考虑横向公平的双渠道销售闭环供应链定价策略与协调研究

考虑双渠道零售商和制造商组成的闭环供应链,分别构建了制造商直接回收、委托第三方回收模式下的动态博弈模型,以公平中性时的均衡策略为参照,对比分析了线下零售商的横向公平偏好对双渠道闭环供应链中各决策主体定价策略及利润的影响。研究表明,无论零售商是否存在横向公平关切行为,制造商直接回收模式都优于委托第三方回收。在直接回收模式下,线下零售商的横向公平偏好使得在正向供应链中的两零售商为提高市场占有率会竞相降低零售价格,制造商为鼓励竞争会降低批发价,并且价格均与横向公平关切系数负相关。在逆向供应链中,制造商会提高废旧产品的回收率;相比公平中性的情况,此定价策略使制造商和整个供应链系统效用增加,而两零售商收益递减。制造商作为渠道管理者为鼓励零售商之间竞相降价,可通过一个三方收益共享的契约实现协调,达到帕累托最优。     

Optimal markdown policy of perishable food under the consumer price fairness perception

Markdown policies are widely used by retailers to sell perishable food. Consumers purchase food at different prices during different sales periods. Some consumers may compare their experience with others who purchase the same items. Price unfairness or inequity is perceived when different prices are quoted without reasonable explanations. This study develops an optimal markdown model for perishable food pricing to optimise the food retailer revenue and enable a maximum aggregated consumer utility considering individuals’ price fairness perception. The model serves as the first step in evaluating trade-offs between food retailer revenue and consumer utility. In addition, it enables consumer utility to be depicted through perceived price fairness by including the effects of food perishability and scarcity. Another innovative feature is the equalisation of the consumer average aggregated utility during different sales periods as a condition of intertemporal price fairness perception. The proposed model is compared with two benchmark models to justify the effectiveness and advantages in the example. Finally, a sensitive analysis based on the food deterioration rate, consumer food desire rate and consumer average reservation price is conducted to justify the manner in which these factors influence the optimal pricing policy, and managerial insights are suggested for food retailers.     

Competing with customer returns policies

Return of products purchased by customers is a common phenomenon in the retail industry and results in costs to retailers. In practice, most retailers implement a full-refund policy, but the terms of customer returns policies vary. A customer returns policy serves as a post-customer service, and is a determinant factor in the customer’s decision to purchase the product, in addition to other factors, such as the price of the product. In this paper, for competing retailers who face customer returns, competition from multiple retailers and uncertain customer valuations of the product, we develop a model to examine when retailers can survive and what pricing strategy they should implement in a competitive market. We identify the co-existence conditions for multiple retailers and the existence conditions of a Nash equilibrium among competing retailers. We also show the impact of customer returns on the retailers’ pricing and market share, as well as on profits in a competitive market. Numerical examples are included to illustrate the major results discussed in the paper.     

需求不确定下考虑顾客策略行为的易逝品定价策略

在市场需求不确定且顾客具有策略行为时，研究易逝品厂商动态定价和价格承诺策略。通过建立厂商和顾客的不完全信息博弈模型，分析了两竞争厂商在2种定价策略下的精炼贝叶斯均衡，求得了均衡定价和期望收益。利用数值分析进一步比较2种定价策略的最佳适用范围，并讨论了需求预期、顾客策略程度和顾客购买意愿对均衡结果的影响。研究表明，在动态定价策略下，当市场处于适度竞争时，顾客策略程度越大，厂商收益越大；顾客购买意愿适中时，动态定价策略更优；顾客策略程度适中，或顾客策略程度较大且需求预期也较大时，价格承诺策略更优。     

网络零售商产品与运费联合定价的优化决策研究

消费者网络购物对运费的认知和商家的偏好存在差异。通过消费者的购买行为分析和效用函数的刻画,研究网络零售商在进行产品与运费联合定价时捆绑定价和分割定价的优化决策问题。讨论商家之间价格竞争的组合形式,提出最优定价存在的情形选项,论证价格决策的边界和适用条件,揭示商家之间采用捆绑定价的对称竞争均衡具有稳定性,及其不同均衡条件下商家利润的相对大小规律。研究结论表明,价格决策的选项取决于商家的产品成本高低,在产品成本给定的条件下,每种价格决策的边界依赖于市场中消费者的属性特征,即运费存怀疑的消费者比例,以及消费者对商家的偏好程度。     

Optimal pricing strategy for the perishable food supply chain

This research investigates the optimal pricing strategy for the perishable food supply chain. Using the setting of a two-echelon supply chain including a supplier and a retailer, we apply the game theory approach to derive the equilibriums for both a single pricing strategy and a two-stage pricing strategy. Through a comparison of the equilibriums, we explore how the two pricing strategies affect the supply chain’s decisions and supplier’s and retailer’s performance individually and collectively. The results of the analysis show that the optimal choice of pricing strategy depends on the price markdown cost and its relationship with the two critical thresholds that are determined by a combination of factors including the potential market size, the price and quality sensitivity factors, the initial quality, the unit product cost, and the quality deterioration rate.     

