新产品定价决策的影响因素分析

新产品的成功销售取决于两个重要的因素:一是具有生产特性的工程变量,比如产品的可靠性水平;一是具有市场特征的影响因素,比如价格和保障机制。为了实现收益,制造商必须认真审视价格、产品可靠性和保障机制的选择。因此,本文将价格作为外生变量,将保障机制与可靠性作为决策变量,建立了以最大化为目标的收益模型,分析可靠性与保障机制的最优策略。另外,探讨当不同变量的敏感性参数发生变化时,最优保障机制与产品可靠性的变化规律。最后,通过算例分析收益函数的基本特性,结论显示消费者总是从产品保障机制的信号中判断产品的可靠性水平,这对新产品销售有一定的借鉴意义。     

Probability distributions of cost,revenue and profit over a warranty cycle

A warranty cycle starts with the sale of a new item and terminates when the warranty servicing obligation of the manufacturer created by this sale ends. Cost and profit measures over a warranty cycle are of interest with regards to accounting, pricing, product quality, warranty policy design, and other issues. For most predictive and decision making purposes, these variables cannot be described adequately by their means alone. In this paper, we obtain the probability distributions of the manufacturer's rebate, cost, revenue and profit during a cycle, under a (combination) freereplacement/pro-rata warranty policy, with the incorporation of the customer repurchase behavior under warranty. We first derive the joint distribution of the numbers of free and pro-rata replacements during a cycle. We then construct and compute the distributions of interest by conditioning on the numbers of such replacements. In so doing, we take into account the warranty policy, in terms of the lengths of the free and pro-rata periods, the cost and rebate profiles, customer repurchase probabilities during a pro-rata period, and the failure time distribution of the product. We provide several numerical examples, using data that are typical of battery warranties.     

基于视情维修的质保政策设计研究

随着产品同质化程度不断提升,完善的质保服务已成为厂商提升品牌形象、刺激用户购买需求和全面反馈市场信息的主要途径。本文以具有退化特性的耐用品为研究对象,建立了视情维修条件下性能退化的维纳过程模型,考虑产品价格、质保期长度和维修费用承担比例对产品需求的影响,以最大化厂商利润为目标,确定了最优的质保期长度和维修费用承担比例。结合算例,比较了无视情维修和提供视情维修两种情形下对应的厂商利润,并分析了产品退化速率、成本参数和产品价格对利润的影响。研究结果表明,在质保服务范围内提供合理的视情维修服务既可将产品可靠性维持在一个较高水平,又可显著提升厂商利润。     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

Optimal pricing,EOL (end of life) warranty,and spare parts manufacturing strategy amid product transition

We study firm’s strategy to determine its product price and warranty period, and plan the spare parts manufacturing so as to maximize its profit and at the same time to fulfill its commitment to providing the customer with the key part continuously over the relevant decision time horizon, i.e., the product’s life cycle plus its EOL service (warranty) period. To examine the research question, we develop and solve a two-stage optimal control theory model. From the numerical analysis, we infer as follows. It is not always true that the longer the EOL warranty period, the better for the company’s profitability, implying there exists an optimal EOL warranty period that balances all the relevant forces like market demand and cost structures. The relationship between optimal EOL warranty period and failure rate (defect rate) is concave: when the defect rate is moderate, the company has to increase its EOL warranty period as the defect rate increases so as to compensate for the deteriorating quality; but, when the defect rate is beyond a threshold level, the company needs to curtail its EOL warranty commitment as the defect rate increases in order to avoid excessive cost to service the failed parts. By depicting key dynamics in this managerial problem, this paper sheds light on how to make decision for optimal pricing and warranty when the product life cycle is finite and the company is obliged to provide after-sales services to customers for an extended period of time after the current product is no longer produced.     

SAA-regularized methods for multiproduct price optimization under the pure characteristics demand model

Utility-based choice models are often used to determine a consumer’s purchase decision among a list of available products; to provide an estimate of product demands; and, when data on purchase decisions or market shares are available, to infer consumers’ preferences over observed product characteristics. These models also serve as a building block in modeling firms’ pricing and assortment optimization problems. We consider a firm’s multiproduct pricing problem, in which product demands are determined by a pure characteristics model. A sample average approximation (SAA) method is used to approximate the expected market share of products and the firm profit. We propose an SAA-regularized method for the multiproduct price optimization problem. We present convergence analysis and numerical examples to show the efficiency and the effectiveness of the proposed method.     

Warranty cost analysis: Increasing warranty repair times

In this study, we model the warranty servicing costs under nonrenewing and renewing free repair warranties. We assume nonzero increasing repair times with the warranty cost depending on the length of the repair time. An increasing geometric process is used to model the consecutive repair times. We introduce the generalised alternating renewal process, which is an alternating process with cycles consisting of an item's operational time followed by the corresponding repair time. We derive analytical results for a generalised alternating renewal process with a finite time horizon and use them to evaluate the warranty costs over the warranty period and over the life cycle of the product under the nonrenewing free repair warranty and renewing free repair warranty. Properties of the model are demonstrated through a simulation study and through the application to warranty claims data from an automotive manufacturer.     

