基于客户偏好的动态定价模型.doc

3、基于客户偏好的动态定价模型一般来说，企业的中心目标是利润最大化，这里的利润不仅包括当前的销售利润，而且还包括未来时期的盈利。这就要求企业与客户建立长期，互利的关系，将客户作为一种宝贵资源融入企业供应链当中，在因特网时代，企业面临的是来自全球的竞争。生产同种产品的企业之间的区别变得越来越难以区分，争取客户的工作的价值也就变得越来越昂贵。因此，用户满意度（效用）最大化也应成为企业追求的目标。 用户一般比较关心产品的价格和大质量。因此根据用户对价格和质量的敏感程度不同，给出用户的效用函数。假设市场存在S个企业和b个用户。卖方提供一种产品（按照产品价格以及质量等级的不同，具有不同的属性）。产品质量等级用+来表示，若产品质量分为N个等级，则质量最高等级+，质量最低等级+。用户购买价格为P，质量等级为+的产品的产效用为+式中+分别为价格参数和质量参数，根据用户对价格，质量偏好程度不同取+之间不同用户的+的取质也不同。+为用户对该产品愿意支付的最高价格；+为用户愿意接受的该产品最低质量等级。在这里包含两个假设；用户了解每一个企业提供的产品的价格及其对应的质量等级。当产品价格超过+或产品质量等级低于+时，交易不发生，用户的效用为0。对于每次交易（成交的产品质量等级相同）而言，企业目标函数有两个，它们分别为：+式中，不为企业的利润；Q为成交的产品数+；P为产品的成交价格；C是产品的边际成本，包括边际生产成本和边际电子商务成本。电子商务成本是指在电子商务环境下经营所负担的传统零售方式并不存在的网站运营成本和因交易方式改变而增加的额支出。电子商务的贸易磋商过程描述了用户与商户之间的信息交流过程，在这个过程中，智能代理可以代表商户对交易物资的价格和数量进行磋商。买卖双方借助于电子商务所构造的虚拟磋商+对交易的价格和数量进行磋商，最后达成共识而成交，双方都希望能在交易中获得最大的收益，双方的利益可以借助于双向+理论来实现。假定市场上卖方提供一种产品或服务，此产品对应不同的价格P有不同的质量等级+。对某一质量等级为+的产品，卖产确定一个卖价+，买方同时给出一个买价+。如果+则交易以+的价格进行，如果+则不发生交易。+为第+个时间段，+为第+时间段。+为+时间段内的质量等级为+的产品的成交量，卖方在+时间段内质量等级为+的产品利润为：+。C为产品的边际成本，服从+区间的均匀分布，固定成本假设为O。买方对商品的估价为+，服从+区间的均匀分布。+和C都是私人信息，对方无法确定。如果买方以价格P购得商品，则可获得+的效用，+和+为价格指数，质量指数（企业可以在CRM系统中通过数据挖掘获得）。在这里假设质量最高等级为1，最低等级为0，+为产品质量相对质，在+之间取值。 在这个静态贝叶斯博+中，如果式和式成立，战略+即为博+的贝叶斯纳+均衡：对+区间内的每一+，+应满足：+其中+为在买方价格大于卖方价格+的条件下，买方价格的期望质。对于+区间内的每一个+，+应满足+其中+为在卖方价格小于买方价格的条件下，卖方价格的期望值。假设买卖双方的战略均为线性战略，Myerson和 Satterthwaite1983年证明了在估价为均匀分布的前提下，线性战略均衡能产生比任何其他贝叶斯纳+均衡更高的期望收益。由一阶条件可得：+=图图 线性战略均衡下的交易区域只有当+时，才发生交易。由式和式可知，在线性均衡中，仅当+时，才会有交易发生（如图1所示）+为交易双方构建了磋商模型，交易双方都可以为获得最大化交易效用进行磋商。买卖双方代理分别按照双方设计的+价模型和报价模型进行磋商，最终在可接受区域成交。4、考虑成本秋竞争的数字产品定价模型。数字产品有较高的沉没成本和较低的边际成本即制作第一件产品的成本很高而它的复制品很低，同时数字产品的需求与时间，产品的流行程度，价格有关，数字产品的特性表明传统的定价方法不再适用，尤其是简单设定价格等于边际成本的方法通常没有足够的收入来抵消固定的成本。41成本加成定价模型+对于产品+，M；P是价格；C表示数学产品的成本，通常中沉没成本，表现为产品的版权和市场+费用；+是涨价幅度，根据实际经验求得；上角标+表示是按照成本加成定价模型来定价的。42竞争参考定价模型+=其中，+表示第N个竞争者，+，N；+是对物品+考虑到竞争者+的价格而建议的价格；上角标+表示该结果是竞争参考定价模型的定价结果，当有多个竞争者的时候，竞争参考定阶模型为+为一个带有权重的原合多个竞争对者影响的模型。43需求模型数字产品的销售量与该产品页面的访问量有关，与顾客购买的可能性有关，而顾客购买的可能性与产品的生命周期，时尚流行程度以及价格有关，顾客越有可能购买，价格也就越高。而产品价格越高，顾客就越不愿意购买，数字化知识产品的销售模型为： S（ti,fi,Pi）=N.exp(-xti).exp(w.fi)exp(-Spi),其中，N表示该X产品页面的访问量，通过上一周期的页面访问量得；ti表示产品i某个定价周期的生命力，fi表示产品I的时尚流行程度，其中ti和fi的大小由产品的具体情况决定；Pi表示产品I的价格；而入w,6分别为产品的生命力，时尚流行程度和价格的影响因子，为常数，可根据专家建议的方法获得。44模型的综合成本加成定价模型和竟争参考定价模型各有自己的基础和对应范围，根据客观情况来选择合适的模型，充分发挥两种定价模型的优点，可采用带有权垂的线性相加模型。Pi =Wi (Ci. (1+Si) )+Wij. Pij其中，Pi是组合模型建议价格；Wi是成本加成定价模型的权垂系数；Wij是第j个竟争对手的权垂系数，j=1,.,n,则销售收益为：G（Pi,Si）=(Pi-Ci).S(ti,fi,Pi)综合以上结果，得最终模型：maxWi(Ci(1+Si)+Wij.Pij-CiXN.exp(-Xti).exp(wfi).exp(-6.Pi)s.t.PiCi,iE1,M 5.结语在消费者领域，电子商务最重要的影响或许在于商品和服务的定价。由于因特网能为消费者提供包括价格信息在内的各种产品信息使顾客更容易成为价格专家，这样基于用户好结构的动念定价是企业在网络时代的一重要的定价方案。同时充分考虑数字产品特证，字合考虑产品成事，竟争和需求等各种因素和约束，以电子商务环境下数字产品销售收益最大化为目标的模型对电子商务企业定价也有很大帮助。电子商务环境下商品定价更加复杂，需考虑多种因素，本文的两种定价模型仍需进一步改进。电子商务环境下商品的定价模式研究1、引言全球商务活动日益受到新兴电子信息技术的影响，电子设备给传统的商务方式带来根本性的变革。电子商务环境中商品的定价一方面受到消费者压力的作用，另一方面又受到企业占领市场的动机的影响，使传统的定价方式难于适用于电子商务的商品定价。在电子商务环境下，交付品定价方案的范围比传统商业模式下产品定价方案的范围更加广泛，更加复杂。企业既可以按照“网上交付的实际效用”向消费者收取费用，也可以按照固定渠道收费以及其它方式收费，下面就电子商务环境下若干定价模型进行讨论。译文：3、Dynamical pricing model based-on clients preferenceGenerally speaking, the main goal of a Enterprise is to get maximum of profit, which not only includes current sales profit, but also includes the future profit. So the enterprise is required to build a long term and mutually beneficial relationship with the clients and make the clients as a important source of its Supply Chains. In the times of Internet, the enterprise is facing the competitions from all over the world. The differences of the enterprises which manufacture the same products are more than less. The value of winning the clients is higher and higher. Therefore, the maximization of client satisfaction becomes the goal of enterprises.Customers usually care for the