Wholesale price discrimination with interdependent retailers

This paper examines the relationship between one manufacturer and two retailers who sell a product on their downstream markets. If a retailer invests in activities that enhance demand and, for example, improve the perceived image of the product, he or she might attract more customers, as well as increase the sales volumes of other retailers. In such a situation, free rider problems arise between the retailers, which finally lead to reduced sales efforts. We show that for linear wholesale prices, the manufacturer’s pricing strategy depends on the retailers’ investment costs and derive conditions for the optimality of wholesale price discrimination. We find that for low and high costs the manufacturer charges the retailers identical wholesale prices and thus does not have to bear any agency costs due to free riding. In all other cases, the manufacturer mitigates this problem by engaging in wholesale price discrimination. Our results indicate why it might make sense for a manufacturer to charge different wholesale prices even when the retailers have equal cost structures, market conditions, and investment options.     

消费者策略行为下全渠道服务区域及定价的优化研究

为了研究消费者策略性采购行为对于全渠道BOPS(buy-online-and-pick-up-in-store)运营服务区域和定价的影响,对全渠道零售商实行BOPS运营模式进行建模,并利用最优化理论(K - T条件)得到全渠道零售商的最优定价及最优服务区域。利用数值分析进一步证明消费者策略性采购行为是全渠道零售商制定BOPS运营服务区域和定价策略时应考虑的重要因素。研究表明,对于距离较远的消费者,全渠道零售商需要考虑顾客策略性采购行为,以争取到更多有顾客策略性采购行为的消费者来本店采购;而对于近处的消费者,全渠道零售商不需要考虑其行为,以减少全渠道零售商的渠道运行成本。此外,最优服务区的确定可以使得零售商以较少的渠道成本为消费者提供更好的服务,减少其运营决策失误。     

Optimal piecewise-constant price under heterogeneous sensitivity to product freshness

When perishable products are priced uniformly, regardless of the amount of time remaining until expiration, consumers may gravitate towards fresher products, leaving some inventory unsold. This research considers dynamic pricing policies as well as replenishment policies in the context of perishable products with a fixed shelf life. Consumers are assumed to be heterogeneous in their sensitivity to freshness, i.e. their willingness to pay more for fresher products. We develop a model for identifying an optimal (profit-maximising) dynamic pricing policy and for evaluating the extent to which both the retailer and the consumer benefit from the implementation of a dynamic pricing policy as opposed to a static policy. The model assumes that the retailer is able to utilise knowledge regarding the heterogeneous characteristics of incoming customers (e.g. the retailer can gather specific information about customers’ historical purchases). Unexpectedly, it is proven that in an optimal pricing policy, the retailer should assign a lower price to fresher products and then raise the price as the products approach expiration. A numerical illustration shows that profits are strongly influenced by the volatility of consumer sensitivity to freshness; specifically, this variable has the potential to reduce optimal profits by up to 8%.     

Optimal purchase and selling strategy for wholesaler of produce: sorted or unsorted selling?

Produce (e.g. fruit and vegetable) varies in quality when it is picked from plants. Then a produce wholesaler has two sales strategies: (1) unsorted selling (US), i.e. selling the produce to the market at one price and (2) sorted selling (SS), i.e. pre-sorting the produce into different grades by quality and selling them at different prices. When the SS strategy is adopted, the demands of the different grades are uncertain and substitutable. In this paper, we study the joint optimal purchase and sales strategy for selling mixed quality produce to customers with heterogeneous quality preferences. We first derive the optimal purchase policies under the two strategies and then identify the conditions under which the SS or US strategy is optimal. We show that the optimal sales strategy is determined by the marginal purchase and sorting cost and the fixed investment cost, the overall quality level of the produce, and the substitution rate for the high-quality and low-quality produce. This finding differs from the conventional wisdom that the SS strategy is optimal in the produce retail business. Finally, we conduct numerical studies based on real-world data to generate managerial insights from the analytical findings.     

