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.     

Dynamic pricing and revenue management process in Internet retailing under uncertainty: An integrated real options approach

Competition and demand volatility often cause modern enterprises to be confronted by uncertain environments. When a firm manages revenue in such competitive and risky environments, the optimization of pricing and capacity allocation, subject to a fixed time and capacity, becomes a complicated problem. Many previous papers concerning revenue management (RM) and pricing require that the firm possesses the ability to know the demand curve (or demand distribution) and set prices on it to maximize profits. However, this assumption may not be the case in some industries. Therefore, this paper focuses on the dynamic lead indicators rather than assumptive lag indicators to establish a concise and flexible decision model for practical use. This paper provides an integrated real options (IRO) approach with analytic hierarchy process (AHP) for the auction RM problem under competitive/dynamic pricing and revenue uncertainty in Internet retailing. A numerical example is also presented to illustrate that the IRO approach can generate better decisions than the naı¨ve (or risk unawareness) approach in revenue quality of safety and profitability. The new perspective and approach proposed by this paper can be extended to other RM fields whenever both profitability and risk are critical to decision making.     

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.     

Pricing and Operational Performance in Discretionary Services

In many services, for example, website or landscape design, the value or quality derived by a customer depends upon the service time, and this valuation differs across customers. Customers procure the service based on the expected value to be delivered, prices charged, and the timeliness of service. We investigate the performance of the optimal pricing scheme as well as two commonly used pricing schemes (fixed fee and time‐based pricing) for such services on important dimensions such as revenue, demand served, and utilization. We propose a novel model that captures the above features and wherein both service rate and demand are endogenous and functions of the pricing scheme. In particular, service time is an outcome of the pricing scheme adopted and the heterogeneous valuations of customers, unlike in the queueing‐based pricing literature. We find that the service system may benefit from a greater variance in consumer valuations, and the performance of pricing schemes is impacted by the shape of the distribution of customers' valuation of service time and the responsiveness desired by customers. Both the fixed fee and time‐based schemes do well relative to the optimal pricing scheme in terms of revenue in many plausible scenarios, but there are substantial differences between the pricing schemes in some important operational metrics. For instance, the fixed fee scheme serves more customers and has higher utilization than the time‐based scheme. We also explore variants of the fixed and time‐based schemes that have better revenue performance and show that the two‐part tariff which is a combination of fixed and time‐based pricing can do as well as the optimal scheme in terms of revenue.     

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。     

Penalizing passenger’s transfer time in computing airlines revenue

Airline strategic alliances result in a form of cooperation where firms can access the resources of others network members in order to create added value for their passengers. The shortcoming of this process is that each member of the network makes individual revenue management decisions to maximize its own income, resulting in a sub-optimal income for the network members.To deal with this problem, this paper suggests a resource allocation based on a transfer pricing mechanism, to cooperatively divide the revenue of a passenger between network members. The method penalizes the total time that a passenger takes for reaching the final destination. The model takes into consideration that the profit is independent of the number of available seats (with a maximum determined for each airline). The method computes the optimal transfer pricing and, at the same time, optimizes the quantity of seats (the booking limits). The solution results in a strong Nash equilibrium, which incorporate both the transfer prices and booking limits. We describe the transfer pricing process using an ergodic, finite and continuous-time Markov game model for multiple players. The revenue of each airline in the supply chain will depend on the number of flight transfers and the transit time of the passenger at the airports: the longer the time to the final destination, the lower the price. We compute a collaborative equilibrium point, useful for understanding the resulting revenue of each member of the network. For solving the game, we employ an iterative method based on a proximal approach that involves time penalization. In our final contribution, we present results from a numerical example, which validates the proposed Markov game model and measures the benefits of the transfer pricing resource allocation.     