The role of repair strategy in warranty cost minimization: An investigation via quasi-renewal processes

Most companies seek efficient rectification strategies to keep their warranty related costs under control. This study develops and investigates different repair strategies for one- and two-dimensional warranties with the objective of minimizing manufacturer’s expected warranty cost. Static, improved and dynamic repair strategies are proposed and analyzed under different warranty structures. Numerical experimentation with representative cost functions indicates that performance of the policies depend on various factors such as product reliability, structure of the cost function and type of the warranty contract.     

Controlled predatory pricing in a multiperiod Stackelberg game: an MPEC approach

We analyze a multiperiod oligopolistic market where each period is a Stackelberg game between a leader firm and multiple follower firms. The leader chooses his production level first, taking into account the reaction of the followers. Then, the follower firms decide their production levels after observing the leader’s decision. The difference between the proposed model and other models discussed in literature is that the leader firm has the power to force the follower firms out of business by preventing them from achieving a target sales level in a given time period. The leader firm has an incentive to lower the market prices possibly lower than the Stackelberg equilibrium in order to push the followers to sell less and eventually go out of business. Intentionally lowering the market prices to force competitors to fail is known as predatory pricing, and is illegal under antitrust laws since it negatively affects consumer welfare. In this work, we show that there exists a predatory pricing strategy where the market price is above the average cost and consumer welfare is preserved. We develop a mixed integer nonlinear problem (MINLP) that models the multiperiod Stackelberg game. The MINLP problem is transformed to a mixed integer linear problem (MILP) by using binary variables and piecewise linearization. A cutting plane algorithm is used to solve the resulting MILP. The results show that firms can engage in predatory pricing even if the average market price is forced to remain higher than the average cost. Furthermore, we show that in order to protect the consumers, antitrust laws can control predatory pricing by setting rules on consumer welfare.     

Modeling and analysis of a warranty policy using new and reconditioned parts

Remanufacturing processes such as refurbishing and reconditioning can extend the life of a product returned from the field. This provides financial opportunities and allows manufacturers to engage in sustainable practices. However, the inability to access a sufficient quantity of reconditioned components from end‐of‐life products can force the concurrent utilization of new components. This paper deals with the determination of an optimal warranty policy where a mixture of new and reconditioned components are used to carry out replacements upon failure for products under warranty. A mathematical optimization model is developed to maximize the manufacturer's expected total profit based on four decision variables: the warranty length, the sale price, the age of reconditioned components, and the proportion of reconditioned components to be used. A numerical procedure is used to compute the optimal solution. Numerical results are provided and discussed to demonstrate the validity and the added value of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

规模效应下产品具有可替代性的竞争企业的外包决策

针对产品具有一定替代性的两个竞争企业(分别为企业1和企业2)和存在规模效应的上游供应商的外包决策问题, 构建了企业1 外包前后各方的利润模型,求解了下游企业的外包和自产的最优策略以及供应商的最佳批发价格,分析了企业1 的外包策略对企业2 和供应商的外包决策的影响,比较了产品替代性对外包前后各决策变量的影响。研究发现:当企业的单位生产成本高于外包成本时,企业也可能选择自产;而当企业的单位生产成本低于外包成本时,企业也可能选择产品外包。并对模型进行进一步的拓展,比较了下游企业作顺序和同时外包决策两种情景的异同。     

考虑企业释放质量信号行为的产品推广策略

为吸引消费者, 一些企业尝试以释放质量信号为手段进行产品推广。本文考虑消费者购买时的参考效用, 通过构建模型, 探讨了短期经营下低质量企业不释放质量信号、短期经营下低质量企业释放质量信号、长期经营下低质量企业不释放质量信号和长期经营下低质量企业释放质量信号等四种情况下的产品定价策略, 并分析了释放质量信号对企业运营带来的利弊。研究发现:长期经营下低质量企业释放质量信号时, 产品质量差距的扩大将提高竞争企业的最优定价, 而释放质量信号程度的增加则将使最优定价降低。同时, 通过释放质量信号, 短期内低质量企业看似可以借此获得大量需求, 但现实中可行性不高。从长期经营来看, 以释放质量信号为手段的推广策略实际上会损害整个市场的利益。     

Uncertain Product Quality, Optimal Pricing and Product Development

A firm is developing a new product. However, the firm is uncertain as to how consumers will perceive the product's desirability or quality. Using a general model of product quality, conditions for an increase in uncertainty to increase the optimal price are derived. General conditions are derived under which the firm prefers the less risky project, the one with lower quality variability. However, if at the optimal price the firm only has positive demand for high quality realizations, then the firm prefers a more risky project. As the uncertainty exists in the consumers' preferences, welfare effects can be determined, unlike in previous work examining uncertainty.     

Network externalities in a dynamic monopoly

We reconsider the role of network externalities in a dynamic spatial monopoly where the firm must invest in order to accumulate capacity, while consumers may have either linear or quadratic preferences. We (1) characterise saddle point equilibria, (2) prove that the extent of market coverage is increasing in the network effect and (3) unlike the existing static literature on the same problem, the monopolist may not make introductory price offers. Then, we briefly deal with the socially optimal solution, showing that, in general, a planner would serve more consumers than a profit-seeking monopolist.      

