Dynamic Pricing,Production, and Channel Coordination with Stochastic Learning

We consider a decentralized two‐period supply chain in which a manufacturer produces a product with benefits of cost learning, and sells it through a retailer facing a price‐dependent demand. The manufacturer's second‐period production cost declines linearly in the first‐period production, but with a random learning rate. The manufacturer may or may not have the inventory carryover option. We formulate the resulting problems as two‐period Stackelberg games and obtain their feedback equilibrium solutions explicitly. We then examine the impact of mean learning rate and learning rate variability on the pricing strategies of the channel members, on the manufacturer's production decisions, and on the retailer's procurement decisions. We show that as the mean learning rate or the learning rate variability increases, the traditional double marginalization problem becomes more severe, leading to greater efficiency loss in the channel. We obtain revenue sharing contracts that can coordinate the dynamic supply chain. In particular, when the manufacturer may hold inventory, we identify two major drivers for inventory carryover: market growth and learning rate variability. Finally, we demonstrate the robustness of our results by examining a model in which cost learning takes place continuously.     

Pricing Policy in a Supply Chain: Negotiation or Posted Pricing

This article examines the choice of pricing policy (posted pricing or negotiation) toward end customers in a supply chain. Many retailers actively decide whether or not to encourage negotiation on the shop floor. Of course, the retailer's pricing policy influences not only the retailer's profit, but also the profits of the manufacturers who sell through the retailer. However, little is known about the forces that shape the pricing policy when two self‐interested parties interact in a supply chain. We consider two alternative models depending on who has the power to decide the pricing policy: the manufacturer or the retailer. We find that an increase in the wholesale price weakens the retailer's ability to price discriminate through negotiation. Therefore, the retailer prefers negotiation at lower wholesale prices and posted pricing at higher wholesale prices. We also find that whenever the retailer prefers negotiation, the manufacturer does too. Therefore, the retailer's discretion over the pricing policy causes friction only when the retailer wants to use posted pricing, while the manufacturer wishes the retailer to use negotiation. We show that such friction arises only when product availability or the cost of negotiation is moderate. In this case, we show that the manufacturer may offer a substantial discount to persuade the retailer to negotiate. Surprisingly, in this region of friction, a decrease in the supply chain's capacity or an increase in negotiation costs (both of which are typically considered as worsening the retailer's business environment) translates into higher profit for the retailer.     

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.     

Inventory‐Based Dynamic Pricing with Costly Price Adjustment

We study an average‐cost stochastic inventory control problem in which the firm can replenish inventory and adjust the price at anytime. We establish the optimality to change the price from low to high in each replenishment cycle as inventory is depleted. With costly price adjustment, scale economies of inventory replenishment are reflected in the cycle time instead of lot size—An increased fixed ordering cost leads to an extended replenishment cycle but does not necessarily increase the order quantity. A reduced marginal cost of ordering calls for an increased order quantity, as well as speeding up product selling within a cycle. We derive useful properties of the profit function that allows for reducing computational complexity of the problem. For systems requiring short replenishment cycles, the optimal solution can be easily computed by applying these properties. For systems requiring long replenishment cycles, we further consider a relaxed problem that is computational tractable. Under this relaxation, the sum of fixed ordering cost and price adjustment cost is equal to (greater than, less than) the total inventory holding cost within a replenishment cycle when the inventory holding cost is linear (convex, concave) in the stock level. Moreover, under the optimal solution, the time‐average profit is the same across all price segments when the inventory holding cost is accounted properly. Through a numerical study, we demonstrate that inventory‐based dynamic pricing can lead to significant profit improvement compared with static pricing and limited price adjustment can yield a benefit that is close to unlimited price adjustment. To be able to enjoy the benefit of dynamic pricing, however, it is important to appropriately choose inventory levels at which the price is revised.     

