Optimal dynamic pricing for deteriorating items with reference-price effects

In this paper, a dynamic pricing problem for deteriorating items with the consumers’ reference-price effect is studied. An optimal control model is established to maximise the total profit, where the demand not only depends on the current price, but also is sensitive to the historical price. The continuous-time dynamic optimal pricing strategy with reference-price effect is obtained through solving the optimal control model on the basis of Pontryagin's maximum principle. In addition, numerical simulations and sensitivity analysis are carried out. Finally, some managerial suggestions that firm may adopt to formulate its pricing policy are proposed.     

Pricing and inventory strategies under quick response with strategic and myopic consumers

We divide consumers in the selling period into two types according to their purchasing behavior: strategic customers and myopic customers. We address the optimal inventory and pricing decision problem of a retailer considering strategic and myopic consumers with and without a quick response. The results indicate that the retailer should establish a higher price to sell only to myopic customers if there is a sufficient presence of myopic customers in the market, and the retailer should set a lower price to sell to myopic and strategic customers if the number of myopic customers in the market is relatively low. A quick response can decrease the initial ordering quantity and increase the retailer's profit when selling only to myopic customers or selling to both myopic and strategic customers. Moreover, a quick response is beneficial for the retailer to improve the product's retail price if the retailer wishes the two types of customers to purchase the product during the selling period. We also find that the pricing strategy considering strategic and myopic consumers under a quick response will increase profits more than the pricing strategy only considering myopic customers. Finally, numerical experiments are conducted to illustrate and validate the proposed models and provide managerial insights.     

基于Cournot-Bertrand 混合竞争的企业集团转移定价决策

研究多部门企业集团在最终产品市场面临Cournot-Bertrand 混合竞争时的转移定价决策问题. 由动态博弈的逆向归纳求解方法可知, 均衡转移定价策略将随着最终产品之间的关系而有所差异. 当竞争对手仅生产最终产品时, 最优转移价格高于边际成本, 且采用价格-产量竞争优于产量-价格竞争; 当竞争对手为垂直一体化企业时, 采用产量-价格竞争的最优转移价格高于边际成本, 采用价格-产量竞争则低于边际成本, 而且采用产量-价格竞争优于价格-产量竞争.

     

Selling luxury fashion to conspicuous consumers in the presence of discount sensitivity behavior

In the luxury fashion industry, with the possibility of stockout, conspicuous consumers may purchase products at the full price rather than wait for any potential discount. However, in the presence of a possible future discount, conspicuous consumers may also feel regret to purchase at the full price if they find that the product is still available at the markdown price. Considering the possible stockout and future discount, in this paper, we evaluate the firm's pricing and production decisions on conspicuous consumers in the presence of discount sensitivity behavior. We build up an analytical model and consider that the customer purchasing utility decreases with discount sensitivity if she/he purchases at the full price. The firm can create scarcity in the market by reducing inventory to induce customers to purchase early. If the fraction of the customers with discount sensitivity is lower than a certain level, the firm should intentionally produce a large amount of products. Moreover, we find that product design enhancement can effectively weaken the negative effects of customer discount sensitivity on the quantity decisions. More managerial insights are discussed.     

考虑参照价格效应的易逝品定价与订购策略

在考虑消费者参照价格效应的基础上,构建一个易逝品的定价与订购联合决策模型,其中产品的需求不仅依赖于销售价格还与该产品在消费者心目中的参照价格相关,变质率为常数,系统不允许缺货.分别讨论了对称参照价格效应和非对称参照价格效应两种情况下零售商的最优定价与订购决策问题,证明并得到关于模型结构的一些性质,进而设计了问题的求解算法.通过数值方法分析了参照价格效应参数和变质率对系统最优解的影响,以及两种情况下最优解之间的关系.结果显示:当面对具有参照价格依赖的消费者时,采用适当的营销策略来提高消费者的参照价格对零售商总是有利的;对高变质率产品而言,零售商可保持一个较稳定的订购策略,更多地关注产品的定价策略;面对损失厌恶型消费者,随着消费者参照价格的逐渐提高,零售商的定价与订购策略均应缓慢地改变,而不宜急剧变化.     

