An Auction Mechanism for Pricing and Capacity Allocation with Multiple Products

We consider a pricing and short‐term capacity allocation problem in the presence of buyers with orders for bundles of products. The supplier's objective is to maximize her net profit, computed as the difference between the revenue generated through sales of products and the production and inventory holding costs. The objective of each buyer is similarly profit maximization, where a buyer's profit is computed as the difference between the time‐dependent utility of the product bundle he plans to buy, expressed in monetary terms, and the price of the bundle. We assume that bundles' utilities are buyers' private information and address the problem of allocating the facility's output. We directly consider the products that constitute the supplier's output as market goods. We study the case where the supplier follows an anonymous and linear pricing strategy, with extensions that include quantity discounts and time‐dependent product and delivery prices. In this setting, the winner determination problem integrates the capacity allocation and scheduling decisions. We propose an iterative auction mechanism with non‐decreasing prices to solve this complex problem, and present a computational analysis to investigate the efficiency of the proposed method under supplier's different pricing strategies. Our analysis shows that the problem with private information can be effectively solved with the proposed auction mechanism. Furthermore, the results indicate that the auction mechanism achieves more than 80% of the system's profit, and the supplier receives a higher percentage of profit especially when the ratio of demand to available capacity is high.     

The Newsvendor Problem and Price‐Only Contract When Bankruptcy Costs Exist

We study a supply chain of a supplier selling via a wholesale price contract to a financially constrained retailer who faces stochastic demand. The retailer might need to borrow money from a bank to execute his order. The bank offers a fairly priced loan for relevant risks. Failure of loan repayment leads to a costly bankruptcy (fixed administrative costs, costs proportional to sales, and a depressed collateral value). We identify the retailer's optimal order quantity as a function of the wholesale price and his total wealth (working capital and collateral). The analysis of the supplier's optimal wholesale price problem as a Stackelberg game, with the supplier the leader and the retailer the follower, leads to unique equilibrium solutions in wholesale price and order quantity, with the equilibrium order quantity smaller than the traditional newsvendor one. Furthermore, in the presence of the retailer's bankruptcy risks, increases in the retailer's wealth lead to increased supplier's wholesale prices, but without the retailer's bankruptcy risks the supplier's wholesale prices stay the same or decrease in retailer's wealth.     

Lifecycle Pricing for Installed Base Management with Constrained Capacity and Remanufacturing

Installed base management is the policy in which the manufacturer leases the product to consumers, and bundles repair and maintenance services along with the product. In this article, we investigate for the optimal leasing price and leasing duration decisions by a monopolist when the production and servicing capacity are constrained. The effect of diffusion of consumers in the installed base is considered, with the ownership of the product resting with the monopolist during the product lifecycle. The monopolist operating the installed base jointly optimizes the profits from leasing the product/service bundle along with maintenance revenues and remanufacturing savings. We formulate the manufacturer's problem as an optimal control problem and show that the optimal pricing strategy of the firm should be a skimming strategy. We also find that the effect of remanufacturing savings on the pricing decision and the length of the leasing duration changes significantly depending on the duration of the product's lifecycle. If the product lifecycle is long and remanufacturing savings are low, the firm should offer a shorter leasing duration, whereas if the remanufacturing savings are high, the firm should optimally offer a higher leasing duration. In contrast, if the time duration of the product lifecycle is low and remanufacturing savings are low, the firm prefers to offer a shorter leasing duration, whereas if the remanufacturing savings are high, the firm should optimally have a longer leasing duration. The article also shows that if the production capacity is small, the manufacturer increases the leasing duration. If the production capacity is very small, the manufacturer sets the leasing duration to be equal to the product lifecycle and does not use remanufacturing.     

The Effect of Delayed Incentives on Supply Chain Profits and Consumer Surplus

We examine the use of consumer cash mail‐in rebates offered by a manufacturer in a Stackelberg game where the manufacturer is the leader and the retailer is the follower. Our analysis indicates that rebates are profitable for manufacturers if consumers are inconsistent in the sense that their rebate valuation when they make purchase decisions is independent of their redemption probabilities when they make redemption decisions. If the manufacturer keeps the wholesale price unchanged, then the rebate increases the retailer's profit by a larger amount than the increase in the manufacturer's profit. If the manufacturer jointly optimizes the wholesale price and rebate, then the increase in the manufacturer's profit is twice the increase in the retailer's profit. The retailer responds to rebates by increasing the retail price, which increases the margin paid by consumers who do not redeem the rebate. On average, consumer surplus decreases when it is optimal for manufacturers to offer rebates. We suggest incentive schemes that make it worthwhile for retailers to limit the price increase. In these incentive schemes, the manufacturer imposes a negative relationship between the rebate value and the retail price. We show that such incentives increase supply chain profits.     