price and quality of a product. So we give a utility function of customers according to the difference of the clients sensitivity of price and quality. Suppose there are S enterprises and b customers. The vender provides products which have different properties according to price and quality grade. The quality grade is represented as +. If the quality of a product can be distinguished by N grades, then the highest grade is +, while the lowest one is +. The purchase price is represented as P. The utility of the product with quality grade of + is +. In this formula, + are price parameter and quality parameter. According the differences of users preference of price and quality, the parameter is between +. Different customers can select different +. + is the highest price the customer would like to give; + is the lowest quality grade the customer can accept. Here we have two assumptions: The customers know the price and corresponding quality grade of a product providing by every enterprise. When the price is over + or the quality grade is lower than +, the transaction will not occur, and the utility of customer is 0.Speaking to every transaction (all the bargains have same quality grade), the enterprise has two goal functions, which are:+In the formula, I is the profit of a enterprise, Q is the number of bargained products; P is the bargained price; C is marginal cost of the product, including marginal production cost and marginal e-commerce cost. E-commerce cost is the website operating cost which is not existed in traditional selling way and additional cost brought by the change of transaction in e-commerce environment.The commerce negotiation process of e-commerce describes the information communication of customers and merchants. In the process, intelligence agents can do negotiation of product price and quantity representing by the merchants. The purchaser and vender negotiate the price and quantity in virtual negotiating + building by e-commerce. Then they get the bargain. The two sides hope to get maximum profit in the transaction, so their benefit can implement by bidirectional + theory.Suppose the vender provides a product or a service in the market. The product has different quality grade + with corresponding different price. For a product with + quality grade, the vender sets a price +, while the purchaser give a buying price +. If +, then the transaction can proceed with price of +. If +, the transaction will not occur. + is the + time period, + is the + time period. + is the bargain amount of the product in + quality grade in + time period. The profit of product with quality grade of + in + time period for vender is: +. C is the marginal cost of the product, obeying uniform distribution in + zone. Fixed cost is supposed to be O. The evaluation of product by purchaser is +. It obeys uniform distribution in + zone. + and C are private information, which the opposite can not determine. If the purchaser buys the product by price P, he can get utility of +. + and + are price index and quality index ( obtained by the enterprise by data mining in CRM system). Here we suppose the highest quality grade is 1, while the lowest one is 0. + is opposite quality of product quality, selecting in +.In this static Bayes +, if formula (1) and (2) hold, strategy + will be rich + Bayesian + Equilibrium. For every + in + zone, + should meet:+Therein, + is the expected value of vender price when the vender price is lower than purchasing price.Suppose the strategies of the two sides are both linear strategy. In 1983, Myerson and Satterthwaite proved linear strategy equilibrium can produce higher expected profit the any other Bayesian + Equilibrium when the evaluation is uniform distribution.We can get these by first-order conditions:+=PicturePicture: transaction zone in linear strategy equilibriumThe transaction can only occur when +. From (1) and (2), the transaction can only occur when + in linear equilibrium, as showed in picture 1.