Optimal pricing and lot-sizing for perishable inventory with price and time dependent ramp-type demand

Product perishability is an important aspect of inventory control. To minimise the effect of deterioration, retailers in supermarkets, departmental store managers, etc. always want higher inventory depletion rate. In this article, we propose a dynamic pre- and post-deterioration cumulative discount policy to enhance inventory depletion rate resulting low volume of deterioration cost, holding cost and hence higher profit. It is assumed that demand is a price and time dependent ramp-type function and the product starts to deteriorate after certain amount of time. Unlike the conventional inventory models with pricing strategies, which are restricted to a fixed number of price changes and to a fixed cycle length, we allow the number of price changes before as well as after the start of deterioration and the replenishment cycle length to be the decision variables. Before start of deterioration, discounts on unit selling price are provided cumulatively in successive pricing cycles. After the start of deterioration, discounts on reduced unit selling price are also provided in a cumulative way. A mathematical model is developed and the existence of the optimal solution is verified. A numerical example is presented, which indicates that under the cumulative effect of price discounting, dynamic pricing policy outperforms static pricing strategy. Sensitivity analysis of the model is carried out.     

Multi-period optimization with loss-averse customer behavior: Joint pricing and inventory decisions with stochastic demand

To maximize a firm's profit over a finite planning horizon, we develop a dynamic optimization model by considering loss aversion when making pricing and inventory decisions. We estimate customer demand through a choice model, which incorporates reference price, utility function and customer loss aversion. Our model forms the core of the expert system for decision support. Through a sequence of Bellman equations, we find that the firm's profit is a concave function of price and inventory, and we solve the model optimally. The profit is positively correlated with the reference price, and the price and inventory decisions are non-monotonic functions of loss aversion intensity. Our results shed new light on pricing and inventory management with customer behavior in a multi-period system. Through various theorem developments, we are able to identify the optimal inventory level and the corresponding price. Numerical examples are provided to illustrate and validate the model and to derive managerial insights. To show the potential significance, we demonstrate how a dynamic programming model yields good results with customer loss aversion under realistic customer behavior assumptions. Our system can improve the efficiency of decision making and provide better customer service.     

考虑参照价格效应和消费者行为的预售及退货策略

生产商通过预售可以提前获取市场需求信息,但由于消费者产品估值的不确定性,生产商可能面临现货期大量退货的风险,制定合理的预售与退货策略成为生产商必须解决的核心问题.鉴于此,运用报童模型和消费者期望效用理论,考虑参照价格效应对消费者购买行为以及生产商预售期定价策略的影响,构建单一预售、预售退货不再出售、预售退货再出售3种策略下的期望利润模型,求解得到相应的最优生产量以及不同退货策略下的退货补偿价格取值范围,并对模型进行对比分析.研究表明:预售退货不再售与退货再售情形下,高价预售与低价预售策略中均存在一个退货补偿价格临界阈值;知情消费者中具有参照价格效应的消费者其比率决定了生产商在预售期的定价策略,且低价预售策略下,预售价格随退货补偿价格与参照价格系数的提高而降低.     

Pricing and inventory policies for Hi-tech products under replacement warranty

Companies, especially in the Hi-tech (high-technology) industry (such as computer, communication and consumer electronic products), often provide a replacement warranty period for purchased items. In reality, simultaneously determining the price and inventory decisions under warranty policy is an important issue. The objective of this paper is to develop a joint pricing and inventory model for Hi-tech products under replacement warranty policy. In the first model, we consider a Hi-tech product feature in which the selling price is declining in a trend. We determine the optimal inventory level for each period and retail price for the first period while maximising the total profit. In the second model, we further determine the optimal retail price and inventory level for each period in the dynamic demand market. This study develops solution approaches to solve the problems described above. Numerical analysis discusses the influence of system parameters on the company's decisions and behaviours. The results of this study could serve as a reference for business managers or administrators.     

The value of modeling with reference effects in stochastic inventory and pricing problems

We analyze a periodic review inventory system in which the random demand is contingent on the current price and the reference price. The reference price captures the price history and acts as a benchmark against which the current price is compared. The randomness is due to additive and multiplicative random terms. The objective is to maximize the discounted expected profit over the selling horizon by dynamically deciding on the optimal pricing and replenishment policy for each period. We study three key issues using numerical computation and simulation. First, we study the effects of reference price mechanism on the total expected profit. It is shown that high dependence on a good history increases the profit. Second, we investigate the value of dynamic programming and show that the firm that ignores the dynamic structure suffers from the revenue. Third, we analyze the value of estimating the correct demand model with reference effects. We observe that this value is significant when the inventory related costs are low.     