考虑策略型消费者的在线零售商库存信息披露及联合定价、库存决策模型

在两期销售环境下,研究了面向策略型消费者的在线零售商库存信息披露及联合定价、库存决策问题。考虑在线零售商库存信息共享和隐藏两种库存披露策略,构建了在线零售商两期销售利润模型。通过分析消费者的购买行为,讨论了在具有策略型消费者的市场中,在线零售商应如何选择库存信息披露策略,以及如何制定最优定价和库存决策。在此基础上,分析了相关参数对在线零售商决策及利润的影响。研究结果表明,在线零售商的最优定价及库存决策受消费者估值折扣系数和第二期定价策略的影响。特别地,当在线零售商选择第一期缺货时,更倾向于共享其库存水平信息;当在线零售商选择第二期缺货或者两期均不缺货时,消费者估值折扣系数存在一个阈值,当低于该阈值时,在线零售商会选择隐藏库存水平信息,当高于该阈值时,在线零售商会选择共享库存水平信息。     

Optimal Policies for Selling New and Remanufactured Products

Because of environmental and economic reasons, an increasing number of original equipment manufacturers (OEMs) nowadays sell both new and remanufactured products. When both products are available, customers will buy the one that gives them a higher (and non‐negative) utility. Thus, if the firm does not price the products properly, then product cannibalization may arise and its revenue may be adversely impacted. In this paper, we study the pricing problem of a firm that sells both new and remanufactured products over a finite planning horizon. Customer demand processes for both new and remanufactured products are random and price‐sensitive, and product returns (also called cores) are random and remanufactured upon receipt. We characterize the optimal pricing and manufacturing policies that maximize the expected total discounted profit. If new products are made‐to‐order (MTO), we show that when the inventory level of remanufactured product increases, the optimal price of remanufactured product decreases while the price difference between new and remanufactured products increases; however, the optimal selling price of new product may increase or decrease. If new products are made to stock (MTS), then the optimal manufacturing policy is of a base‐stock policy with the base‐stock level decreasing in the remanufactured product inventory level. To understand the potential benefit in implementing an MTO system, we study the difference between the value functions of the MTO and MTS systems, and develop lower and upper bounds for it. Finally, we study several extensions of the base model and show that most of our results extend to those more general settings.     

Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

It is common for a firm to make use of multiple suppliers of different delivery lead times, reliabilities, and costs. In this study, we are concerned with the joint pricing and inventory control problem for such a firm that has a quick‐response supplier and a regular supplier that both suffer random disruptions, and faces price‐sensitive random demands. We aim at characterizing the optimal ordering and pricing policies in each period over a planning horizon, and analyzing the impacts of supply source diversification. We show that, when both suppliers are unreliable, the optimal inventory policy in each period is a reorder point policy and the optimal price is decreasing in the starting inventory level in that period. In addition, we show that having supply source diversification or higher supplier reliability increases the firm's optimal profit and lowers the optimal selling price. We also demonstrate that, with the selling price as a decision, a supplier may receive even more orders from the firm after an additional supplier is introduced. For the special case where the quick‐response supplier is perfectly reliable, we further show that the optimal inventory policy is of a base‐stock type and the optimal pricing policy is a list‐price policy with markdowns.     

Pricing and Replenishment of Competing Perishable Product Variants under Dynamic Demand Substitution

I consider pricing and ordering decisions faced by a retailer selling a perishable product with a two‐period shelf life over an infinite horizon. In the first period, the product is “new”; in the next, it becomes “old.” The new product is perceived by customers to have a higher quality than the old product. Every period, the retailer makes three decisions: prices for the new and old products and how much new product to order. I first show, with some simple cases, that demand uncertainty can make the sale of the old product profitable. I then consider a more realistic case with dynamic demand substitution among customers. I recognize that the retailer's decisions may be constant or may vary across different periods, under different contexts. For instance, varying the price of the new product can sometimes be difficult due to the negative impact it generates among customers. I find that (i) the benefit obtained from selling the old product with constant decisions is much higher than the benefit from allowing all the decisions to vary; (ii) the former benefit increases with a higher procurement cost, a higher quality of the new product, and higher demand volatility; however, the latter benefit is non‐monotone in these parameters; (iii) most of the latter benefit can be obtained by just changing the order quantity; and (iv) as the inventory of the old product increases, when all the decisions vary, the optimal price of the new product may increase or decrease.     

