基于数据和整体的航空网络静态定价模型

建立了一个静态定价与座位分配联合模型.利用模型的性质,将问题简化为一个可分的凹规划模型.特别地,在一个三航段网络上,从模型的网络流形式推出最优目标函数具有良好的性质,并对模型的最优价格决策进行了灵敏度分析.最后给出了一个双枢纽网络上对细分产品定价的算例.     

两阶段双寡头垄断市场Hotelling定价模型

激烈的双寡头垄断市场竞争环境下,单一定价和歧视定价成为厂商选择的两大定价策略.考虑到网络外部效用的广泛存在性与对称性,对传统的Hotelling模型加以改进,分价格竞争和策略选择两个阶段,对双寡头垄断厂商的定价策略进行了博弈分析,指出了各种均衡情况及需满足的条件,并验证了歧视定价相对单一定价的边际成本、网络外部效应、消费者对产品的忠诚度等因素对厂商进行定价策略选择的重要影响,为其制定最优定价策略提供了指导.     

随机需求下具有不对称信息的闭环供应链的最优差别定价模型

在随机需求条件下建立了由一个制造商和一个零售商所组成的闭环供应链差别定价模型。在制造商成本信息对称和信息不对称情况下,分别讨论了闭环供应链的最优差别定价问题,得到了在不同信息条件下的最优定价组合以及最优的订购量.最后通过数值算例分析了成本信息不对称对两种产品的零售价以及订购量的影响.     

非对称信息下供应链多产品最优合同决策

研究二级供应链中具有多种可替代产品,而零售商成本为私有信息时的制造商最优合同定价问题.利用委托代理理论中的显示原理,建立了制造商定价的最优线性规划模型,并通过图解法求出了零售商为高、低成本时制造商的最优销售额,进而求出了制造商的最优价格合同.用计算机仿真进行了数值实例分析.     

具有产品回收的闭环供应链差别定价策略研究

研究一个制造商与一个销售商组成的具有产品回收的闭环供应链差别定价问题.利用博弈理论对几种差别定价模型进行了分析,得到了闭环供应链成员的最优定价策略和最终利润.进一步对几种模型的效率进行了分析,发现分散式决策使得整个闭环供应链利润损失了25%,最后提出一种收益共享协调差别定价策略,使得分散式闭环供应链的效率与集成式闭环供应链效率等同.     

二手市场对耐用品垄断厂商再制造决策的影响分析

考虑耐用品可多周期使用的特点,从消费者效用角度建立了无限周期中存在二手市场时耐用品垄断厂商再制造决策模型。运用稳态均衡分析方法得到,二手市场会降低耐用品垄断厂商选择再制造策略的成本临界值;提高再制造耐用品的最优定价、降低新耐用品的最优定价;新耐用品价值越高、再制造成本越低,二手市场对耐用品垄断厂商的最优决策影响越大。最后,通过数值分析验证了理论分析的结论。     

考虑策略性消费者受不确定性社交影响的双渠道定价策略研究

随着互联网等新兴技术的发展,消费者对产品的价格追踪以及学习更加便利,其购买决策也会受到其他参与者决策的影响.消费者根据产品的上市价格和清仓时的可获得性决策购买时间,这种自身策略等待及受外部他人社交影响的行为加剧了市场需求的不确定性.承诺定价与差价补偿定价策略能有效地缓解消费者的策略等待行为,但相对动态定价策略缺少灵活性与便利性.因此文章研究零售商在动态定价、承诺定价、差价补偿定价策略中的选择问题.运用消费者偏好理论、博弈论和最优化理论求解各种模型的最优解及存在条件,进一步探讨消费者学习能力和社交影响对最优解的影响.结论表明,当消费者学习能力大于一定水平时,零售商应选择差价补偿定价,否则承诺定价为最优选择;消费者的学习能力增加了实体渠道的最优零售价和零售商整体利润,但降低了线上渠道的最优价格:社交影响有利于双渠道最优价格和零售商最优利润的增加.最后通过数值分析验证了上述模型的有效性和可靠性.     

考虑捆绑销售的多产品供应链定价策略

以一个制造商向一个零售商同时销售两种互补产品的二级供应链为研究对象,研究了制造商、零售商分别采用不同捆绑策略下的供应链定价博弈问题,并对四种定价模型(分开—分开,分开—捆绑,捆绑—分开,捆绑—捆绑)进行比较分析,探讨了产品互补程度、边际利润水平与供应链利润、最优捆绑策略的关系。研究结果表明,对领导者制造商而言,采取分开定价是占优决策;对于追随者零售商而言,是否采取捆绑定价取决于产品互补程度与产品边际利润水平比值,当产品互补程度变大或者边际利润比值降低时,零售商的最优策略由捆绑策略向分开定价策略转变。     

