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。     

Flexible Capacity Investments and Product Mix: Optimal Decisions and Value of Postponement Options

In this article, we study a firm's interdependent decisions in investing in flexible capacity, capacity allocation to individual products, and eventual production quantities and pricing in meeting uncertain demand. We propose a three‐stage sequential decision model to analyze the firm's decisions, with the firm being a value maximizer owned by risk‐averse investors. At the beginning of the time horizon, the firm sets the flexible capacity level using an aggregate demand forecast on the envelope of products its flexible resources can accommodate. The aggregate demand forecast evolves as a Geometric Brownian Motion process. The potential market share of each product is determined by the Multinomial Logit model. At a later time and before the end of the time horizon, the firm makes a capacity commitment decision on the allocation of the flexible capacity to each product. Finally, at the end of the time horizon, the firm observes the demand and makes the production quantity and pricing decisions for end products. We obtain the optimal solutions at each decision stage and investigate their optimal properties. Our numerical study investigates the value of the postponed capacity commitment option in supplying uncertain operation environments.     

The Usage of Opportunity Cost to Maximize Performance in Revenue Management*

To meet customer requirements efficiently, a manager needs to supply adequate quantities of products, capacity, or services at the right time with the right prices. Revenue management (RM) techniques can help firms use differential pricing strategies and capacity allocation tactics to maximize revenue. In this article, we propose a marginal revenue‐based capacity management (MRBCM) model to manage stochastic demand in order to create improved revenue opportunities. The new heuristic employs opportunity cost estimation logic that is unique and is the reason for the increased performance. The MRBCM model generates order acceptance policies that allocate available capacity to higher revenue generating market segments in both service and manufacturing environments. To evaluate these models, we design and conduct simulation experiments for 64 scenarios using a wide range of operating conditions. The experimental results show that the MRBCM model generates significantly higher revenues over the first come, first served rule when capacity is tight. In addition, we also show that the MRBCM model generally performs better than a recent RM model published in the literature.     

Dynamic Pricing to Minimize Maximum Regret

We consider a dynamic pricing problem that involves selling a given inventory of a single product over a short, two‐period selling season. There is insufficient time to replenish inventory during this season, hence sales are made entirely from inventory. The demand for the product is a stochastic, nonincreasing function of price. We assume interval uncertainty for demand, that is, knowledge of upper and lower bounds but not a probability distribution, with no correlation between the two periods. We minimize the maximum total regret over the two periods that results from the pricing decisions. We consider a dynamic model where the decision maker chooses the price for each period contingent on the remaining inventory at the beginning of the period, and a static model where the decision maker chooses the prices for both periods at the beginning of the first period. Both models can be solved by a polynomial time algorithm that solves systems of linear inequalities. Our computational study demonstrates that the prices generated by both our models are insensitive to errors in estimating the demand intervals. Our dynamic model outperforms our static model and two classical approaches that do not use demand probability distributions, when evaluated by maximum regret, average relative regret, variability, and risk measures. Further, our dynamic model generates a total expected revenue which closely approximates that of a maximum expected revenue approach which requires demand probability distributions.     

A comparison of fixed and dynamic pricing policies in revenue management

We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grow large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. We suggest two simple dynamic heuristics that continuously update prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the first heuristic has a consistent and remarkable performance leading to at most 0.2% gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the first heuristic for which the performance is monotone in the frequency of price changes. We conclude that dynamic pricing should be considered as a more favorable option in practice.     

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.     

竞争环境下客户服务投入对企业利润影响的均衡分析

客户服务投入是企业吸引新顾客和维持现有顾客的重要手段之一。然而,服务投入究竟是否能给企业带来价值？对于这一问题,业界和学界都没有明确的答案。本文通过建模的方法研究在竞争的市场环境下,固有的市场因素对客户服务投入价值的影响。研究发现,服务竞争的市场均衡结构是两家厂商都投入客户服务。服务投入给企业带来的价值随着产品差异度的提高而提高,随着厂商自身市场份额的增加而增加。即,在产品差异度高的市场,服务投入更容易给企业带来价值。而在集中度高的市场,服务投入更容易给市场份额大的企业带来价值。     

