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.     

基于M-CVaR和生产资金约束的供应链协调研究

本文针对供应商面临生产资金约束的情况,在需求随机条件下研究了由一个风险中性零售商和一个具有风险偏好的供应商组成的二级供应链的协调问题。文章在零售商享有批发价折扣的提前支付和供应商银行信贷两种融资方式下,分别建立了零售商的最优决策模型以及基于M-CVaR测度工具的供应链整体订购决策模型,并给出了采用两种不同融资模式时零售商和供应链整体的最优订购量以及供应链的协调条件,分析了供应商的风险偏好对供应链整体最优决策及协调条件的影响。最后通过算例验证了文章的主要结论。研究表明,当提前支付价格折扣大于临界值时,零售商会选择提前支付货款;提前支付模式下供应链整体的最优订购量大于银行信贷模式;随着供应商的风险偏好由风险规避向风险喜好转变,供应链整体的最优订购量逐渐增大。     

物价、利率与收入对居民消费需求影响研究——基于时变参数状态空间模型

运用时变参数状态空间模型对我国改革开放三十年来物价、利率与收入对农村和城镇居民消费需求影响的动态特征进行了研究。发现物价、收入对农村和城镇居民的消费需求弹性不同,农村消费需求受收入影响较大,而城市居民消费需求受物价影响较大;利率对农村和城镇居民消费需求影响不显著,利率机制目前还不是调解中国消费需求的理想工具。在此基础上给出了相应的政策建议。     

Dynamic Pricing via Dynamic Programming<Superscript>1</Superscript>

This article specifies an efficient numerical scheme for computing optimal dynamic prices in a setting where the demand in a given period depends on the price in that period, cumulative sales up to the current period, and remaining market potential. The problem is studied in a deterministic and monopolistic context with a general form of the demand function. While traditional approaches produce closed-form equations that are difficult to solve due to the boundary conditions, we specify a computationally tractable numerical procedure by converting the problem to an initial-value problem based on a dynamic programming formulation. We find also that the optimal price dynamics preserves certain properties over the planning horizon: the unit revenue is linearly proportional to the demand elasticity of price; the unit revenue is constant over time when the demand elasticity is constant; and the sales rate is constant over time when the demand elasticity is linear in the price. ¹We acknowledge professor robert e. kalaba for initiating this work and suggesting solution methods.     

On a multiple credit rating migration model with stochastic interest rate

In this paper, we explore a pricing model for corporate bond accompanied with multiple credit rating migration risk and stochastic interest rate. The bond price volatility strongly depends on potentially multiple credit rating migration and stochastic change of interest rate. A free boundary problem of partial differential equation is presented, which is the equivalent transformation of the pricing model. The existence, uniqueness, and regularity for the free boundary problem are established to guarantee the rationality of the pricing model. Due to the stochastic change of interest rate, the discontinuous coefficient in the free boundary problem depends explicitly on the time variable but is convergent as time tends to infinity. Accordingly, an auxiliary free boundary problem is constructed, whose coefficient is the convergent limit of the coefficient in the original free boundary problem. With some constraint on the risk discount rate satisfied, we prove that a unique traveling wave exists in the auxiliary free boundary problem. The inductive method is adopted to fit the multiplicity of credit rating. Then we show that the solution of the original free boundary problem converges to the traveling wave in the auxiliary free boundary problem. Returning to the pricing model with multiple credit rating migration and stochastic interest rate, we conclude that the bond price profile can be captured by a traveling wave pattern coupling with a guaranteed bond price with face value equal to one at the maturity.     

The infinite time horizon dynamic pricing problem with multi-unit demand

This paper studies a dynamic pricing problem for a monopolist selling multiple identical items to potential buyers arriving over time, where the time horizon is infinite, the goods are imperishable and the buyers’ arrival follows a renewal process. Each potential buyer has some private information about his purchasing will, and this private information is unknown to the seller and therefore characterized as a random variable in this paper. Thus, the buyers may have multi-unit demand. Meanwhile, the seller needs to determine the optimal posted price such that his expected discounted revenue is maximized. This problem is formulated as a stochastic dynamic programming in this paper and then how to obtain the solution is explored. A numerical study shows that the optimal posted price performs better than that of optimal fixed price, and this advantage becomes obvious as the interest rate and/or the number of initial items increases.     