Quality‐Speed Competition in Customer‐Intensive Services with Boundedly Rational Customers

We consider a system in which two competing servers provide customer‐intensive services and the service reward is affected by the length of service time. The customers are boundedly rational and choose their service providers according to a logit model. We demonstrate that the service provider revenue function is unimodal in the service rate, its decision variable, and show that the service rate competition has a unique and stable equilibrium. We then study the price decision under three scenarios with the price determined by a revenue‐maximizing firm, a welfare‐maximizing social planner, or two servers in competition. We find that the socially optimal price, subject to the requirement that the customer actual utility must be non‐negative, is always lower than the competition equilibrium price which, in turn, is lower than the revenue‐maximizing monopoly price. However, if the customer actual utility is allowed to be negative in social optimization, the socially optimal price can be higher than the other two prices in a large market.     

Service Package Switching in Hotel Revenue Management Systems

Revenue Management Systems (RMS) are commonly used in the hotel industry to maximize revenues in the short term. The forecasting‐allocation module is a key tactical component of a hotel RMS. Forecasting involves estimating demand for service packages across all stayover nights in a planning horizon. A service package is a unique combination of physical room, amenities, room price, and advance purchase restrictions. Allocation involves parsing the room inventory among these service packages to maximize revenues. Previous research and existing revenue management systems assume the demand for a service package to be independent of which service packages are available for sale. We develop a new forecasting‐allocation approach that explicitly accounts for this dependence. We compare the performance of the new approach against a baseline approach using a realistic hotel RMS simulation. The baseline approach reflects previous research and existing industry practice. The new approach produces an average revenue increase of at least 16% across scenarios that reflect existing industry conditions.     

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.     

Dynamic Pricing in e‐Services under Demand Uncertainty

High volatility of the e‐services market, due to increasing competition, low life cycle of products, and easy availability of information about competing service offerings to customers, makes the demand for service offerings quite uncertain. Revenue management in such markets calls for real‐time techniques to learn the demand and its dependence on both the price and the service level associated with the service offering. We assume firms reply on exploratory approaches for demand estimation, in which firms experiment with different service offerings in order to simultaneously learn the demand while doing business. Such exploration and learning process can be costly without supervision. As reported by Rothschild (Journal of Economic Theory, 9 185‐202, 1974), traditional Bayesian dynamic control approaches may conclude with suboptimal offerings. We propose a novel demand learning approach that is guaranteed to converge to the optimal offering. The approach combines simulated annealing algorithm with Bayesian learning. We further present intelligent techniques that adaptively reduce the effort of exploration on suboptimal service offerings so as to improve the long‐run average profit.     

基于异质性顾客心理期望等待时间的优先权服务定价研究

本文以非抢占式M/M/1排队系统为背景,以企业收益最大化为目标,基于顾客异质性(单位时间等待成本不同)将顾客分为两类,针对顾客的心理期望等待时间对服务提供商最优定价策略的影响进行研究。首先研究优先权顾客心理期望等待时间对企业收益的影响以及相应的优先权定价,然后研究优先权顾客和普通顾客同时存在心理期望等待时间对企业收益的影响和相应的优先权定价。研究表明:仅考虑优先权顾客的心理期望等待时间,企业应通过提高优先权定价来获得最优收益;当优先权顾客和普通顾客同时存在心理期望等待时间时,企业仍然采取提高优先权定价的策略,若普通顾客的价值大(获取服务的基本费用大),企业应对普通顾客提供一定的折扣来消除其心理期望等待时间增加企业收益;如果普通顾客的价值较小,企业应"有意"流失部分普通顾客,吸引更多顾客到优先权队列获取服务来获得更多收益。本文研究对于服务提供商在考虑顾客心理期望等待时间基础上设置最合理的队列机制有一定的指导意义和实际应用价值。     

Revenue Management for Intermodal Transportation: The Role of Dynamic Forecasting

We study a joint capacity leasing and demand acceptance problem in intermodal transportation. The model features multiple sources of evolving supply and demand, and endogenizes the interplay of three levers—forecasting, leasing, and demand acceptance. We characterize the optimal policy, and show how dynamic forecasting coordinates leasing and acceptance. We find (i) the value of dynamic forecasting depends critically on scarcity, stochasticity, and volatility; (ii) traditional mean‐value equivalence approach performs poorly in volatile intermodal context; (iii) mean‐value‐based forecast may outperform stationary distribution‐based forecast. Our work enriches revenue management models and applications. It advances our understanding on when and how to use dynamic forecasting in intermodal revenue management.     