Cooperative Advertising and Pricing in a Dynamic Stochastic Supply Chain: Feedback Stackelberg Strategies

Cooperative (co‐op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co‐op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi's stochastic sales‐advertising model. We obtain the condition when offering co‐op advertising is optimal for the manufacturer. We provide in feedback form the optimal advertising and pricing policies for the manufacturer and the retailer. We contrast the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.     

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.     

Efficient frontiers for electricity procurement by an LDC with multiple purchase options

In meeting its retail sales obligations, management of a local distribution company (LDC) must determine the extent to which it should rely on spot markets, forward contracts, and the increasingly popular long-term tolling agreements under which it pays a fee to reserve generator capacity. We address these issues by solving a mathematical programming model to derive the efficient frontier that summarizes the optimal tradeoffs available to the LDC between procurement risk and expected cost. To illustrate the approach, we estimate the expected procurement costs and associated variances that proxy for risk through a spot-price regression for the spot-purchase alternative and a variable-cost regression for the tolling-agreement alternative. The estimated regressions yield the estimates required to determine the efficient frontier. We develop several such frontiers under alternative assumptions as to the forward-contract price and the tolling agreement's capacity payment, and discuss the implications of our results for LDC management.     

国有控股公司IPOs定价及抑价模型

从信息不对称的角度出发,结合我国国有控股公司的治理结构特点,引入控制租金概念,通过模型构造和推演,给出了最优发行价的表达式,并认为新股抑价是保证国有控股公司成功上市和国有股东在约束条件下获得效用最大化的一种均衡状态。     

Supply Chain Sourcing Under Asymmetric Information

We study a supply chain with two suppliers competing over a contract to supply components to a manufacturer. One of the suppliers is a big company for whom the manufacturer's business constitutes a small part of his business. The other supplier is a small company for whom the manufacturer's business constitutes a large portion of his business. We analyze the problem from the perspective of the big supplier and address the following questions: What is the optimal contracting strategy that the big supplier should follow? How does the information about the small supplier's production cost affect the profits and contracting decision? How does the existence of the small supplier affect profits? By studying various information scenarios regarding the small supplier's and the manufacturer's production cost, we show, for example, that the big supplier benefits when the small supplier keeps its production cost private. We quantify the value of information for the big supplier and the manufacturer. We also quantify the cost (value) of the alternative‐sourcing option for the big supplier (the manufacturer). We determine when an alternative‐sourcing option has more impact on profits than information. We conclude with extensions and numerical examples to shed light on how system parameters affect this supply chain.     

基于提前支付且考虑银行存贷的资金约束供应链最优定价决策

针对由单一制造商和单一零售商组成的供应链，考虑制造商或零售商在资金闲置与资金约束时向银行存款与贷款的情形，研究了供应链Stackelberg定价策略。首先，给出了市场需求函数；然后，考虑销售收入的零存整取收益、利润的存款收益以及贷款损失，分别构建了制造商资金约束与零售商资金约束两种情形下基于提前支付且考虑银行存贷的供应链成员利润函数；进一步地，依据Stackelberg理论，确定了两种权力结构下供应链的最优策略；在此基础上，分析了零存整取利率、存款利率和贷款利率对供应链最优策略的影响；最后，针对不同资金约束对象与不同权力结构，对比分析了银行利率对供应链最优策略的影响差异，揭示其背后的影响机理。研究结果表明，三种银行利率均会影响供应链的最优策略，相对于供应链权力结构，其影响与供应链资金约束对象更加相关。     

Manufacturer's pricing strategy for supply chain with warranty period-dependent demand

This article presents a review of the issues associated with a manufacturer's pricing strategies in a two-echelon supply chain that comprises one manufacturer and two competing retailers, with warranty period-dependent demands. The manufacturer, as a Stackelberg leader, specifies wholesale prices to two competing retailers who face warranty period-dependent demand and have different sales costs. The manufacturer considers three pricing options: (1) setting the same price for both retailers, while disregarding their difference with regard to sales cost; (2) setting a different price to each retailer on the basis of their sales cost; and (3) setting the same price to both retailers according to the average sales cost of the industry. In this article, the retailers' optimal warranty periods and their optimal profit, manufacturer's optimal wholesale price, and his/her optimal profit associated with different pricing strategies have been derived using the game theory. Our analysis shows that the results for retailers are the same with Strategy 1 or Strategy 3. In addition, we compared the effects of different pricing strategies of the manufacturer on supply chain decisions and profit. We conclude from the results that the manufacturer should either adopt Strategy 2 with symmetrical sales cost information or Strategy 3 if retailers' sales costs are asymmetrical.     

