搜寻成本下可替代产品的定价策略与库存决策

为探寻存在搜寻成本情况下消费者购买可替代产品时的定价与库存问题,从消费者效用出发,对厂商收益构建了基于马尔可夫决策过程的优化模型。在消费者方面,分析了其购买与继续搜寻的条件,并分别在搜寻成本不变和搜寻成本边际递减的情况下研究了消费者保留效用的变化情况以及购买相应产品的概率。此外,与很多相关文献不同的是,由于搜寻成本的存在,该情形下的消费者并不一定会在完成购买之前搜寻完所有的产品。在厂商方面,根据实际情况构建不同搜寻顺序下的收益模型并求解出最优定价策略与库存策略,并将定价模型与库存策略扩展到了动态的环境,为厂商制定价格及库存方案提供相应的决策支持。     

Signaling advertising by multiproduct firms

We consider the use of advertising expenses as quality signals in multiproduct firms, extending previous results on single product firms. In our model, a firm introduces sequentially two products whose qualities are positively correlated. We investigate whether there exist information spillovers from the first to the second market. We show that, when correlation is high, the equilibrium in market 2 depends on the quality reputation the firm has gained in market 1. Moreover, if a firm with a high-quality product 1 wants to separate from its low-quality counterpart, it needs to advertise more in this market than if the qualities of the two products are unrelated. This advertising level signals not only high quality in the first market, but also the likely quality of the second product. Thus, advertising in the first market has information spillovers in the second market.     

基于在线评论的多个竞争制造商和零售商的产品定价策略

在线评论作为一种产品信息传播载体,越来越受到网上电商及消费者的重视,并在很大程度上影响消费者的购买决策。本文在多个竞争性制造商为在线零售商提供可替代性产品并通过零售商销售给网络消费者的电子商务环境下,研究在线评论信息如何影响网络消费者购买决策及在线零售商和制造商的定价策略。以neo-Hoteling模型为基础,构建了依赖零售渠道在线评论的消费者选择模型,并通过模型求解定量分析了二级供应链结构分散系统下在线评论对多个竞争性制造商及零售商最优决策的影响。得到当制造商基于评论制定最优定价策略时,在线评论对市场竞争强度没有影响,但决定潜在市场大小;各产品的均衡批发价及销售价按一定的比例随评论揭示的该产品与其他产品质量均值之差(正或负)增加或减少,评论信息通常会使制造商因好评而获利,由于评论增加了不同产品需求的不对称性,零售商因而具有更大的调价空间,往往通过提高(降低)占据有利(不利)评论的产品价格获得更高的利润。     

考虑无缺陷退货的在线商品信息发布策略

消费者网络购物面临的不确定性往往导致非质量原因的退货。合理发布产品信息,并提供退货保障,是网络零售商促进消费者购买和提高利润的有效策略。基于消费者效用理论和博弈论,构建了产品信息影响消费者购买和退货模型,研究了零售商在垄断和竞争情形下的产品信息发布决策问题,发现垄断性零售商的最优信息发布策略和竞争性零售商在发布产品信息量和信息内容方面的均衡策略均取决于产品价值和退货成本特征,提出了不同市场结构下基于产品特征的在线商品信息发布策略。     

A joint dynamic pricing and advertising model of perishable products

Advertising and dynamic pricing play key roles in maximizing profit of a firm. In this paper a joint dynamic pricing and advertising problem for perishable products is investigated, where the time-varying demand rate is decreasing in sales price and increasing in goodwill. A dynamic optimization model is proposed to maximize total profit by setting a joint pricing and advertising policy under the constraint of a limited advertising capacity. By solving the dynamic optimization problem on the basis of Pontryagin’s maximum principle, the analytical solutions of the optimal joint dynamic pricing and advertising policy are obtained. Additionally, to highlight the advantage of the joint dynamic strategy, the case of the optimal advertising with static pricing policy is considered. Numerical examples are presented to illustrate the validness of the theoretical results, and some managerial implications for the pricing and advertising of the perishable products are provided.     

A simulation of the impacts of dynamic price management for perishable foods on retailer performance in the presence of need-driven purchasing consumers

Numerous studies have investigated dynamic pricing for perishable products. The models have been designed to determine an optimal pricing structure and improve retailer performance. Previous studies on pricing models for perishable products have considered various assumptions of consumer demand and purchasing behaviour from deterministic and stochastic price-dependent demands to myopic and strategic consumer purchasing behaviour. They have not, however, considered consumer demand in reaction to a situation where the display stock of a particular product has different qualities (such as shelf-life) and prices available at the same time. This is particularly applicable in the analysis of dynamic pricing models for perishable foods. In this paper, we investigate the impact of frequency of discount during a product’s selling period on retailer performance, by considering changes in consumer purchasing behaviour in response to the display stock of a particular food product having different remaining shelf-life and prices. On the basis of a literature review and data obtained from interviews with food retailers, a simulation study is performed to compare the performance of different pricing policies. The results demonstrate the benefits gained by adopting more dynamic price policies.     