双渠道下库存与定价策略的研究

为分析实体店零售商建立自己网络渠道存在的两个基本问题,本文探讨了为满足网络渠道需求网络渠道是自持有库存、还是共享实体店的库存问题,及如何解决网络渠道与实体渠道的销售冲突问题。在总结动态库存配给策略相关研究基础上,采用了动态定价策略的思路分析解决渠道冲突的问题;通过对双渠道是否共享库存的两种方案进行模拟对比,分析讨论了相关库存决策问题,并评价了共享库存所带来的共享效应的大小,以期使实体店零售商建立网络销售渠道取得更大的收益。研究结果表明,共享库存有比较显著的优势,库存共享效应能使需求波动更平滑、需求预测更精准;动态定价会带来更大的收益,在验证该结果时,对动态定价策略也进行了结构特征的分析。该思路可为相关研究提供借鉴。     

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.     

Why Do We Observe Stockless Operations on the Internet? Stockless Operations Under Competition

Due to the proliferation of electronic commerce and the development of Internet technologies, many firms have considered new pricing‐inventory models. In this paper, we study the role of stockless (i.e., zero‐inventory) operations in online retailing by a considering duopoly competition in which two retailers compete to maximize profit by jointly optimizing their pricing and inventory decisions. In our model, the retailers are allowed to choose either an in‐stock policy or stockless operations with a discounted price. We first present the characteristics and properties of the equilibrium. We then demonstrate that the traditional outcome of asymmetric Bertrand competition is observed under head‐to‐head competition. However, when the two firms choose different operational policies, with corresponding optimal pricing, they can share the market under certain conditions. Finally, we report interesting observations on the interaction between pricing and inventory decisions obtained from an extensive computational study.     

考虑广告影响下的新产品垄断动态定价研究

针对垄断零售商的新产品定价问题,提出了一个新产品动态定价策略。在顾客对以往的价格和广告具有"学习"能力的条件下,提出了具有"学习"功能的需求函数。在给定各周期广告水平下,给出了零售商最优的动态定价策略,分析了零售商定价规律,发现其定价规律具有"振荡"性,并趋近于一定值。在零售商要同时决策零售价格和广告水平的条件下,给出了各周期最优的零售价格和广告水平。在一定条件下,当周期数趋近无穷大时零售价格趋近于顾客的保留价格或者单位成本。     

Combined Pricing and Portfolio Option Procurement

In this paper, we study a single‐product periodic‐review inventory system that faces random and price‐dependent demand. The firm can purchase the product either from option contracts or from the spot market. Different option contracts are offered by a set of suppliers with a two‐part fee structure: a unit reservation cost and a unit exercising cost. The spot market price is random and its realization may affect the subsequent option contract prices. The firm decides the reservation quantity from each supplier and the product selling price at the beginning of each period and the number of options to exercise (inventory replenishment) at the end of the period to maximize the total expected profit over its planning horizon. We show that the optimal inventory replenishment policy is order‐up‐to type with a sequence of decreasing thresholds. We also investigate the optimal option‐reservation policy and the optimal pricing strategy. The optimal reservation quantities and selling price are shown to be both decreasing in the starting inventory level when demand function is additive. Building upon the analytical results, we conduct a numerical study to unveil additional managerial insights. Among other things, we quantify the values of the option contracts and dynamic pricing to the firm and show that they are more significant when the market demand becomes more volatile.     