大规模客运专线网络运营优化模型与求解算法

本文在分析铁路运营优化模型的研究进展的基础上,提出了一个适合大规模客运专线网络运营的优化模型,并提出了求解此模型的列生成算法和启发式快速算法。目的是将客运专线网路的开行方案优化与动态收益优化问题结合起来,解决更大、更复杂的客运网络运营优化问题。模型以列车运营总收益最大化为目标。用随机生成数据进行的模型试验表明,模型及算法可以在较短的时间内求解较大规模的收益管理优化问题。     

二级物流服务供应链定价及其效率研究

研究了需求不确定条件下,基于利润最大化原则的二级物流服务供应链的定价及效率问题。基于物流服务供应链中集成商市场和供应商市场的四种不同市场组合,建立了以集成商为主导的集成商与供应商之间的Stackelberg博弈模型,求得集成商的最优定价和最优订购量,比较了不同集成商和供应商市场组合下的物流服务供应链的效率高低情况。最后,进行了数值计算,得出集成商的最优定价和最优订购量,验证了不同市场组合下的物流服务供应链效率高低情况。结果表明:集成商的最优定价和最优订购量同时受集成商和供应商所处的市场环境影响;集成商市场寡头垄断、供应商市场完全竞争的情形下物流服务供应链效率最高,集成商市场垄断、供应商市场寡头垄断的情形下物流服务供应链效率最低。     

考虑服务约束的第三方仓库收益与设计优化模型

第三方仓库作为服务提供商, 主要以期望收益最大化为目标, 但是必须满足一定的顾客服务标准。针对高需求环境, 考虑顾客服务水平约束, 提出了一个基于排队论的随机设计优化模型以使仓库的期望收益最大化。采用动态优化算法对模型求解, 选取实例进行了数值实验。结果显示, 模型的优化设计显著地提高了高需求环境下该第三方仓库的期望收益。在此基础上, 找到了服务约束的可行范围和有效范围, 为决策者制定服务标准提供了依据。     

Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

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.     

Optimal Dynamic Upgrading in Revenue Management

We consider a revenue management problem involving a two compartment aircraft flying a single leg, with no cancellations or over‐booking. We apply the practice of transforming a choice revenue management model into an independent demand model. Within this assumed independent model, there are two sets of demands, business and economy, each with multiple fare class products. A business passenger can only be accepted into business. An economy passenger can be accepted into economy or upgraded into business. We define a two‐dimensional dynamic program (DP) and show that the value function is sub‐modular and concave in seat availability in the two compartments. Thus the bid prices are non‐decreasing with respect to these state variables. We use this result to propose an exact algorithm to solve the DP. Our numerical investigation suggests that in contrast to standard backward induction, our method could be included in production revenue management systems. Further, when the economy compartment is capacity constrained, we observe a substantial monetary benefit from optimal dynamic upgrading compared to the static upgrading procedures currently used in practice.     

Randomization Approaches for Network Revenue Management with Customer Choice Behavior

In this study, we present new approximation methods for the network revenue management problem with customer choice behavior. Our methods are sampling‐based and so can handle fairly general customer choice models. The starting point for our methods is a dynamic program that allows randomization. An attractive feature of this dynamic program is that the size of its action space is linear in the number of itineraries, as opposed to exponential. It turns out that this dynamic program has a structure that is similar to the dynamic program for the network revenue management problem under the so called independent demand setting. Our approximation methods exploit this similarity and build on ideas developed for the independent demand setting. We present two approximation methods. The first one is based on relaxing the flight leg capacity constraints using Lagrange multipliers, whereas the second method involves solving a perfect hindsight relaxation problem. We show that both methods yield upper bounds on the optimal expected total revenue. Computational experiments demonstrate the tractability of our methods and indicate that they can generate tighter upper bounds and higher expected revenues when compared with the standard deterministic linear program that appears in the literature.     

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.