Pricing and market segmentation using opaque selling mechanisms

In opaque selling certain characteristics of the product or service are hidden from the consumer until after purchase, transforming a differentiated good into somewhat of a commodity. Opaque selling has become popular in service pricing as it allows firms to sell their differentiated products at higher prices to regular brand loyal customers while simultaneously selling to non-loyal customers at discounted prices. We develop a stylized model of consumer choice that illustrates the role of opaque selling in market segmentation. We model a firm selling a product via three selling channels: a regular full information channel, an opaque posted price channel and an opaque bidding channel where consumers specify the price they are willing to pay. We illustrate the segmentation created by opaque selling as well as compare optimal revenues and prices for sellers using regular full information channels with those using opaque selling mechanisms in conjunction with regular channels. We also study the segmentation and policy changes induced by capacity constraints.     

Efficient formulations for pricing under attraction demand models

We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly.     

Utility indifference pricing and hedging for structured contracts in energy markets

In this paper we study the pricing and hedging of structured products in energy markets, such as swing and virtual gas storage, using the exponential utility indifference pricing approach in a general incomplete multivariate market model driven by finitely many stochastic factors. The buyer of such contracts is allowed to trade in the forward market in order to hedge the risk of his position. We fully characterize the buyer’s utility indifference price of a given product in terms of continuous viscosity solutions of suitable nonlinear PDEs. This gives a way to identify reasonable candidates for the optimal exercise strategy for the structured product as well as for the corresponding hedging strategy. Moreover, in a model with two correlated assets, one traded and one nontraded, we obtain a representation of the price as the value function of an auxiliary simpler optimization problem under a risk neutral probability, that can be viewed as a perturbation of the minimal entropy martingale measure. Finally, numerical results are provided.     

Coordinating pricing and production decisions in the presence of price competition

In this paper we study the effects of coordinating pricing and production decisions on the improvement of a firm’s position in a price-competitive environment. Assuming duopolistic market conditions, we use game-theoretic concepts and models to analyze two scenarios. A firm’s marketing and production departments may vertically coordinate their pricing and production quantity decisions and the two firms may horizontally compete for price-sensitive random demand. The two scenarios include (i) no coordination and (ii) coordination in both firms. We show that by coordinating their pricing and production decisions, competing firms can increase their profitability—especially when conditions are unfavourable (i.e., with smaller market sizes, higher unit costs and lower unit revenues). While it may be intuitive to expect that coordination will outperform non-coordination, our models provide a means for formalizing and quantifying the differences between the two policies.     

A nonnegative extension of the affine demand function and equilibrium analysis for multiproduct price competition

We derive a nonnegative extension of the affine demand function for differentiated substitute products from the optimization problem facing a representative consumer whose utility function is quadratic. We show that the extended demand function reduces to a linear program. The linear program has a simple intuitive interpretation in terms of a shifted price vector. We prove the existence and uniqueness of the Bertrand equilibrium in oligopolies consisting of multiproduct firms under the proposed demand function. The equilibrium, available in closed form, coincides with that obtained when allowing negative demands.     

EPR制度下的家电以旧换新回收策略优化模型

研究生产者责任延伸制度(EPR)约束下,家电生产销售企业集中决策下实施以旧换新进行废旧产品回收的问题。在对家电消费者市场结构进行分析基础上,建立以企业利润最大化为目标的实施以旧换新回收策略的优化模型,并根据我国家电行业EPR制度的特点,构建政府与企业间竞争的Stackelberg博弈模型,研究在政府环境效益最优时的补贴和基金征收标准下,企业以旧换新回收产品最优定价决策;同时,与企业不直接参与废旧产品回收时单一定价相应结果进行比较。结果表明:在EPR约束下,政府环境效益最优时的补贴和基金征收标准,对企业实施以旧换新回收策略的产品销量、总利润和废旧产品回收量的影响取决于企业成本结构、消费者结构、消费者效用和废旧产品回收处理能力。企业决策者需根据不同情形决定是否参与以旧换新回收实践。     

Stocking and pricing decisions under endogenous demand and reference point effects

In this paper, we study the newsvendor’s pricing and stocking decisions under reference point effects. The demand faced by the newsvendor is endogenous and the customers may also decide to procure the product from an outside option. We characterize the firm’s optimal pricing and stocking decisions. Our analysis reveals a threshold policy on the firm’s ordering and pricing decisions while considering the impact of reference point effects. We also find that as the level of optimism increases, the firm’s optimal ordering level decreases and optimal price increases. We further study the impact of loss aversion on the firm’s ordering and pricing decisions.     

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.     

Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model

We consider a manufacturer who sells both the new and remanufactured versions of a product over its life cycle. The manufacturer’s profit depends crucially on her ability to synchronize product returns with the sales of the remanufactured product. This gives rise to a challenging dynamic optimization problem where the size of both the market and the user pool are dynamic and their current values depend on the entire history. We provide an analytical characterization of the manufacturer’s optimal pricing, production, and inventory policies which lead to a practical threshold policy with a small optimality gap. In addition, our analysis offers a number of interesting insights. First, the timing of remanufacturing activity and its co-occurrence with new product manufacturing critically depends on remanufacturing cost benefits, attractiveness of the remanufactured product and product return rate. Second, there is a small upward jump in the price of the new product when remanufacturing is introduced. Third, the manufacturer keeps the new product longer on the market as the cost of remanufacturing decreases. Fourth, partially satisfying demand for the remanufactured item is never optimal, i.e., it is satisfied either fully or not at all. Finally, user pool and inventory of returned products are substitutes in ensuring the supply for future remanufacturing.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

Pricing policies for complementary products in a dual-channel supply chain

This paper investigates the pricing problem of complementary products in a supply chain with two manufacturers and one retailer, one of the two manufacturers uses dual channels including an online channel and a traditional retail channel to sell its product. We formulate four pricing game models through considering different market power structures of channel members, and derive the corresponding optimal pricing strategies. Based on the theoretical and numerical analysis, we study the effects of consumer channel loyalty, the level of complementarity, and the market power structures on the pricing strategies and the maximal profits of two complementary products. Some interesting and valuable managerial insights are obtained.     

基于回收风险的闭环供应链差异定价决策研究

随着资源的匮乏和环境污染的加剧,越来越多的企业和消费者开始关注废旧产品的回收再制造。针对制造商唯一寡头垄断市场竞争结构,引入回收风险,分别对制造商(OEM)自行回收废旧产品的闭环供应链、第三方回收商回收废旧产品的闭环供应链建立数学模型,分析给出各企业的最优差异定价规则,并从经济学意义上得到相关管理启示;数值实验的结果则进一步验证回购价格、回收风险、价格竞争强度对最优解的影响。研究结果表明:(1)闭环供应链结构会影响再制品价格及废旧产品的回收价格,但对OEM新品定价无影响。(2)回收风险的变化对价格决策的影响取决于闭环供应链的结构特征。当回收风险较低时,在激发消费者对再制品需求、促使消费者返回废旧产品、提升闭环供应链整体效率等方面,OEM自行回收模式优于第三方回收商回收模式;而当回收风险较高时,则第三方回收商回收模式优于OEM自行回收模式。(3)回收风险的降低使得闭环供应链总利润呈现出增长的趋势,进而进一步体现到再制造的经济价值。(4)OEM自行回收废旧产品需考虑到新品与再制品间的价格竞争强度,当价格竞争强度较弱时,OEM自行回收废旧产品可为OEM带来更多的利润;新品与再制品间的价格竞争也有利于再制品需求的提升。     

考虑网络外部性的生鲜企业渠道选择策略研究

考虑到生鲜产品容易变质而且线上配送时间较长,并且线上销售可为消费者带来额外网络外部性,传统生鲜企业在电商冲击的背景下需要考虑是否入驻电商平台开拓线上业务。为解决此类企业所面临渠道选择问题,本文考虑一个传统生鲜企业和一个主导电商市场的电商平台,并通过构建理论模型研究企业最优生鲜产品定价和渠道选择策略。研究结果表明,若平台所收取年服务费较低,则企业应入驻平台;反之,企业不应入驻平台。此外,消费者网络外部性敏感程度对企业入驻平台行为具有正影响。在拓展模型,本文考虑分散式供应链情形下企业最优渠道选择,结果表明相较于集中式决策,分散式供应链情形下零售商更不愿意入驻平台。此外,本文通过设计收益共享契约以协调生鲜企业与电商平台,并发现通过契约协调,零售商更愿意入驻电商平台。     

Optimal Pricing and Production Planning for Multi-product Multi-period Systems with Backorders

In this paper, we develop models for production planning with coordinated dynamic pricing. The application that motivated this research is manufacturing pricing, where the products are non-perishable assets and can be stored to fulfill the future demands. We assume that the firm does not change the price list very frequently. However, the developed model and its solution strategy have the capability to handle the general case of manufacturing systems with frequent time-varying price lists. We consider a multi-product capacitated setting and introduce a demand-based model, where the demand is a function of the price. The key parts of the model are that the planning horizon is discrete-time multi-period, and backorders are allowed. As a result of this, the problem becomes a nonlinear programming problem with the nonlinearities in both the objective function and some constraints. We develop an algorithm which computes the optimal production and pricing policy on a finite time horizon. We illustrate the application of the algorithm through a detailed numerical example.