存在战略购买需求的定价、供给、机制选择和配给研究

本文研究存在战略购买需求的易逝资产销售策略问题。垄断厂商基于利润最大化目标确定易逝资产定价、供给、机制选择和配给策略,战略消费者通过锚定预期价格安排战略购买时机。不同于通常基于效用理论研究定价的思路,本文首先基于锚定效应和跨期价格均衡思想探寻不同战略等待购买规模的市场预期需求曲线和动静态定价区域;其次在众多预期需求曲线中寻找市场有效定价前沿（即有效预期需求曲线）;再次在利润曲面上找出与有效定价前沿对应的容量扩展线（即最大利润曲线）;最后沿容量扩展线和有效定价前沿搜寻最大期望利润及相应策略。研究表明,消费者保留价异质和需求不确定性是动态定价和战略购买存在的根本原因;市场在不同战略等待购买规模状态拥有不同预期需求曲线,最大战略等待购买规模状态预期需求曲线是市场有效定价前沿。动静态定价机制各有其所适用的容量和价格空间,消费者保留价水平和战略消费者规模决定动态定价空间大小,随机需求分布差异只影响动态定价空间形状（即影响需求弹性）。在跨期价格均衡区域内,提价和扩容都会加剧消费者战略购买程度,供给越大定价往往越低。战略购买不仅会降低厂商供给、定价和利润水平,改变不同类型消费者之间高低价购买机会,甚至还可能影响定价机制选择和配给策略。压缩过度供给和虚高价格空间可降低战略购买导致的利润损失。本文研究结果可为考虑消费者行为的需求价格理论研究和运营管理实践提供参考。     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

Optimizing the conditional value-at-risk in revenue management

Many service industries use revenue management to balance demand and capacity. The assumption of risk-neutrality lies at the heart of the classical approaches, which aim at maximizing expected revenue. In this paper, we give a comprehensive overview of the existing approaches, most of which were only recently developed, and discuss the need to take risk-averse decision makers into account. We then present a heuristic that maximizes conditional value-at-risk (CVaR). Although CVaR has become increasingly popular in finance and actuarial science due to its beneficial properties, this risk measure has not yet been considered in the context of revenue management. We are able to efficiently solve the optimization problem inherent in CVaR by taking advantage of specific structural properties that allow us to reformulate this optimization problem as a continuous knapsack problem. In order to demonstrate the applicability and robustness of our approach, we conduct a simulation study that shows that the new approach can significantly improve the risk profile in various scenarios.     

考虑退货风险的制造商双渠道供应链定价决策研究

针对事前不确定性导致的退货问题,从消费者行为出发,建立考虑定价差异和退货风险双重因素的市场需求函数,通过Stackelberg博弈模型研究四种不同市场需求情形在不同定价模式下双渠道供应链的最优决策。在数值仿真部分,对不同情形决策之间比较、供应链收益进行比较分析。研究表明：电子渠道销售价格与电子渠道的市场基本需求成正比,批发价和传统渠道销售价格与传统渠道的市场基本需求成正比,实体店体验服务水平和传统渠道的市场基本需求的关系（线性关系）则根据某些条件而定;退货风险对供应链决策的影响与定价模式、市场需求影响因素相关;制造商偏好于定价不相等模式,零售商偏好于定价相等模式;退货风险与定价差异对供应链成员收益的影响与定价模式相关,对整体供应链收益的影响与定价模式和退货率大小有关。     

需求不确定下生产能力与竞争优势之间的关系

在需求不确定的条件下,用生产能力刻画产量决策的柔性,用古诺模型描述企业间的(产量)竞争,建立一个两企业战略竞争博弈模型,并利用博弈均衡构建柔性水平与竞争优势之间的函数关系。比较静态分析结果表明,(1)其他条件不变,一家企业的相对竞争优势随着自己的生产能力增加而增加,但随着对手的生产能力增加而降低;(2)生产能力较高的企业将获得较高的绝对竞争优势。这些结果暗示,柔性水平与竞争优势之间呈现一种正向的变动关系。这一结论一方面在一定程度上澄清了战略管理文献中呈现出的"战略柔性与竞争优势之间的联系方向模凌两可"这一问题;另一方面,由于引入了竞争性战略互动,从而将基于个人理性决策的结果扩展到战略相互依赖的竞争性情形下。     

Committed Versus Contingent Pricing Under Competition

Should capacitated firms set prices responsively to uncertain market conditions in a competitive environment? We study a duopoly selling differentiated substitutable products with fixed capacities under demand uncertainty, where firms can either commit to a fixed price ex ante, or elect to price contingently ex post, e.g., to charge high prices in booming markets, and low prices in slack markets. Interestingly, we analytically show that even for completely symmetric model primitives, asymmetric equilibria of strategic pricing decisions may arise, in which one firm commits statically and the other firm prices contingently; in this case, there also exists a unique mixed strategy equilibrium. Such equilibrium behavior tends to emerge, when capacity is ampler, and products are less differentiated or demand uncertainty is lower. With asymmetric fixed capacities, if demand uncertainty is low, a unique asymmetric equilibrium emerges, in which the firm with more capacity chooses committed pricing and the firm with less capacity chooses contingent pricing. We identify two countervailing profit effects of contingent pricing under competition: gains from responsively charging high price under high demand, and losses from intensified price competition under low demand. It is the latter detrimental effect that may prevent both firms from choosing a contingent pricing strategy in equilibrium. We show that the insights remain valid when capacity decisions are endogenized. We caution that responsive price changes under aggressive competition of less differentiated products can result in profit‐killing discounting.     

