基于需求转移的易逝性产品最优动态定价策略

本文针对易逝性产品中新产品对老产品需求的转移作用,应用收入管理方法得出老产品的最优动态定价策略,并应用最大凹向包络理论给出了简化算法的方法.数值算例表明在存在需求转移的情况下,应更早的提供较低的价格.最后作者给出了包含生产和定价的综合模型.     

On the Benefit of Inventory‐Based Dynamic Pricing Strategies

We study the optimal pricing and replenishment decisions in an inventory system with a price‐sensitive demand, focusing on the benefit of the inventory‐based dynamic pricing strategy. We find that demand variability impacts the benefit of dynamic pricing not only through the magnitude of the variability but also through its functional form (e.g., whether it is additive, multiplicative, or others). We provide an approach to quantify the profit improvement of dynamic pricing over static pricing without having to solve the dynamic pricing problem. We also demonstrate that dynamic pricing is most effective when it is jointly optimized with inventory replenishment decisions, and that its advantage can be mostly realized by using one or two price changes over a replenishment cycle.     

可加效用下基于消费者惰性的易逝品动态定价

本文在考虑销售商的风险规避态度和消费者惰性的情况下,研究了易逝品的动态定价策略。首先给出风险规避的销售商实施动态定价的马尔可夫决策过程,并运用MNL随机效用模型来刻画惰性消费者的购买决策,在此基础上,以风险规避销售商的期望效用最大化为目标,利用动态规划方法建立了可加效用下的易逝品动态定价模型,并探讨了消费者的惰性行为和销售商的风险规避态度对最优价格的影响。结论表明：在销售商的风险态度为风险规避的情况下,考虑消费者惰性行为的最优价格随库存水平的增加而降低,随剩余销售时间的增加而提高,消费者的惰性行为和销售商的风险规避态度对最优价格都存在负向影响,即最优价格随惰性深度的增加而降低,随惰性宽度的增加而降低,同时,销售商的风险规避态度越强烈,其制定的产品价格越低。     

随机需求下单向替代的两产品订货与定价联合决策研究

考虑了存在单向替代的两产品订货和定价联合决策问题。通过构建订货与定价联合决策模型,研究了单周期两产品的最优订货量和价格的存在条件,进一步将研究拓展到多周期的情况,建立了多周期的订货和定价联合决策模型,并进行了模型结构分析。同时,分析了信息对订货与定价联合决策的影响程度。     

需求替代情形下反应能力的价值分析

本文通过对竞争报童模型加以拓展以研究需求替代情形下企业运用反应能力产生的价值。文中考虑了两种不同的需求结构:第一种中企业总需求是竞争双方库存量的分段线性函数,第二种中企业总需求的均值是双方库存水平任意形式的函数。根据需求结构的不同,建立了不同的库存竞争模型并提出了相应的均衡库存策略。基于这些均衡结论,进一步探讨了反应能力的价值。分析表明运用反应能力能在降低企业库存水平的同时提高顾客服务水平。此外,在不同的需求结构下,运用反应能力产生的价值均随可用反应能力以及缺货惩罚成本递增,而随单位反应能力的使用成本递减。     

Measuring the Impact of Increased Product Substitution on Pricing and Capacity Decisions Under Linear Demand Models

We consider two substitutable products and compare two alternative measures of product substitutability for linear demand functions that are commonly used in the literature. While one leads to unrealistically high prices and profits as products become more substitutable, the results obtained using the other measure are in line with intuition. Using the more appropriate measure of product substitutability, we study the optimal investment mix in flexible and dedicated capacities in both monopoly and oligopoly settings. We find that the optimal investment in manufacturing flexibility tends to decrease as the products become closer substitutes; this is because (1) pricing can be used more effectively to balance supply and demand, and (2) the gains obtained by shifting production to the more profitable product are reduced due to increased correlation between the price potentials of the substitutable products. The value of flexibility always increases with demand variability. We also show that, as long as the optimal investments in dedicated capacity for both products are positive, the optimal expected prices and production quantities do not depend on the cost of the flexible capacity. Manufacturing flexibility simply allows the firm to achieve those expected values with lower capacity, while leading to higher expected profits.     

