伸保修购买决策,并给出了特定条件下存在的双赢延伸保修价格区间,最后通过实例验证了模型的有效性。     

Return policy: Hassle‐free or your money‐back guarantee?

This article compares the profitability of two pervasively adopted return policies—money‐back guarantee and hassle‐free policies. In our model, a seller sells to consumers with heterogeneous valuations and hassle costs. Products are subject to quality risk, and product misfit can only be observed post‐purchase. While the hassle‐free policy is cost advantageous from the seller's viewpoint, a money‐back guarantee allows the seller to fine‐tune the consumer hassle on returning the product. Thus, when the two return policies lead to the same consumer behaviors, the hassle‐free policy dominates. Conversely, a money‐back guarantee can be more profitable even if on average, high‐valuation consumers experience a lower hassle cost than the low‐valuation ones. The optimal hassle cost can be higher when product quality gets improved; thus, it is not necessarily a perfect proxy or signal of the seller's quality. We further allow the seller to adopt a mixture of these policies, and identify the concrete operating regimes within which these return policies are optimal among more flexible policies. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 403–417, 2014     

Strategic investment to reduce setup times in the economic lot scheduling problem

This article considers the Economic Lot Scheduling Problem where setup times and costs can be reduced by an initial investment that is amortized over time. The objective is to determine a multiple-item single facility cyclic schedule to minimize the long run average holding and setup costs plus the amortized investment. We develop a lower bound on the long run average inventory carrying and setup costs as a function of the setup times, and show that this lower bound is increasing concave on the setup times when the out-of-pocket setup costs are zero or proportional to the setup times. We then develop a model that may be helpful in deciding the magnitude and the distribution of a one-time investment in reducing the setup times when the investment is amortized over time. Numerical results based on randomly generated problems, and on Bomberger's ten item problem indicate that significant overall savings are possible for highly utilized facilities. Most of the savings are due to a significant reduction in the long run average holding cost. © 1995 John Wiley & Sons, Inc.     

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     

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     

Engineering costs and customer costs in designing product support

Product support encompasses activities undertaken by durable goods producers to ensure their customers the continued use of the product. Examples of product support elements include after the sale activities such as providing repair services and warranty programs, as well as all the activities undertaken at the design and production stage to improve the reliability of products before they reach the market. The implications of incorporating customer costs while designing product support packages are the concern of this study. We study how the parameters of support package impact the costs incurred by customers and provide insights about selecting appropriate levels of product support. We show that the engineering orientation of maximizing the product's availability ignores market characteristics, and results in a mismatch between the corporation's support package and the customer's needs. The research is intended to be a step in understanding the interaction between design engineering parameters and customer's costs. © 1993 John Wiley & Sons, Inc.     

Lot sizing when yields increase during the production run

We investigate the problem of determining lot sizes for multiple items when the expected percentage of acceptable output increases with the duration of the production run, usually due to adjustments made during the early part of the production run. Such problems arise in metal stamping, textile finishing processes, and a variety of other industries. The goal is to minimize the total cost of production, inventory holding costs, and setup costs (where applicable). We develop a heuristic procedure based on a Lagrangian relaxation that differs from relaxations used in earlier studies. We use various properties of the objective function to guide the adjustment of the initial solution from the relaxation toward feasibility. Computational results indicate that, on the average, the heuristic produces solutions within 4.9% of the lower bound obtained from the Lagrangian relaxation. © 1996 John Wiley & Sons, Inc.     

Calculation of the cost of warranty policies as a function of estimated life distributions

Two types of warranties are analyzed. These are the free-replacement warranty, under which failed items are replaced free of charge until a specified total operating time has been achieved, and the pro rata warranty, under which items that fail prior to a specified time are replaced at pro rata cost to the buyer. Both the buyer's and seller's points of view are considered. The basis of the analysis is a comparison of warranted and unwarranted (otherwise identical) items with regard to long-run cost to the buyer and long-run profit to the seller. Application of the results requires knowledge of certain characteristics of the life distribution of the items in question. Parametric and nonparametric methods of estimation of these characteristics from incomplete data are discussed. Single and multiple failure-mode situations are considered. Some solutions to the problem are illustrated using incomplete data on failure times of an aircraft component.     

One- and two-stage scheduling of two products with distributed inserted idle time: The benefits of a controllable production rate

Consider the problem of scheduling two products on a single machine or through two machines in series when demand is constant and there is a changeover cost between runs of different products on the same machine. As well as setting batch sizes, it is assumed that the production scheduler can choose the production rate for each product, provided an upper bound is not exceeded. This is equivalent to permitting distributed inserted idle time over the production run. It is shown that characteristic of the optimum schedule is that there is no idle time concentrated between runs; it is all distributed over the run. If the inventory charge is based on average inventory then one product is always produced at maximum rate on the bottleneck stage; however, if there is an inventory constraint based on maximum inventory then in the single-stage case it can occur that neither product is produced at maximum rate.     

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.     

Warranty analysis and renewal function estimation

Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.     

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。     

Free riding in a multi‐channel supply chain

Free riding in a multichannel supply chain occurs when one retail channel engages in the customer service activities necessary to sell a product, while another channel benefits from those activities by making the final sale. Although free riding is, in general, considered to have a negative impact on supply chain performance, certain recent industry practices suggest an opposite view: a manufacturer may purposely induce free riding by setting up a high‐cost, customer service‐oriented direct store to allow consumers to experience the product, anticipating their purchase at a retail store. This article examines how the free riding phenomenon affects a manufacturer's supply chain structure decision when there are fixed plus incremental variable costs for operating the direct store. We consider factors such as the effort required to find and buy the product at a retail store after visiting the direct store, the existence of competing products in the market, and the extent of consumer need to obtain direct‐store service. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009