网络服务中基于流量的定价策略

本文分析了网络服务中带宽的类似公共产品使用和ISP与顾客间主从博弈，导致拥塞，接着证明基于流量的定价策略较之固定定价策略更能控制网络拥塞，随后在基于流量的定价策略下，分析了垄断的市场中社会总福利达不到最优，ISP间的竞争会增加顾客效用，最后指出社会总福利达到最优时的价格是一影子价格。     

基于在线评论的新产品定向市场播种最优策略研究

定向市场播种,即选择特定的消费群体对其免费发放新产品,由此获得的在线评论对其他潜在消费者的购买决策有较大的影响作用,但还没有 相关研究。以在线销售的新产品为研究对象,基于Hoteling模型,加入在线评论对消费者预期值的影响作用来构建企业最优收益模型,研究垄断厂商最优的定向播种策略。研究结果揭示了(1)最优播种目标与消费者对产品的初始预期值相关:预期值较高时,可不播种;预期值处于中等水平,可选择均匀播种;预期值较低时,应选择高匹配用户播种;(2)三种播种方式下各自的最优播种比例及其定价策略;(3)当消费者初始预期值与产品不匹配成本发生变化时,三种播种策略下最优的播种比例和定价策略的调整方案。研究结果为探究在线评论对播种策略的影响提供了新的研究方向和理论依据。     

Optimal control of price and production in an assemble-to-order system

We study the optimal control of an assembly system that produces one assembled-to-order final product with multiple made-to-stock components and sells it at variable price. It is shown that a threshold control on component production, product price, and product orders maximizes total discounted profit over an infinite horizon.     

服务水平约束下动态定价与库存管理

本文研究服务水平约束下的动态定价与库存管理问题。企业在有限期内销售某种产品,产品的需求为随机需求,且期望需求依赖于产品价格。在每一期期初,企业需要在满足服务水平约束的条件下同时决定订货量和产品价格。本文首先构建了动态定价和订购联合决策的随机动态规划模型,并证明了最优解的存在性。进一步,通过对最优解的结构进行刻画,将原问题的求解转化为若干子问题的求解,降低了问题求解的难度。通过对最优解的分析发现,当期初库存增大时,产品最优价格降低。通过分析目标服务水平对利润的影响,证明了服务水平与利润之间存在权衡,实现高的服务水平需要承受利润损失。数值模拟表明,相对于传统的静态定价策略,采用动态定价策略可以降低追求服务水平所带来的利润损失,验证了动态定价策略的有效性。     

Responsive pricing under supply uncertainty

Consider a retailer orders a seasonal product from a supplier and sells the product over a selling season. While the product demand is known to be a linear function of price, the supply yield is uncertain and is distributed according to a general discrete probability distribution. This paper presents a two-stage stochastic model for analyzing two pricing policies: No Responsive Pricing and Responsive Pricing. Under the No Responsive Pricing policy, the retailer would determine the order quantity and the retail price before the supply yield is realized. Under the Responsive Pricing policy, the retailer would specify the order quantity first and then decide on the retail price after observing the realized supply yield. Therefore, the Responsive Pricing policy enables the retailer to use pricing as a response mechanism for managing uncertain supply. Our analysis suggests that the retailer would always obtain a higher expected profit under the Responsive Pricing policy. In addition to examining the impact of yield distribution and system parameters on the optimal order quantities, retail prices, and profits under these two pricing policies, we analyze two issues arising from responsive pricing. The first issue deals with the case in which the retailer can place an emergency order with an alternative source after observing the realized yield, while the second issue deals with a situation in which the retailer has to allocate his order among multiple suppliers.     

Pricing problems with a continuum of customers as stochastic Stackelberg games

The pricing problem where a company sells a certain kind of product to a continuum of customers is considered. It is formulated as a stochastic Stackelberg game with nonnested information structure. The inducible region concept, recently developed for deterministic Stackelberg games, is extended to treat the stochastic pricing problem. Necessary and sufficient conditions for a pricing scheme to be optimal are derived, and the pricing problem is solved by first delineating its inducible region, and then solving a constrained optimal control problem.The research work reported here as supported in part by the National Science Foundation under Grant ECS-81-05984, Grant ECS-82-10673, and by the Air Force Office of Scientific Research under AFOSR Grant 80-0098.     

Dynamic Slotting and Pricing Decisions in a Durable Product Supply Chain

We consider a supply chain in which a manufacturer sells an innovative durable product to an independent retailer over its life cycle. We assume that the product demand follows a Bass-type diffusion process and that it is determined by the market influences, retail price of the product, and shelf space allocated to it. We consider the following retailer profit optimization strategies: (i) the myopic strategy of maximizing the current-period profit and (ii) the far-sighted strategy of maximizing the life-cycle profit. We characterize the optimal dynamic shelf-space allocation and retail pricing policies for the retailer and wholesale pricing policies for the manufacturer. We compute also these policies numerically. Surprisingly, we find that the manufacturer, and sometimes even the retailer, is better off with a myopic retailer strategy in some cases.     