Replenishment Policies for Multi‐Product Stochastic Inventory Systems with Correlated Demand and Joint‐Replenishment Costs

This study analyzes optimal replenishment policies that minimize expected discounted cost of multi‐product stochastic inventory systems. The distinguishing feature of the multi‐product inventory system that we analyze is the existence of correlated demand and joint‐replenishment costs across multiple products. Our objective is to understand the structure of the optimal policy and use this structure to construct a heuristic method that can solve problems set in real‐world sizes/dimensions. Using an MDP formulation we first compute the optimal policy. The optimal policy can only be computed for problems with a small number of product types due to the curse of dimensionality. Hence, using the insight gained from the optimal policy, we propose a class of policies that captures the impact of demand correlation on the structure of the optimal policy. We call this class (s, c, d, S)‐policies, and also develop an algorithm to compute good policies in this class, for large multi‐product problems. Finally using an exhaustive set of computational examples we show that policies in this class very closely approximate the optimal policy and can outperform policies analyzed in prior literature which assume independent demand. We have also included examples that illustrate performance under the average cost objective.     

考虑顾客策略行为的易逝品定价与再制造柔性补货机制研究

本文将再制造作为一种柔性补货机制,研究了考虑顾客策略行为的易逝品定价和再制造柔性补货问题。研究表明顾客策略行为减少了零售商的期望利润,再制造柔性补货机制可以缓解顾客策略行为的影响,提高零售商的期望利润,最后分析了该机制对消费者剩余和社会福利的影响。     

Optimal Control of Replenishment and Substitution in an Inventory System with Nonstationary Batch Demand

We study an inventory system in which a supplier supplies demand using two mutually substitutable products over a selling season of T periods, with a single replenishment opportunity at the beginning of the season. As the season starts, customer orders arrive in each period, for either type of products, following a nonstationary Poisson process with random batch sizes. The substitution model we consider combines the usual supplier‐driven and customer‐driven schemes, in that the supplier may choose to offer substitution, at a discount price, or may choose not to; whereas the customer may or may not accept the substitution when it is offered. The supplier's decisions are the supply and substitution rules in each period throughout the season, and the replenishment quantities for both products at the beginning of the season. With a stochastic dynamic programming formulation, we first prove the concavity of the value function, which facilitates the solution to the optimal replenishment quantities. We then show that the optimal substitution follows a threshold rule, and establish the monotonicity of the thresholds over time and with respect to key cost parameters. We also propose a heuristic exhaustive policy, and illustrate its performance through numerical examples.     

Joint Inventory and Pricing Coordination with Incomplete Demand Information

In retailing operations, retailers face the challenge of incomplete demand information. We develop a new concept named K‐approximate convexity, which is shown to be a generalization of K‐convexity, to address this challenge. This idea is applied to obtain a base‐stock list‐price policy for the joint inventory and pricing control problem with incomplete demand information and even non‐concave revenue function. A worst‐case performance bound of the policy is established. In a numerical study where demand is driven from real sales data, we find that the average gap between the profits of our proposed policy and the optimal policy is 0.27%, and the maximum gap is 4.6%.     

基于不同保鲜方式的生鲜品定价订货决策

本文考虑两种不同保鲜方式下生鲜品的不同变质率以及相互需求替代,构建了联合定价和订货模型。研究无库存约束、单一库存约束和双库存约束三种情形下零售商对不同保鲜方式生鲜品的定价和订货决策。探讨市场容量、生鲜变质率、需求替代率以及最大订货量对最优决策的影响。研究显示：市场容量越大、需求替代率越高,生鲜品零售商的获利空间越大;提高保鲜投入和保鲜努力,降低高(低)变质率保鲜方式生鲜品的变质率可以提高两种保鲜方式生鲜品的销售价格和高(低)变质率保鲜方式生鲜品的销售量;高(低)变质率保鲜方式生鲜品单一库存约束会提高该生鲜品的最优价格和低(高)变质率保鲜方式生鲜品的最优订货量;双库存约束时,两种保鲜方式生鲜品的最优价格都会提高,最优订货量为最大订货量。     

消费者锚定效应下的动态定价与库存控制研究

在零售商-消费者两级供应链中, 零售商垄断销售市场, 研究基于消费者锚定效应的动态定价与库存问题。将消费者的锚定效应纳入决策模型中, 探讨消费者锚定的参考价格与产品的市场需求、价格的动态变化关系;利用动态规划理论建立了消费者锚定效应的动态定价与库存模型;在此基础上考虑利润折现和库存积压问题, 并分别构建了相应模型。数值分析表明, 消费者会根据市场价格的变化决定最佳的购买时机, 零售商的期望收益随着销售时间的延长而增加。     

Optimal Policies for a Two‐Product Inventory System under a Flexible Substitution Scheme

