网络销售中退货担保与定价决策

本文采用退货担保期权综合完全退货策略与部分退货策略的优点,构建了网络销售中基于期权的退货与定价模型,以商品的价格、退货策略和退货担保期权价格为决策变量,讨论了存在退货期权和不存在退货期权两种情况下,最优决策存在的条件,求解出销售商最优价格、退货策略和退货担保期权价格,分析了各个市场参数变化对最优值的影响,通过对担保退货期权与退货策略同时存在和购买期权才能退货二种策略的比较,发现供应商最优策略是前者。算例验证了以上结论,做了敏感性分析,总结了相关管理启示与未来研究方向。所得结论对网络销售商开展网上销售有重要参考价值。     

How Costs and Heterogeneous Consumer Price Sensitivity Interact with Add‐On Pricing

Firms often cite cost savings as a reason why they charge separately for add‐ons. Firms also often face situations where consumers' price sensitivity is correlated with their valuation of add‐ons. While cost savings may directly translate into profit gains in some scenarios, this study examines the strategic implications of add‐on pricing and is the first to suggest that cost savings from add‐on pricing may in fact result in profit loss for firms when consumers are heterogeneous in price sensitivity. This is because add‐on pricing can trigger a revenue loss that exceeds any cost savings, thus leading to a negative net profit change for competing firms. Even if firms have the capability to pre‐commit to not adopting add‐on pricing, we show that competing firms can be locked in a prisoner's dilemma where all choose to adopt add‐on pricing and lose profits (as compared to none adopting add‐on pricing). We further show the possibility that the greater the cost of providing the add‐on (and the greater the cost savings generated from add‐on pricing), the worse this profit loss gets.     

考虑策略型消费者行为的零售商订货及忠诚计划联合决策研究

顾客忠诚计划是零售商的重要销售策略之一. 本文针对两期折扣问题中零售商的订货和积分回馈计划投入的联合决策问题,基于完全理性假设,并结合问题的实际情况,考虑了全价期单期以及全价期和折扣期两期的积分回馈计划,构建了基于这两种积分回馈计划下的策略型消费者决策模型. 分析了不同积分回馈计划对策略型消费者行为的影响,进而讨论了零售商在不同决策下的收益情况,探索了零售商订货和积分回馈计划联合决策的制定. 研究发现：(1)积分回馈计划会对策略型消费者行为产生影响,从而影响零售商的决策和收益;(2)订货和忠诚计划制定的联合决策有利于零售商提高收益;(3)对于单位成本低的商品,面向全价期的积分回馈计划的最优收益提升较大;(4)对于商品价值与实际价格差异较小的商品,积分回馈计划对最优收益的提升作用较大. 具体而言,如果商品单位成本小于等于折扣价,则面向全价期的积分回馈计划的最优收益提升较大,反之,则面向全价期和折扣期的积分回馈计划的最优收益提升较大.     

An inventory model with random discount offerings

We consider an inventory model in which a supplier makes deal offers with random discount prices at random points in time. Assuming that discount offerings follow a Poisson process and discount price is a discrete random variable with a known distribution, we propose a continuous-review control policy for the model and derive optimality conditions for the policy parameters. The model is then extended to the case of multiple suppliers that offer discount deals with supplier-specific Poisson processes and discount prices. Numerical examples are presented to demonstrate cost savings due to discount offers.     

Two Backorder Compensation Mechanisms in Inventory Systems with Impatient Customers

We study a compensation mechanism design problem with customer‐choice behavior in a continuous review setting where the production and demand processes are stochastic. When a stockout occurs, the firm controls backorders on the basis of certain compensation policies. Customers make decisions to maximize their utility, which is decreasing in the price, the waiting time, and the customer's impatience factor. We assume that the impatience factor is private information held by the customer only. Two compensation mechanisms are designed to control backorders, namely uniform compensation and priority auction with an admission price. Under uniform compensation, the firm offers the same discount to all customers, whereas under auction compensation, priority is granted according to the customers' bid prices. We obtain the optimal stockout price and base stock level under each mechanism, and analyze the properties of the respective optimal policies. Assuming linear waiting costs with uniformly distributed impatience factor, we find that the auction mechanism (1) maintains a lower base stock level and results in greater profit and (2) benefits customers with relatively lower or higher impatience factors, but customers with a medium impatience factor may be rendered worse off. We further show that both compensation mechanisms are suitable for products with a high unit profit, a high lost sales penalty cost, and a high holding cost.     