竞争环境下考虑需求学习的动态定价策略

为了分析在顾客到达率不确定且面临市场竞争的情况下,零售商如何通过需求学习来动态地调整价格,以达到收益最大化的目的,运用博弈理论和动态规划方法建立了多周期随机动态定价优化模型,分析了需求学习下的价格竞争均衡。研究表明,在竞争和需求学习的市场环境下,零售商的价格博弈存在均衡,且多个均衡价格存在时,各零售商的收益与均衡价格成正比。应用算例分析了需求学习的效果,求出了需求学习下零售商竞争的价格均衡,并得出一些管理启示。     

不同主导力量下考虑公平偏好的旅游供应链定价策略

为了研究不同主导力量下决策者的公平偏好特征对旅游供应链定价策略的影响,建立了由一个景区和一个旅行社组成的旅游供应链Stackelberg主从博弈模型,在景区主导和旅行社主导两种供应链权势结构下,引入从属方的公平偏好特征,研究公平偏好信息对称与不对称情形下的定价策略,并进行对比分析。结果表明,景区主导情形下,旅行社公平偏好信息对称时,景区将采取降低门票批发价格行为,旅行社最优销售价格不变;旅行社公平偏好信息不对称时,景区最优门票价格不变,旅行社最优销售价格逐渐增大。旅行社主导情形下,无论景区公平偏好信息对称与否,景区最优门票批发价格逐渐增大,旅行社最优销售价格不变,但信息不对称下的景区最优门票价格小于信息对称情形。     

Dynamic quality and pricing decisions in customer-intensive service systems with online reviews

In this paper, we investigate dynamic quality and pricing decisions for customer-intensive service systems with online reviews. We construct a dynamic programming model to determine the optimal quality and pricing strategies. We find that with online reviews, the supplier is forced to provide a higher quality at a higher price for fewer customers, especially when the customer intensity is high. Interestingly, although online reviews deliver quality information for later consumers, the provided quality may decrease over time. Next, we compare the optimal strategies with those of models of either quality flexibility or pricing flexibility, respectively, to examine the merits of our developed model of both quality and pricing flexibilities. The comparison results demonstrate that our model can achieve higher profits, and the advantages of our model increase with the number of periods. In addition, quality (pricing) flexibility is more valuable when consumers are more sensitive to service price (quality). Furthermore, we compare our formulated model with the model for a regular service system, and we illustrate that the optimal quality and pricing strategies in our system are quite different from those of the regular service system.     

Optimal two-level piecewise-constant price discrimination for a storable perishable product

Price differentiation over time is an additional policy that firms might consider when determining prices for perishable products. The common policy of a fixed price regardless of freshness might result in leaving some expired inventory unsold. Price differentiation can impact the demand for perishable products, which declines as the expiration date approaches. We develop an optimisation model with the goal of evaluating the monetary effectiveness of the strategy of simultaneously combining price discrimination across heterogeneous consumers with price differentiation over time for perishable inventory under separable multiplicative demand factors of price and time. Necessary optimality equations are derived, and their solutions are proved to constitute a unique global optimal solution. It is proved that an optimal pricing policy is to implement price discrimination with respect to consumers’ sensitivity to freshness, while dynamically changing the price over time, starting with a lower price at the early stages of the product’s shelf life and increasing it at a later stage. The monetary benefit that the retailer and consumer can derive from the suggested pricing policy is evaluated by comparing the model to other models in which price discrimination or dynamic pricing are not implemented. A numerical example that illustrates the significance is introduced. From the analysis of a numerical illustration of the model, it is concluded that a dynamic price discrimination policy can be approximated by an identical-to-all dynamic pricing policy in order to maximise the retailer’s profit and thus, mitigate the retailer’s risk from failing in the process of implementing price discrimination.     

Managing production of high-tech products with high production quality variability

We consider production systems in technology industries where output quality of a single production run has a large variance. Firms operating such systems classify products into different quality bins and sell units in one bin at the same tagged quality level and the same price. Consumers have heterogeneous quality preferences and choose that quality that maximises their net utility. We examine firms’ assortment, production and pricing problem. We present a three-stage solution procedure that optimises the production quantity, quality specification and number of bins. In that regard, we show that for a manufacturing technology with known quality distribution and known distribution of customers’ quality preference, the optimal assortment and production quantity are set such that on average, the demand of each bin is exactly fulfilled. We examine the impact of an improved manufacturing technology, variation in consumer preferences and changing price premium on the optimal assortment, lot size, market share, yield loss and the overall profitability. We further show that when the quality distribution of the manufacturing process is unknown, downward substitution leads to product offering of higher quality and higher prices. Finally, we discuss practical considerations for pricing, technology and optimal product offerings, and explain the proliferation of bins witnessed in the last decade in the processor industry.     