Competitive Delivered Pricing by Mail-Order and Internet Retailers

Mail-order and internet sellers must decide how customers pay shipping charges. Typically, these sellers choose between two pricing policies: either “uniform pricing,” where the firm delivers to any customer at a fixed delivery charge (that may be volume dependent), or “mill pricing,” where the firm bills the customer a distance-related shipping charge. This paper studies price competition between a mail-order (or internet) seller and local retailers, and the mail-order firm’s choice of pricing policy. The price policy choice is studied when retailers do not change price in reaction to the mail-order firm’s policy choice, and when they do. In the second case, a two-stage non-cooperative game is used and it is found that for low customer willingness to pay, mill pricing is favored but as willingness to pay rises, uniform pricing becomes more attractive. These results are generalized showing that larger markets, higher transportation rates, higher unit production cost, and greater competition between retailers all increase profit under mill pricing relative to uniform pricing (and vice versa). On the other hand, cost asymmetries that favor the mail-order firm will tend to induce uniform rather than mill pricing. Some empirical data on retail and mail-order sales that confirm these results are presented.     

面向乘客策略行为的航空公司舱位控制与动态定价模型

将动态控制舱位开放作为策略,研究乘客具有策略行为时航空公司舱位控制与动态定价问题.通过建立以舱位开放和价格变化为决策变量的多周期动态规划模型,讨论开放舱位和最优定价应满足的条件,并通过比较得出:实行动态舱位控制策略可缓解乘客策略行为对航空公司期望收益的影响.最后应用算例分析乘客策略程度对航空公司价格和期望收益的影响,同时发现:舱位控制不能完全消除乘客策略行为对期望收益的影响,但供应水平越高或乘客策略程度越大,其缓解策略行为的效果越明显.     

服务差异化背景下基于行为的定价策略

在竞争企业具有服务差异化的背景下,研究一种定价歧视策略-----基于行为的定价(behavior-based pricing,BBP).采用博弈论方法构建两周期动态定价模型,通过价格和利润的对比分析进一步探讨服务水平差异化企业最优定价策略,最后分析BBP与服务差异化的交互作用.主要研究结论如下:1)服务差异化程度和相对服务成本两大因素交互影响着企业的最优定价策略.具体地,服务差异化程度较低(高)且相对服务成本较小(大)时,竞争企业均不采用(采用)BBP;服务差异化程度较低(高)但服务提升成本较大(小)时,竞争企业存在混合战略纳什均衡,双方有一定概率采用BBP.2)混合战略纳什均衡情形下,BBP导致的激烈价格竞争并不总是损害竞争双方的利润.当服务差异化程度较低且服务提升成本较大时,高服务水平企业反而能在这种价格竞争中实现利润增加.3)当服务差异化程度较高且相对服务成本较大时,BBP与服务差异化的交互作用能够实现服务差异化企业利润的帕累托改进,实现双赢的局面.     

公平视角下全渠道服务商定价和服务能力分配策略

随着移动互联网的发展,基于本地服务的全渠道运营模式被广大服务运营商和消费者所接受.对于有限服务能力的服务商在全渠道运营的过程中,需要考虑其服务能力在不同渠道中的公平分配.针对同时运营实体和O2O渠道的服务商进行研究,探索考虑公平的服务商不同分配机制下的渠道定价及分配策略的选择.通过消费者效用模型的构建,刻画消费者的渠道...     

Optimal inventory control policy and supply chain coordination problem with carbon footprint constraints

Carbon footprint constraints exert pressure on supply chains to reexamine decisions. In this paper, we consider carbon transfer cost and carbon holding cost in a supply chain. A multiperiod dynamic programming model with carbon footprint constraints is presented to investigate the impact of carbon transfer cost and carbon holding cost on inventory control policy as well as the supply chain coordination problem. A two‐control limit inventory control policy is proved to be optimal and a contract with wholesale price, subsidy, and fixed setup cost is verified analytically to coordinate the supply chain. Finally, a numerical study is conducted to reveal managerial insights. We find that when the supply chain is coordinated, the chain's profit is more sensitive to carbon transfer cost while inventory level is more sensitive to carbon holding cost. Additionally, because of the complexity of the coordinated contract, when it is not easy to coordinate the supply chain, it is better to keep the values of wholesale price, subsidy, and fixed setup cost below the corresponding values for the coordinated supply chain.     