Allocation of Returned Products among Different Recovery Options through an Opportunity Cost–Based Dynamic Approach*

In a make‐to‐order product recovery environment, we consider the allocation decision for returned products decision under stochastic demand of a firm with three options: refurbishing to resell, parts harvesting, and recycling. We formulate the problem as a multiperiod Markov decision process (MDP) and present a linear programming (LP) approximation that provides an upper bound on the optimal objective function value of the MDP model. We then present two solution approaches to the MDP using the LP solution: a static approach that uses the LP solution directly and a dynamic approach that adopts a revenue management perspective and employs bid‐price controls technique where the LP is resolved after each demand arrival. We calculate the bid prices based on the shadow price interpretation of the dual variables for the inventory constraints and accept a demand if the marginal value is higher than the bid price. Since the need for solving the LP at each demand arrival requires a very efficient solution procedure, we present a transportation problem formulation of the LP via variable redefinitions and develop a one‐pass optimal solution procedure for it. We carry out an extensive numerical analysis to compare the two approaches and find that the dynamic approach provides better performance in all of the tested scenarios. Furthermore, the solutions obtained are within 2% of the upper bound on the optimal objective function value of the MDP model.     

Some aspects of price strategy

A firm's success, within a rapidly growing and dynamic market, depends upon its ability to respond to market demand and to react to competitive forces. A key factor determining success is the pricing policy employed by the firm. Product pricing, however, is not simple; supply and demand, as well as the interaction and reaction of competitors, must be taken into consideration. By simulating a competitive market environment, however, a firm should be able to evaluate different pricing strategies prior to employing a strategy in practice. The goal of this research was to propose a simulation model to serve this purpose. Particularly, the objective was to demonstrate that if an industry can be characterized as one in which cost as well as price decline with cumulative volume, a pricing policy leading to market dominance exists. A simulation model is desirable for evaluating the proper pricing strategy for achieving such a market position.     

Maximizing customer equity subject to capacity constraints

This paper considers a firm that wants to optimally allocate limited capacity to heterogeneous customer segments in order to maximize its customer equity. The decision whether to accept or to reject a customer׳s request in a current period influences his repurchase behavior in later periods. The allocation process becomes complex, when demand exceeds capacity, because the isolated determination and optimization of a single customer׳s lifetime value is no longer feasible. Using a Markov decision process formulation, we study how to trade off short-term attainable revenues and long-term customer relationships. Furthermore, we analyze when and how intertemporal customer behavior influences capacity allocation. Finally, we investigate the impact of limited capacity on the customer lifetime value by introducing an opportunity cost-based approach that understands customer profitability as a customer׳s contribution to customer equity.     

A Nonatomic‐Game Approach to Dynamic Pricing under Competition

We study a revenue management problem involving competing firms. We assume the presence of a continuum of infinitesimal firms where no individual firm has any discernable influence over the evolution of the overall market condition. Under this nonatomic‐game approach, the unanimous adoption of an equilibrium pricing policy by all firms will yield a market‐condition process that in turn will elicit the said policy as one of the best individual responses. For both deterministic‐ and stochastic‐demand cases, we show the existence of equilibrium pricing policies that exhibit well‐behaving monotone trends. Our computational study reveals many useful insights, including the fact that only a reasonable number of firms are needed for our approach to produce near‐rational pricing policies.     

Coordinating pricing and production decisions for multiple products

We consider a dynamic problem of joint pricing and production decisions for a profit-maximizing firm that produces multiple products. We model the problem as a mixed integer nonlinear program, incorporating capacity constraints, setup costs, and dynamic demand. We assume demand functions to be convex, continuous, differentiable, and strictly decreasing in price. We present a solution approach which is more general than previous approaches that require the assumption of a specific demand function. Using real-world data from a manufacturer, we study problem instances for different demand scenarios and capacities and solve for optimal prices and production plans. We present analytical results that provide managerial insights on how the optimal prices change for different production plans and capacities. We extend some of the earlier works that consider single product problems to the case of multiple products and time variant production capacities. We also benchmark performance of proposed algorithm with a commercial solver and show that it outperforms the solver both in terms of solution quality and computational times.     

信息不对称条件下的企业集团转移定价研究

本文研究了信息不对称条件下企业集团的转移定价决策问题,提出了歧视转移定价法。即在信息不对称条件下,当上游子企业对中间产品具有完全垄断能力时,企业集团将转移定价决策权下放给上游子企业,上游子企业根据内外部市场需求的差异,采用差别定价策略。通过与市场基础转移定价和边际成本转移定价相比较,得出歧视转移定价可以增加企业集团的整体利润。