市场利率环境下银企信贷信息共享信号传递博弈模型

在市场利率环境下,运用信号传递博弈理论,在成本倒挂情况下,采取利息补贴承诺的方法,设计一种以风险分担实现利润共享的契约机制,利润共享参数起到了传递信息的信号作用。研究结果表明,在该契约下企业没有撒谎的动机,契约参数是传达信息的信号。该契约机制下不仅可以实现信贷资金供求信息的共享,而且能够保证系统的协调,系统收益达到最优,使企业能够得到新产品生产所需资金,银行解决信贷资金的风险损失的问题。     

Two-phase pricing and inventory management for deteriorating and fashion goods under trade credit

This study models a finite horizon inventory problem for deteriorating and fashion goods under trade credit and partial backlogging conditions. Demand may vary with price or time. The supplier can extend credit to the retailer. As a result, the retailer does not have to pay for goods immediately upon acquiring them, and can instead earn interest on the retail price of the goods between the time they are sold and the end of the credit period. The proposed model considers two-phase pricing and inventory decisions. In other words, it determines both the optimal prices and the lengths of the in-stock and stock-out period. This paper is the first to consider different price decisions for in-stock and stock-out periods under trade credit. We develop an algorithm to determine the optimal pricing and replenishment strategy while still maximizing the total profit. Further, this study shows that the proposed two-phase pricing strategy is superior to a one-phase pricing strategy in terms of profit maximization. Computational analysis illustrates the solution procedures and the impacts of the related parameters on decisions and profits. The results of this study can serve as references for business managers or administrators.     

考虑维修时间的总质保需求预测模型

激烈的市场竞争迫使制造商们逐渐向以顾客需求为中心的公司转变。在近 20 年内,作为影响顾客满意度的主要因素,产品的质保服务管理的相关研究开始成为学术界的焦点。良好的质保服务会给企业节省较多的运营成本,故对于刚投入市场的新产品而言,准确地预测质保需求对制造商合理分配资金等具有重要意义。以往对质保需求的预测模型都局限于分析长期意义上一个产品的总质保成本,忽略了产品的维修时间和动态销售过程对准确预测产品的总质保需求及成本的影响。为此,以销售期内的产品所产生的维修需求为主要的研究对象,深入探讨维修时间对预测质保需求的影响。模型中,利用非齐次泊松过程模拟产品的动态销售过程,并利用复合随机过程中的交错更新理论来刻画维修时间对总质保需求的影响。最后的参数分析,为企业更好地管理质保服务提供了重要的现实依据。     

A pricing model for secondary market yield based floating rate notes subject to default risk

The purpose of this article is to price secondary market yield based floating rate notes (SMY-FRNs) subject to default risk. SMY-FRNs are derivatives on the default-free term structure of interest rates, on the term structures for default-risky credit classes, and on the structure of a determined pool of bonds. The main problem in SMY-FRN pricing (as compared to the pricing of standard interest rate or credit derivatives) is market incompleteness, which makes traditional no-arbitrage pricing by replication fail. In general, SMY-FRNs are subject to two types of default risk. First, the SMY-FRN issuer may go bankrupt (direct default risk). Second, the possibility of the bankruptcy of the issuers in the underlying pool has an influence on the SMY-FRN coupons (indirect default risk). This article is the first one which provides a no-arbitrage pricing model for SMY-FRNs with direct and indirect default risks. It is also the first article applying incomplete market pricing methodology to SMY-FRNs.     

基于可信性理论的PPP项目特许期-价格联合调整策略研究

需求预测误差是影响PPP项目收益预测准确性的主要因素。为减少谈判争议,确保风险和收益的动态均衡,本文基于模糊数学可信性理论,构建了考虑需求不确定的特许期-价格联合调整模型。将项目运营期间的需求预测误差作为模糊变量,将运营期内特许期和价格的联合调整策略作为决策变量,通过模糊模拟求解出不同特许期和价格调整组合下的期望收益误差以及正收益预期下的可信性,进而得到特许期和价格的联合调整策略可行解集。并将该模型应用于某污水项目中,结果表明,该模型能够有效地解决需求不确定性风险对特许期测算影响的问题,弥补了目前PPP项目特许期和价格调整决策研究中未考虑需求预测误差的不足,对PPP项目特许期和价格的调整决策有着重要的参考意义。     

Equilibrium model of a credit market: Statement of the problem and solution methods

An equilibrium model of a credit market is proposed and examined. The credit price or the interest rate in the model is determined by the consistent interaction of two macroscopic factors: supply and demand. Methods for computing an equilibrium interest rate are suggested. The methods are interpreted as market-balancing dynamics. The convergence of the methods is proved.     