Optimal pricing of online products based on customer anchoring-adjustment psychology

Online product pricing is an important factor that affects the purchase of customers and the earnings of e-commerce platform enterprises. It has an increasingly prominent influence on consumers’ purchasing decisions. To study the influence of customers’ anchoring psychology and product pricing on customers’ purchasing behaviors, this paper proposes a pricing model that considers online consumers to be anchored by the product price and sales. The cognitive bias of online consumers is described by a utility function based on an anchoring-adjustment heuristic, and consumer choice behavior and an online product pricing strategy are studied with a multinomial logit model. Then, it studies the influence of the anchoring point and anchoring degree on optimal pricing, sales and profit. In particular, when consumers are anchored only by sales of goods, the optimal solution is monotonic with respect to the anchoring degree. However, when consumers are anchored by both price and sales, both factors affect consumer behaviors and produce more complex results. This paper provides a flexible pricing mechanism for platform enterprises, and it can provide a theoretical basis and decision support for dynamic pricing of platform enterprises based on historical consumption data.     

Pricing and production lot-size/scheduling with finite capacity for a deteriorating item over a finite horizon

Although the lately evolved manufacturing technologies such as enterprise resource planning (ERP) provide a unified platform for managing and integrating core business processes within a firm, the decision-making between marketing and production planning still remains rather disjoint. It is due in large parts to the inherent weaknesses of ERP such as the fixed and static parameter settings and uncapacitated assumption. To rectify these drawbacks, we propose a decision model that solves optimally the production lot-size/scheduling problem taking into account the dynamic aspects of customer's demand as well as the restriction of finite capacity in a plant. More specifically, we consider a single product that is subject to continuous decay, faces a price-dependent and time-varying demand, and time-varying deteriorating rate, production rate, and variable production cost, with the objective of maximizing the profit stream over multi-period planning horizon. We propose both coordinated and decentralized decision-making policies that drive the solution of the multivariate maximization problem. Both policies are formulated as dynamic programming models and solved by numerical search techniques. In our numerical experiments, the solution procedure is demonstrated, comparative study is conducted, and sensitivity analysis is carried out with respect to major parameters. The numerical result shows that the solution generated by the coordinated policy outperforms that by the decentralized policy in maximizing net profit and many other quantifiable measures such as minimizing inventory investment and storage capacity.Scope and purposeWe consider a manufacturing firm who produces and sells a single product that is subjected to continuous decay over a lifetime, faces a price-dependent and time-varying demand function, shortages are allowed and a completely backlogged, and has the objective of determining price and production lot-size/scheduling so as to maximize the total profit stream over multi-period planning horizon. We develop a tactical-level decision model that solves the production scheduling problem taking into account the dynamic nature of customer's demand which is partially controllable through pricing schemes. As analogous to the sales and operations planning, the proposed scheme can be used as a coordination center of the APS system within a generic enterprise resource planning framework which integrates and coordinates distinct functions within a firm.This paper differs from the existing works in several ways. First, we propose a dynamic version of the joint pricing and lot-size/scheduling problem taking into account the capacitated constraint. Second, several key factors being considered in the model, such as the demand rate, deteriorating rate, production rate, and variable production cost are assumed time-varying that reflect the dynamic nature of the market and the learning effect of the production system. A third difference between the past research and ours is that the price can be adjusted upward or downward in our model, making the proposed pricing policy more responsive to the structural change in demand or supply.     

Competitive pricing with dynamic asymmetric price effects

We model the temporal pricing strategies for two firms with asymmetric costs and differing market power (i.e. big‐box retailer versus smaller local merchant). A firm's demand is a function of its price, a reference price and its competitor's price. Price effects may be asymmetric, i.e. consumers respond differently if they perceive a good to be over‐priced versus under‐priced. We derive analytical results for optimal prices. We show through a series of numerical examples under what settings firms choose various pricing strategies as well as profit implications for firms with differing costs.     

竞争视角下考虑技术创新的逆向供应链微分博弈

针对由再制造商、线上线下竞争回收商和消费者组成的逆向供应链,考虑技术创新研究竞争背景下逆向供应链的微分博弈问题.利用伊藤过程刻画再制造技术先进度的随机演化过程,基于成员的利润结构,构建逆向供应链的随机微分博弈模型.运用贝尔曼连续型动态规划理论,求解动态和稳定均衡状态下成员的反馈策略,揭示再制造技术先进度的动态随机演化特征.最后结合算例,分析两种均衡状态下,回收商的竞争程度和消费者对直接回收价格的敏感系数对各成员均衡策略以及利润的影响.研究表明:提高再制造技术先进度可降低直接回收价格和转移回收价格;由于随机干扰因素的影响,再制造技术先进度始终围绕其期望上下波动,最终稳定于一个稳态值;回收商的竞争有利于激励再制造商投入更多的技术创新努力以提高再制造技术先进度,进而提高电子废弃物的整体可再制造率,但会降低回收商的单位获利,并且过度的竞争不利于电子废弃物的回收.