A WTP‐Choice Model: Empirical Validation,Competitive and Centralized Pricing

Willingness To Pay (WTP) of customers plays an anchoring role in pricing. This study proposes a new choice model based on WTP, incorporating sequential decision making, where the products with positive utility of purchase are considered in the order of customer preference. We compare WTP‐choice model with the commonly used (multinomial) Logit model with respect to the underlying choice process, information requirement, and independence of irrelevant alternatives. Using WTP‐choice model, we find and compare equilibrium and centrally optimal prices and profits without considering inventory availability. In addition, we compare equilibrium prices and profits in two contexts: without considering inventory availability and under lost sales. One of the interesting results with WTP‐choice model is the “loose coupling” of retailers in competition; prices are not coupled but profits are. That is, each retailer should charge the monopoly price as the collection of these prices constitute an equilibrium but each retailer's profit depends on other retailers' prices. Loose coupling fails with dependence of WTPs or dependence of preference on prices. Also, we show that competition among retailers facing dependent WTPs can cause price cycles under some conditions. We consider real‐life data on sales of yogurt, ketchup, candy melt, and tuna, and check if a version of WTP‐choice model (with uniform, triangle, or shifted exponential WTP distribution), standard or mixed Logit model fits better and predicts the sales better. These empirical tests establish that WTP‐choice model compares well and should be considered as a legitimate alternative to Logit models for studying pricing for products with low price and high frequency of purchase.     

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.     

The Effects of Sharing Upstream Information on Product Rollover

The process of introducing new and phasing out old products is called product rollover. This paper considers a periodic‐review inventory system consisting of a manufacturer and a retailer, where the manufacturer introduces new and improved products over an infinite planning horizon using the solo‐roll strategy. We consider two scenarios: (1) the manufacturer does not share the upstream information about new‐product introduction with the retailer and (2) the manufacturer shares the information. For each scenario, we first derive the decentralized ordering policy and the system‐optimal ordering policy with given cost parameters. We then devise an optimal supply chain contract that coordinates the inventory system. We demonstrate that when the inventory system is coordinated, information sharing improves the performance of both supply chain entities. However, this may not be true if the inventory system is not coordinated. We also show that under the optimal contract, the manufacturer has no incentive to mislead the retailer about new‐product information in the information‐sharing model. When demand variability increases, information sharing adds more benefits to the coordinated supply chain. Our research provides insights about coordinating product, financial, and information flows in supply chains with product rollover.     

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。     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

零售商主导下生鲜农产品供应链的定价策略对比研究

运用RFID技术来监控与管理产品,零售商可以依据记录、传递的产品实时价值信息制定更为灵活的定价和订货策略,提升自身以及供应链的利润。针对生鲜农产品在价值损耗及消费者需求等方面进行特征分析,分别在固定定价、动态定价以及带有降价时点考虑的定价三种不同模式下,构建了单周期零售商的决策模型,得到各自的最优定价与订货策略,通过分析最优策略与关键参数之间的关系,发现:价值衰减系数越大,库存成本参数越大,三种模式下的总体零售价格都越小,价格的下调幅度越大;而两个参数对降价折扣时间点的影响却截然相反。进一步,着力在最优销售价格、订货总量与利润值三个方面对三种定价策略进行对比分析,结果显示基于RFID技术的灵活定价模式有助于零售商获取更大的市场需求量及更大的收益。数值实验进一步验证了理论研究的结果,为生鲜农产品供应链中对RFID技术的应用以及相应定价模式的选择提供了参考依据。     

Advance Selling by a Newsvendor Retailer

Retailers often face a newsvendor problem. Advance selling helps retailers to reduce demand uncertainty. Consumers, however, may prefer not to purchase in advance unless given a discount because they are uncertain about their valuation for the product in advance. It is then unclear whether or when advance selling to pass some uncertainty risk to consumers is optimal for the retailer. This paper examines the advance selling price and inventory decisions in a two‐period setting, where the first period is the advance selling period and the second is the selling (and consumption) period. We find that an advance selling strategy is not always optimal, but is contingent on parameters of the market (e.g., market potential and uncertainty) and the consumers (e.g., valuation, risk aversion, and heterogeneity). For example, we find that retailers should sell in advance if the consumers' expected valuation exceeds consumers' expected surplus when not buying early by a certain threshold. This threshold increases with the degree of risk aversion but decreases with stock out risk. If the degree of risk aversion varies across consumers, then a retailer should sell in advance if the probability for a consumer to spot buy is less than a critical fractile.