基于期权的易逝品订购预售联合策略研究

由需求不确定所引起的库存过剩或产品脱销通常会给企业的正常运营带来极大风险，本文考虑一种运输时间影响损耗率的易逝品，在消费者估值不确定的情况下，从集成的角度出发，针对零售商的订购与预售联合策略展开研究。需求端零售商可通过批发价订购方式或组合订购方式采购易逝品，销售端可提供折扣预售和期权预售两种策略。通过模型构建详细分析了几种不同的订购预售联合策略，求解了不同策略下的最优订购量和最优预售价格以及不同策略的适用情形。研究发现柔性采购（组合订购方式）和期权预售联合决策可以有效降低需求波动带来的库存积压和产品短缺风险，且期权预售策略比折扣预售策略的应用范围更广。     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

Optimal Quantity Discount Design with Limited Information Sharing*

In this article we address the optimal quantity discount design problem of a supplier in a two‐stage supply chain where the supplier and the buyer share annual demand information only. The supply chain faces a constant deterministic demand that is not price sensitive and operates with fixed setup costs in both stages. We show that the supplier can actually moderate a cost‐minimizing buyer to order in quantities different than the buyer's optimal order quantity in the traditional setting and develop a multi‐breakpoint quantity discount scheme that maximizes supplier's expected net savings. The proposed multi‐breakpoint discount scheme can be easily computed from the available information and, while also maximizing the supplier's net savings, is very effective in achieving high levels of supply chain coordination efficiency in the presence of limited information.     

A Stochastic Inventory Model With Fast‐Ship Commitments

We present a multiperiod model of a retail supply chain, consisting of a single supplier and a single retailer, in which regular replenishment occurs periodically but players have the option to support fast delivery when customers experience a stockout during a replenishment period. Because expedited shipments increase the supplier's transportation cost, and possibly production/inventory costs, the supplier typically charges a markup over and above the prevailing wholesale price for fast‐shipped items. When fast shipping is not supported, items are backordered if customers are willing to wait until the start of the next replenishment period. We characterize the retailers and the supplier's optimal stocking and production policies and then utilize our analytical framework to study how the two players respond to changes in supply chain parameters. We identify a sufficient condition such that the centralized supply chain is better off with the fast‐ship option. We find a range of markups for fast‐ship orders such that the fast‐ship option is preferred by both the supplier and the retailer in a decentralized chain. However, a markup that is a win–win for both players may not exist even when offering fast‐ship option is better for the centralized chain. Our analysis also shows that depending on how the markup is determined, greater customer participation in fast‐ship orders does not necessarily imply more profits for the two players. For some predetermined markups, the retailer's profit with the fast‐ship option is higher when more customers are willing to wait. However, the retailer may not be able to benefit from the fast‐ship option because the supplier may choose not to support the fast‐ship option when fast‐ship participation increases due to the fact that the fast‐ship participation rate adversely affects the initial order size.     

网络购物平台最优价格促销策略：价格折扣还是现金券？

平台价格促销已成为平台营销中的重要问题，不同于传统模式下商家决定商品的价格促销，平台价格促销是以平台作为价格促销的决策者。本文建立了平台价格折扣和现金券两种由平台作为决策者的价格促销模型，探讨平台的最优价格促销策略，并在原有模型的基础上考虑商家广告投资决策并构建了扩展模型。研究结果表明，(1)只有当商品的基本需求、消费者价格敏感度和商品价格满足一定条件时，平台价格促销才能提升平台利润。(2)在两种价格促销都能提升平台利润情况下，平台的交易费率较高且商品价格较低则平台实施现金券策略的利润高于价格折扣策略；其他情况下平台实施价格折扣策略的利润高于现金券策略。(3)在平台交易费率较低的情况下，价格折扣策略下消费者能得到更多优惠；否则现金券策略下消费者得到更多优惠。(4)增加商家广告投资能够提高平台促销活动的利润，但是平台的价格优惠降低，且平台实施价格促销活动的条件区间减小。     