+ construct a negotiation model from the both sides in the transaction that they can negotiate for the maximum transaction utility. The agents of venders and purchasers will do negotiation according to + price model and pricing model designed by the both sides. At last, they will agree to trade in their acceptable range.4 pricing model for digital products considering cost and competitionDigital products have high sunk cost and low marginal cost. That is to say, they have high cost when making the first product, but low cost when duplicate it. At the same time, the demand of digital products is related to timing, popularity and price. The characteristics of digital products show its not suitable to use traditional pricing methods, especially in which the method of setting price to marginal cost simply usually cant get enough profit to balance out fixed cost.4.1 Cost-Oriented Pricing Model+For product +, M; the price is P; C is the cost of digital product, which usually is sunk cost, representing as the copyright and marketing + cost; + is markup, gained by practical experience; superscript + represents it is price-quoted according to Cost-Oriented Pricing Model.4.2 Competition Reference Pricing Model+=+ represent Nth competitor, +，N; + is the suggested price by considering product + to competitor +; superscript + is the pricing result of Competition Reference Pricing Model. When there are several competitors, the Competition Reference Pricing Model is +, which is weighted model combining multi competitor effect.4.3 Demand ModelThe sales volume of digital products is related to the web traffic of the product and the possibility of purchase which is related to life-cycle, popularity and price of the product. the price is higher if the possibility of purchase is higher. While the customers are less willing to buy it when it has a higher price. So the Sale Model of digital intellectual products is:S（ti,fi,Pi）=N.exp(-xti).exp(w.fi)exp(-Spi),Here, N is the web traffic of product X, got by the web traffic of last periods; ti is the viability of certain pricing periods of product i; fi is the popularity of product I; the value of ti and fi are determined to physical circumstance of a product; pi is the price of product I; xti, w, spi are separately the viability, popularity and price factor of a product, which is a constant got by professional suggested methods.4.4 Model IntegrationCost-Oriented Pricing Model and Competition Reference Pricing Model both have their own basis and application field. Selection a proper model according to objective situation can get many advantages. We can use a weighted linear summarization model.Pi =Wi (Ci. (1+Si) )+Wij. PijHere, pi is the suggested price of integrated model; wi is weight factor of Cost-Oriented Pricing Model; Wij is the weight factor of the Jth competitor, j=1,.,n. The sale profit is:G（Pi,Si）=(Pi-Ci).S(ti,fi,Pi)From the result mentioned above, we can get an final model: maxWi(Ci(1+Si)+Wij.Pij-CiXN.exp(-Xti).exp(wfi).exp(-6.Pi)s.t.PiCi,iE1,M 5 Conclusion.The most important effect of e-commerce in consumer field may be the pricing of products and services. Because Internet can provide all kinds of product information including price information that the consumers is easy to become professional in pricing, Dynamical Pricing based on customer preference becomes an importa