新鲜度差异下两种可替代生鲜品的多阶段定价策略研究

研究单个零售商销售2种可替代生鲜产品时的价格决策,建立3种定价策略下的决策模型,得到2种产品的最优固定价格、最优折扣价格和最优捆绑价格售价;通过数值仿真分析影响零售商价格决策的因素及其影响大小。研究结果表明,3种策略下产品价格都与产品新鲜度临界值同方向变化;最优固定价格随销售期临近度的增大而变高;对比3种策略下零售商的利润发现,有时捆绑价格是占优策略,有时折扣价格是占优策略,参数的大小是关键因素。     

Dynamic pricing for fashion goods with partial backlogging

In today’s very competitive business environment, one way that companies endeavour to cut their costs is by reducing inventory. In addition to the use of inventory management, retailers of fashion goods usually employ dynamic pricing to influence market demand, such as non-periodic clearance sales or markdowns to increase sales volume and deplete stocks of goods. This paper deals with the specific demand style of fashion goods under the condition in which partial backlogging is allowed and the number of replenishments is constrained in order to fit in the real world situation of limited supply. The optimal replenishment quantities and the corresponding intervals are obtained with consideration of customers’ reserve prices and their influence on demand. In addition, discrete dynamic pricing is considered to frequently change the product prices to meet the customer requirements in different periods and to avoid high inventory holding costs from unsold products. A numerical example is used to validate the feasibility and effectiveness of the proposed approach, and sensitivity analyses are performed to investigate the important factors that influence the replenishment cycle and profit.     

An encompassing view on markdown pricing strategies: an analysis of the Austrian mobile phone market

Fierce competition and rapid technological progress have considerably reduced the life cycle length for mobile phones in the last decade. Once a new mobile phone is launched, providers on the market under consideration practice a markdown strategy. Profits of the providers are generated mainly via the monthly (base plus variable) fees accruing during contract duration whereas the mobile phones are over large parts of their life cycle sold below the constant purchase price charged by the OEM supplier. The problem of applying such markdown strategies has recently been further emphasized by an increased competition among the providers cutting back revenues generated by the contracts. Although providers frequently complain about this situation of pre- and cross financing the mobile phones, none of them has yet risked stopping the practiced markdown pricing strategies. In our contribution, we investigate a new model for the analysis of the effects of alternative (markdown) pricing strategies. Building on previous research that has investigated the dynamics and feedbacks between pricing and inventory decisions caused by delays and inaccurate forecasts, we develop a more encompassing view on the market considering the dependency and dynamics between customer satisfaction, loyalty, and repeat purchase rates. Furthermore, we explicitly model price and reference price effects and their impact on the attraction of new customers. Various data sources are employed to calibrate a system dynamics model for one of the providers and its interrelation with a typical supplier and the customers. Our model indicates that a reduction of the currently practiced markdown strategy would reduce the provider’s overall profit for contract customers. In contrast, the results for prepaid customers could be improved by a careful reduction of markdowns.This research was supported by WWTF project: Mathematical Modeling for an integrated Demand and Supply Chain Management. The authors wish to thank Alf Kimms, the editor and the anonymous referees for their valuable comments     

Online hot selling period and its impact on e-retailer’s pricing strategies

The express delivery industry is often overloaded in some hot online selling seasons, which causes consumers’ dissatisfaction. Under such a circumstance, the e-retailer can utilise two opposite strategies, i.e. to set-up either a low price with a pre-announced markdown pricing (PMDP) strategy, or a high price with a pre-announced markup pricing (PMUP) strategy for the hot selling period. As both the prices and the express service quality are different between the regular period and the hot selling period, consumers can strategically choose their purchase time, which will in turn influences the e-retailer’s pricing strategy. To investigate under what condition one pricing strategy will dominate the other, we propose a two period pricing model in which the selling season are divided into regular and hot selling period, and all consumers are assumed to be strategic. The e-retailer determines the prices over the two kinds of periods to maximise its profit. The comparison shows that a PMUP (resp. PMDP) strategy is preferred when the overloading degree in the hot selling period is slight (resp. heavy). Furthermore, we extend our model by incorporating the competition of traditional retailers.