Improving Profits by Bundling Vertically Differentiated Products

We consider a firm managing a category of vertically differentiated goods, that is, products which differ with respect to an attribute for which all consumers prefer more to less. The goods can be sold individually, in which case they are referred to as components, or in bundles. The firm chooses the assortment of components and bundles and their selling prices to maximize profit. We show that each bundling strategy (pure components, pure bundling or mixed bundling) can be optimal and obtain closed‐form expressions for the optimal selling prices. We provide insights on the structure of the optimal assortment and prices. In particular, we show that, when consumers benefit from consuming the components jointly, the products in the optimal assortment form nested sets. When consumers do not benefit from the joint consumption of components, the bundles should be offered at a positive discount. We find that bundling vertically differentiated products can significantly improve profits, even if consumers do not benefit from consuming the components jointly. The value of bundling comes from increased sales: a firm, which understands that its customers may buy multiple types of components, offers bundles of components, incentivizing customers to buy more.     

Discount Pricing Policies and the Coordination of Decentralized Distribution Systems*

A challenge of supply chain management is to align the objectives, and hence coordinate the activities, of independent supply chain members. In this study, we approach this problem in a simple way by extending traditional quantity discounts that are based solely on buyers' individual order size to discount policies that are based on both buyers' individual order size and their annual volume. We show that discount policies are able to achieve nearly optimal system profit and, hence, provide effective coordination, for a decentralized two‐echelon distribution system, whereby a supplier sells a product to a group of heterogeneous and independent retailers each facing a downward‐sloping demand curve of its retail price. When buyers are heterogeneous, a critical issue of coordination is to motivate different customers to increase their demand and lot size according to their potential so as to improve profits. We show that market heterogeneity presents an effective discriminating factor for the supplier to segment customers in the design of a coordination mechanism.     

Pricing of Full‐Service Repair Contracts with Learning,Optimized Maintenance,and Information Asymmetry

This article considers the optimal pricing of full‐service (FS) repair contracts by taking into account learning and maintenance efficiency effects, competition from service , and asymmetric information. We analyze on‐call service (OS) and FS contracts in a market where customers exhibit heterogeneous risk aversion. While the customers minimize their disutility over the equipment lifetime, the service provider maximizes expected profits arising from the portfolio of OS and FS contracts. We show that the optimal FS price depends inter alia on the customer's prior cost experience and on OS repair and maintenance costs. The optimal FS price is shown to increase as fewer OS customers are lost to competition, whereas improved repair learning enabled by FS reduces the optimal price. A numerical study based on data from a manufacturer of forklifts highlights the importance of learning in maintenance operations, which constitutes the key benefit of FS contracts; 81% of the customers select the FS option and are willing to pay an insurance premium of around 1.5% of total OS cost against volatility of repair costs.     

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.     

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

We consider a periodic‐review inventory system with regular and expedited supply modes. The expedited supply is faster than the regular supply but incurs a higher cost. Demand for the product in each period is random and sensitive to its selling price. The firm determines its order quantity from each supply in each period as well as its selling price to maximize the expected total discounted profit over a finite or an infinite planning horizon. We show that, in each period if it is optimal to order from both supplies, the optimal inventory policy is determined by two state‐independent thresholds, one for each supply mode, and a list price is set for the product; if only the regular supply is used, the optimal policy is a state‐dependent base‐stock policy, that is, the optimal base‐stock level depends on the starting inventory level, and the optimal selling price is a markdown price that decreases with the starting inventory level. We further study the operational impact of such supply diversification and show that it increases the firm's expected profit, reduces the optimal safety‐stock levels, and lowers the optimal selling price. Thus that diversification is beneficial to both the firm and its customers. Building upon these results, we conduct a numerical study to assess and compare the respective benefit of dynamic pricing and supply diversification.     