We study a two‐product inventory model that allows substitution. Both products can be used to supply demand over a selling season of N periods, with a one‐time replenishment opportunity at the beginning of the season. A substitution could be offered even when the demanded product is available. The substitution rule is flexible in the sense that the seller can choose whether or not to offer substitution and at what price or discount level, and the customer may or may not accept the offer, with the acceptance probability being a decreasing function of the substitution price. The decisions are the replenishment quantities at the beginning of the season, and the dynamic substitution‐pricing policy in each period of the season. Using a stochastic dynamic programming approach, we present a complete solution to the problem. Furthermore, we show that the objective function is concave and submodular in the inventory levels—structural properties that facilitate the solution procedure and help identify threshold policies for the optimal substitution/pricing decisions. Finally, with a state transformation, we also show that the objective function is ‐concave, which allows us to derive similar structural properties of the optimal policy for multiple‐season problems.     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

Recent Developments in Dynamic Pricing Research: Multiple Products,Competition, and Limited Demand Information

Dynamic pricing enables a firm to increase revenue by better matching supply with demand, responding to shifting demand patterns, and achieving customer segmentation. In the last 20 years, numerous success stories of dynamic pricing applications have motivated a rapidly growing research interest in a variety of dynamic pricing problems in the academic literature. A large class of problems that arise in various revenue management applications involve selling a given amount of inventory over a finite time horizon without inventory replenishment. In this study, we identify most recent trends in dynamic pricing research involving such problems. We review existing research on three new classes of problems that have attracted a rapidly growing interest in the last several years, namely, problems with multiple products, problems with competition, and problems with limited demand information. We also identify a number of possible directions for future research.     

零售商的动态定价和服务模型分析

假定需求是价格,服务水平的线性函数,采用最优控制方法求解最优价格和服务函数,分析了时间衰变因子对最优价格的影响以及两种需求弹性的性质。最后借助数值计算的方法研究了控制变量和状态变量的轨迹以及模型参数对目标函数值的影响情况。     

Sequence Matters: Shelf‐Space Allocation under Dynamic Customer‐Driven Substitution

Customers who face a stockout situation often decide to purchase a different product in the same category. We analyze the resulting dynamic substitution problem in a retail environment, where customers serve themselves from the store shelves, such that the sequence of customer arrivals affects how scarce products are allocated to customers. We consider a setting with constrained shelf space, and we study how a retailer should optimally allocate such space between substitute products. We characterize environments where the sequence of customer arrivals can have a substantial impact on profitability.     

电子市场中时间价格敏感需求下的交货期定价决策

电子市场中,如何通过交货期报价来增大需求、提高收益,对于网络营销企业来说是至关重要的.本文假定在一个包含网络营销企业与其客户的运作系统中,需求同时对价格与时间都敏感的条件下,以最优化自身收益为目标、以满足必须达到规定的服务水平为主要约束条件,构建了交货期定价决策模型.通过数值算例,探讨了在电子市场中消费者为价格敏感或交货期敏感时,网络营销企业的最优定价策略.上述结论可以为网络营销企业在电子市场中的定价决策提供有益的指导.     

随机需求下考虑不同竞争情形的网约车平台动态定价

针对乘车需求波动下网约车平台间存在乘车需求竞争和乘运供应竞争的最优定价问题,以平台期望收益最大化为目标,运用最优控制论方法,构建不同竞争情形下的网约车平台动态定价模型,并利用哈密尔顿函数及模型推导,求得最优动态竞争价格解以及乘运供应率与需求率的变化轨迹。结果表明：平台最优动态竞争价格随市场需求的波动而动态变化,且最优价格可以有效调控平台供应能力,促使平台供需匹配,优化平台期望收益。此外,乘车需求市场竞争越激烈,平台最优价格越低,而乘运供应市场竞争越激烈,最优价格越高。平台间竞争的加剧将降低平台的期望收益,且平台期望收益随着固定佣金报酬率的提高先增大后减小。     

Dynamic Pricing in the Presence of Myopic and Strategic Consumers: Theory and Experiment

We investigate retailers’ dynamic pricing decisions in a stylized two‐period setting with possible supply constraints and demand from both myopic and strategic consumers. We present an analytical model and then test its predictions in a behavioral experiment in which human subjects played the role of pricing managers. We find that the fraction of strategic consumers in the market systematically moderates the optimal pricing structure. When this fraction exceeds a certain threshold, the retailer offers relatively small late season markdowns to discourage strategic consumers from waiting and to incentivize them to buy during the early season; otherwise, the retailer offers relatively large markdowns to divert all strategic consumers to the late season, where the majority of revenue is made. Our model analyses suggest that the latter policy is optimal under fairly broad conditions. Our experiment shows that after some significant learning, aggregate behavior is able to approximate the key qualitative predictions from our model analysis, with one notable deviation: in the presence of a mixture of myopic and strategic consumers, subjects act somewhat myopically – they underprice and oversell in the main selling season, which significantly limits their ability to generate revenue in the markdown season.