Price and quality competition: The effect of differentiation and vertical integration

This paper studies an instance of price and quality competition between firms as seen in the recent Internet market. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. Characterizing this competition from a microeconomic viewpoint, we consider two possible business strategies that firms can utilize to overcome the competition—the differentiation and the vertical integration with another complementary firm. We show an interesting result not seen in the well-known Bertrand price competition: not only does the differentiation always increase the firms’ profits, but also it can increase the consumer’s welfare in a quality-sensitive market. We further derive that under some mild conditions the monopolistic vertical integration that excludes the combination-purchase with a competitor’s product is beneficial for both the integrated firm and its consumers.     

Inventory competition in a dual-channel supply chain with delivery lead time consideration

Aimed at the inventory competition of perishable products in a dual-channel supply chain with consideration of the delivery lead time in the online direct channel, we extend the Newsvendor model considering stock-out-based consumer switching behavior to include the delivery lead time. We examine the retailer's optimal order quantity decision in the retail channel and the manufacturer's optimal inventory level decision in the online direct channel, explore the manufacturer's optimal delivery lead time decision in the online direct channel, discuss the impact of the product price and consumer switching behavior on the optimal decisions of supply chain members, and compare the optimal decisions between decentralized and centralized scenarios. The results show that, compared with the centralized scenario, at least one of the supply chain members will overstock in the decentralized scenario and that consumers in the online direct channel enjoy a shorter delivery lead time and hence better service in the decentralized scenario. Finally, we present numerical examples to analyze the impact of relevant parameters on the supply chain members’ profits and the supply chain efficiency.     

考虑消费者具有质量和价格偏好的双渠道供应链最优决策

产品价格和质量是消费者永恒的关注点。虽然多渠道给消费者带来了便捷的购物途径, 但是不同渠道的产品存在质量和价格分差异, 消费者在购买时须面对一个渠道、价格和质量的协调选择问题。本文提出了消费者对产品质量和价格偏好的双渠道定价决策模型, 并讨论了以制造商为领导者的分散决策和集中决策情形下的最优策略。比较了消费者偏好及产品质量水平对不同决策情形下的供应链决策的影响, 并通过设计收益共享契约机制实现了渠道的协调并证明了其有效性。研究表明:当产品质量在一定范围内时, 制造商和零售商可以获得最大利润;当消费者对质量的偏好逐渐增加时, 制造商的利润和零售商的利润随着消费者对质量的偏好提高而下降;制造商和零售商可以通过协调销售价格消除供应链的双重边际效应,从而实现供应链的协调。最后利用算例分析了消费者的质量、价格偏好对总利润的影响并给出了相应的管理启示。     

Maintenance models in warranty: A literature review

Along with increasing the warranty period for complex systems, reducing the warranty servicing costs has become an issue of great importance to the manufacturers. One possible way to reduce the expected warranty servicing cost is by making sound decision on the product warranty and maintenance strategies. Therefore, warranties (basic warranty and extended warranty) and maintenance (corrective and preventive) are strongly interlinked and of great interest to both manufacturers and customers. This paper is the first identifiable academic literature review to deal with warranty and maintenance. It provides a classification scheme for the articles that link warranty and maintenance published between 2001 and 2011 covering 44 journals and proposes a taxonomy scheme to classify these articles. Nine hundred articles were identified for their relevance to warranty and were carefully reviewed. One-hundred and twenty-two articles were subsequently selected for their relevance to maintenance and included in the classification.     

An integrated product returns model with logistics and marketing coordination

We develop an integrated approach for analyzing logistics and marketing decisions within the context of designing an optimal returns system for a retailer servicing two distinct market segments. At the operational level, we show that the optimal refund price is not unique. Moreover, it is such that if both market segments return a purchased product, then neither segment will receive a full money-back refund; and it is such that if one or both segments do not return a purchased product, then a refund premium over the purchase price is possible, but the refund premium will not be enough to offset a customer's total net cost of purchase and return. We also show that any improvement to the returns system that results in increased logistical efficiency or marketing effectiveness will be accompanied by an increase in the selling price of the product. At the strategic level, we show that if the retailer does not coordinate its logistics and marketing efforts to improve the overall returns system, then it will tend to over-invest in one of the functions and under-invest in the other. Finally, we illustrate how our model can be generalized to the case in which a customer's ex post valuation of the product falls along a continuum.     

A general age-replacement model with minimal repair under renewing free-replacement warranty

A general age-replacement model in which incorporates minimal repair, planned and unplanned replacement, is considered in this paper for products under a renewing free-replacement warranty policy. For both warranted and non-warranted products, cost models from the user’s perspective are developed, and the corresponding optimal replacement ages are derived such that the long-run expected cost rate is minimized. The impacts of a product warranty on the optimal replacement model are investigated analytically. Furthermore, we show that the optimal replacement age for a warranted product is closer to the end of the warranty period than for a non-warranted product. Finally, numerical examples are given for illustration.