Optimization of maintenance policy under warranty length‐based demand with consideration of both manufacturer and buyer satisfaction

This study proposes a model to optimize postsale services consisting of four factors: (a) the basic warranty length, (b) the extended warranty length, (c) the preventive maintenance level, and (d) the preventive maintenance interval. Furthermore, consumer demand for the product and extended warranty are considered as functions of the length of the basic warranty and extended warranty periods, respectively. Because buyer dissatisfaction with a product can lead to the loss of potential buyers and the switch of current customers to the competitors, both manufacturer and buyer satisfaction are considered in the model. Three comparative studies are done for showing the effectiveness of the model. The first one compares the results of simultaneous optimization from the two perspectives of manufacture and customer with the single‐objective optimization results from each of the mentioned viewpoints. The second comparison studies the provision of extended warranty contract in the proposed model, and the third comparison investigates the effect of preventive maintenance actions on the results of the model.     

Dynamic programming algorithms for the optimal cutting of equal rectangles

This paper presents dynamic programming algorithms for generating optimal guillotine-cutting patterns of equal rectangles. The algorithms are applicable for solving the unconstrained problem where the blank demand is unconstrained, the constrained problem where the demand is exact, the unconstrained problem with blade length constraint, and the constrained problem with blade length constraint. The algorithms are able to generate the simplest optimal patterns to simplify the cutting process. When the sheet length is longer than the blade length of the guillotine shear used, the dynamic programming algorithm is applied to generate optimal layouts on segments of lengths no longer than the blade length, and the knapsack algorithm is employed to find the optimal layout of the segments on the sheet. The computational results indicate that the algorithms presented are more efficient than the branch-and-bound algorithms, which are the best algorithms so far that can guarantee the simplest patterns.     

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。     

Channel coordination under two-level trade credits and demand uncertainty

This study considers a decentralized supply chain where a retailer has an opportunity to order a product from a supplier prior to the sales season to satisfy uncertain demand. The retailer provides trade credit to end customers and makes credit period and order quantity decisions to maximize profits. The end demand is both random and credit period-dependent. On the basis of the newsvendor model, this paper focuses on channel coordination when a retailer provides trade credit to end customers. When the supplier also provides trade credit to the retailer, we show that the traditional trade credit contract cannot coordinate the channel. Four composite contracts based on trade credit (trade credit cost sharing with buy back or quantity flexibility; modified trade credit with buy back or quantity flexibility) are provided to induce the retailer to make decisions while optimizing the channel profit. This paper shows that the retailer provides a longer credit period to its customers and orders a larger quantity from the supplier under the composite contracts. With these contracts, the profit sharing between both parties depends on the wholesale price (Pareto improvement) for the fixed retail price and the purchasing cost.     

随机产出与需求下农户融资模式选择研究

农业是国民经济的基础,但农业融资一直存在许多困难。本文在考虑农户的破产风险,产出随机性以及市场需求不确定的基础之上,构建由单一公司与资金约束的单一农户构成的订单农业供应链决策模型,得到了农户在面对银行信贷、贸易信贷、组合信贷时的最优决策的选择策略。研究表明,当公司利率大于银行利率且农产品生长周期较长,或者当公司利率小于银行利率且农产品生产周期较短时,农户应在银行利率较小时选择银行信贷,在银行利率较大时选择贸易信贷。而在其余情况中,农户需要综合考虑农产品价格敏感系数等因素来决定是否选择组合信贷模式。     

按比例保修策略下多保修期差别定价研究

保修策略是联系厂商和顾客的一种合同责任,它往往用于促进产品的销售。产品保修期长短与其定价有着紧密的联系。本文在考虑一个厂商采用按比例保修策略及设定多个保修期的基础上,以产品的保修期和价格为决策变量,以厂商收益最大化为目标,研究了产品故障次数成指数分布下最优保修期和价格的组合策略,并通过算例比较了差别定价和单一定价下厂商的收益。最后,通过灵敏度分析,研究了消费者保修期偏移弹性对厂商收益所产生的影响。