Pricing policies for substitutable products in a supply chain with Internet and traditional channels

This study considers pricing policies in a supply chain with one manufacturer, who sells a product to an independent retailer and directly to consumers through an Internet channel. In addition to the manufacturer’s product, the retailer sells a substitute product produced by another manufacturer. Given the wholesale prices of the two substitute products, the manufacturer decides the retail price of the Internet channel, and the retailer decides the retail prices of the two substitute products. Both the manufacturer and the retailer choose their own decision variables to maximize their respective profits. This work formulates the price competition, using the settings of Nash and Stackelberg games, and derives the corresponding existence and uniqueness conditions for equilibrium solutions. A sensitivity analysis of an equilibrium solution is then conducted for the model parameters, and the profits are compared for two game settings. The findings show that improving brand loyalty is profitable for both of the manufacturer and retailer, and that an increased service value may alleviate the threat of the Internet channel for the retailer and increase the manufacturer’s profit. The study also derives some conditions under which the manufacturer and the retailer mutually prefer the Stackelberg game. Based on these results, this study proposes an appropriate cooperation strategy for the manufacturer and retailer.     

Integration of pricing and capacity allocation for perishable products

For years pricing and capacity allocation decisions in most revenue management models have been carried out independently. This article presents a comprehensive model to integrate these two decisions for perishable products. We assume that the supplier sells the same products to different micro-markets at distinct prices. Throughout the sales season, the supplier faces decisions as to which micro-markets or customer classes should be served and at what prices. We show that (i) at any time, a customer class is active (being served) if and only if the price offered is over a threshold level, but the optimal price may not be the highest one of the supplier’s choice; (ii) when the price decision is made in conjunction with inventory, it is similar to the procedure shown in pure pricing models, i.e., the optimal price comes from a subset of prices that forms a maximum increasing concave envelope; (iii) because of dynamic changes in the optimal prices, the nested-price structure does not necessarily hold in general and needs to be redefined; and (iv) the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory, price and demand intensity. Numerical examples are provided.     

Product variety, pricing and differentiation in a supply chain

Manufacturers typically sell consumer products through retailers and the presence of intermediaries has interesting ramifications for their product variety and pricing decisions. Retailers may want higher variety to help reduce price competition but the costs of variety are borne by the manufacturer. The increased variety may increase demand and profits for the manufacturer too but this depends on market-specific factors as well as costs. We explore these interactions through a model wherein a manufacturer sells multiple product variants at a wholesale price to two retailers who in turn compete for consumers. Consumers choose between the retailers based on the price and variety offered by each retailer and the search or transportation cost incurred by the consumer, equivalent to the level of retailer differentiation in our model. Several insights emerge from the analysis. The manufacturer offers the same variety to both retailers and this variety increases with market size and consumer sensitivity to variety. We find that some retailer differentiation benefits the retailers (not the manufacturer) but too much differentiation hurts both the retailers and the manufacturer. If the market is fully covered, then the channel is coordinated even with a simple wholesale pricing contract. If the retailers incur costs to sell the product, the manufacturer surprisingly loses out more than the retailers and in fact absorbs some or all of the retailer costs. Finally, asymmetry between retailers has some unexpected consequences. For example, variety is not impacted by asymmetry in consumer preferences for a retailer and the manufacturer offers the same variety to both retailers.     

一种电子商务环境下耐用品的动态定价模型与策略

针对电子商务环境下消费者对价格歧视的抗拒问题,以及耐用品生命周期长、产品需求依赖于时间、价格等特点,提出了一种动态定价模型与策略。该模型通过构造转移概率矩阵,推导出在线消费者浏览到耐用品的不同价格状态下的概率,接着根据消费者多阶段效用函数分析消费者的购买决策行为,进而给出零售商利润达到最大化时的最优定价策略集合。为了验证模型与策略的有效性,通过数值模拟实验,分析模型主要参数变化对最优定价策略的影响。研究发现当效用折扣因子越高,零售商应该降低促销频率和高价格并且提高低价格,从而诱导高端消费者在高价格购买产品。折扣效用因子大小还决定了网上零售商是否要隐藏自己的促销概率。     

Inventory control by different service levels

This paper examines the multiple period inventory control problem of a single product with multiple (two) prices, depending on service level, in which optimal pricing and ordering decisions are made in each period. Traditional inventory and pricing models consider only single products, single prices, and single service levels. However, this research paper finds that a seller can improve inventory control and revenue by offering multiple prices depending on service level. This research considers a single product with multiple (two) pricing policies corresponding to service level as follows: if the customer is willing to delay the shipment, he/she will be offered a lower regular price. Otherwise, the customer will pay the regular price plus extra charges for express service. In this paper, I show the following: (1) there is an optimal pricing and replenishment policy that can control inventory and (2) there exists a finite threshold for inventory levels such that if the inventory level at the beginning of each period is higher than the threshold, the customer will be offered the express service at the regular price, without any extra charge.