To sell or not to sell to an off-price retailer in the presence of strategic consumers

In the newsvendor model, strategic consumers choose between buying the product at the regular price or waiting to try to buy the product at the discount price. Retailers can benefit from the ability to decrease strategic consumers’ perceived probability of finding a unit available at the discount price. Selling some inventory to an off-price retailer, who has a large number of thrift consumers, enables retailers to change consumers’ perceived probability of product availability at a reduced price, but at a cost of losing some strategic consumers to the off-price retailer. We show that without the off-price retailer’s exclusive consumers and even if the off-price retailer buys the product for a price below the retailer’s cost, the retailer can still be better-off with the off-price retailer. We also find that the retailer benefits more when the off-price retailer charges higher price for the product and has a large consumer segment of its own.     

PRICE‐DEPENDENT INVENTORY MODELS WITH DISCOUNT OFFERS AT RANDOM TIMES*

We consider an inventory model with a supplier offering discounts to a reseller at random epochs. The offer is accepted when the inventory position is lower than a threshold level. We compare three different pricing policies in which demand is induced by the resellers price variation. Policy 1 is the EOQ policy without discount offers. Policy 2 is a uniform price, stock‐independent policy. Policy 3 is a stock level‐dependent, discriminated price policy. Assuming constant demand rates, expressions are obtained for the optimal order quantities, prices, and profits. The numerical experiments show that if it is better to accept a suppliers discount, then it benefits the reseller to transfer the discount to downstream customers.     

考虑战略顾客行为时的供应链性能分析与协调

动态定价策略的广泛应用使得越来越多的顾客具有了战略性,战略顾客会根据产品在销售期内的价格路径确定最优购买时机,零售商则根据顾客的购买行为确定订货数量和销售价格.研究了双方静态博弈时的理性预期均衡解和零售商进行数量承诺时的情形.研究表明:理性预期均衡时的最优销售价格、最优存货数量和最优期望利润分别小于标准报童模型的情形;数量承诺时的最优存货数量小于理性预期均衡时的最优存货数量;最优期望利润则大于理性预期均衡时的最优期望利润,并且在一定条件下可能会大于标准报童模型的最优期望利润,战略顾客行为的存在对零售商可能有利.最后分析了在分散式供应链中如何利用收入分享契约和数量折扣契约实现供应链协调.     

When Does a Retailer's Advance Selling Capability Benefit Manufacturer,Retailer, or Both?

Advance selling (AS) from a retailer to consumers is commonly observed in practice. With an AS capability, a retailer has the option to sell in advance or not. Having the AS option seems to increase flexibility and thus profit for a retailer. However, we show that the AS option can hurt the retailer's profit as well as supply chain performance. We identify two thresholds for a product's marginal production cost. A retailer's AS option benefits both the manufacturer and retailer when the marginal production cost is high, that is, above both thresholds. It benefits the manufacturer but hurts the retailer when the marginal production cost is moderate, that is, between the two thresholds. The result is ambiguous when the marginal production cost is low, that is, below both thresholds. We find that consumer valuation uncertainty under AS is the key driving force for the surprising result that having the retailer's AS option can hurt the retailer. When compared to the scenario where the retailer does not have the AS option, we find that the manufacturer's optimal wholesale price weakly decreases under the retailer's AS option if the marginal production cost is high. The statement is reversed if the marginal production cost is moderate or low.     

基于可控提前期和延迟供货的短生命周期产品库存模型

本文用斜坡型函数来描述短生命周期产品需求变化特征,用持有成本不断增加的形式来表示存货的无形变质所带来的损失,通过向供应商支付额外的赶工成本来缩短提前期,同时在允许缺货的情况下设置合理的缺货期价格折扣来控制订单的流失,即以价格折扣的损失来挽留住更多的顾客,使其总成本到达最优。本文在此基础上建立了短生命周期产品的库存模型,并提出了最优解的求解方法。