Price and Service Competition in an Outsourced Supply Chain

We consider a buyer who outsources the manufacturing of a product to multiple symmetric make‐to‐stock suppliers who compete on price and service (fill rate). The buyer allocates demand to the suppliers using a score function with an exponential form, which specifies the relative importance of price vs. service, in order to minimize his costs, while the suppliers choose their prices and fill rates to maximize their profits. For the case of dual‐sourcing, we characterize the optimal parameter of the exponential score function, considering the impact of the buyer's decisions on the suppliers, and considering how the suppliers compete against each other to earn a portion of the buyer's demand. We prove the existence of a unique equilibrium and characterize the equilibrium behavior of the system. We then consider a general number of suppliers and show that the equilibrium prices and fill rates, and the buyer's cost, are increasing in the number of suppliers. We compare these results to a model of single‐sourcing, in which the buyer is the Stackelberg leader and extracts all profits from the supplier. We find that the buyer always prefers single‐sourcing to multisourcing. Finally, we study a centralized system and use the results to develop a coordinating contract for the decentralized system.     

The Value of Free Water: Analyzing South Africa's Free Basic Water Policy

This paper analyzes South Africa's Free Basic Water Policy, under which households receive a free water allowance equal to the World Health Organization's recommended minimum. I estimate residential water demand, evaluate the welfare effects of free water, and provide optimal price schedules derived from a social planner's problem. I use a data set of monthly metered billing data for 60,000 households for 2002–2009 from a particularly disadvantaged suburb of Pretoria, with rich price variation across 20 different nonlinear tariff schedules. I find that the free allowance acts as a lump‐sum subsidy, without large effects on water consumption. However, it is possible to reallocate the current subsidy to form an optimal tariff without a free allowance, which would increase welfare while leaving the water provider's profit unchanged. This optimal tariff would also reduce the number of households consuming low quantities of water, a desirable policy goal according to the WHO.     

Market‐Triggered Changes in Capital Structure: Equilibrium Price Dynamics

We analyze the internal consistency of using the market price of a firm's equity to trigger a contractual change in the firm's capital structure, given that the value of the equity itself depends on the firm's capital structure. Of particular interest is the case of contingent capital for banks, in the form of debt that converts to equity, when conversion is triggered by a decline in the bank's stock price. We analyze the problem of existence and uniqueness of equilibrium values for a firm's liabilities in this context, meaning values consistent with a market‐price trigger. Discrete‐time dynamics allow multiple equilibria. In contrast, we show that the possibility of multiple equilibria can largely be ruled out in continuous time, where the price of the triggering security adjusts in anticipation of breaching the trigger. Our main condition for existence of an equilibrium requires that the consequences of triggering a conversion be consistent with the direction in which the trigger is crossed. For the design of contingent capital with a stock price trigger, this condition may be interpreted to mean that conversion should be disadvantageous to shareholders, and it is satisfied by setting the trigger sufficiently high. Uniqueness follows provided the trigger is sufficiently accessible by all candidate equilibria. We illustrate precise formulations of these conditions with a variety of applications.     

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.     

考虑消费者预期的电动汽车分时租赁市场价格竞争模型

分时租赁平台作为电动汽车推广的主要方式，其特征与打车软件类似，在风险资本的推动下极易引发价格战。各租车公司的市场需求量不仅与自己的定价有关，也与竞争对手的定价策略相关，目标都是各自利润的最大化。本文在考虑消费者预期的基础上，研究了需求函数为线性情形下的多人博弈，证明了此博弈是超模博弈以及Nash均衡的存在性和唯一性。并进一步揭示了降价幅度、交叉价格和价格敏感消费群体占比对均衡价格、均衡需求量和利润的影响关系，讨论了价格竞争过程中各租车公司的决策过程与利弊关系。结果表明：任意租车公司的降价行为都会引发整个市场的降价反应，且降价幅度随着博弈阶段的推进逐渐减小，最终收敛于均衡价格；动态定价博弈存在最优组合策略，市场竞争时应当把握好降价幅度，避免过度的价格竞争；均衡价格是关于消费者预期的单调减函数，价格敏感的消费群体占比越大，租车公司间价格竞争越激烈，降价幅度会越大，均衡价格越低；对于市场份额大的租车公司利润是关于价格敏感型消费者占比的单调增函数，但对中小租车公司而言则是单调减函数，价格敏感的消费者越多，对大公司有利，对中小公司不利。     

双渠道零售商和传统零售商的定价策略

在单制造商和两个具有竞争行为零售商的供应链系统中，本文研究了双渠道零售商和传统零售商的定价决策问题。首先，在零售商间进行Stackelberg博弈假设前提下，分别针对双渠道零售商和传统零售商作为领导者的情况，构建了两种模式下的零售商定价决策模型，给出了零售商的最优定价策略；其次，分析了零售商在特定情形下的定价策略；最后，用数值算例分析了模型参数对最优结果的影响。通过对比研究和数值算例分析发现：对于零售商来说，作为Stackelberg的领导者时的总利润要比作为追随者时的总利润大；对于供应商而言，传统渠道的零售商做主导者时的总利润要比双渠道零售商做主导者时的总利润大。     

Optimal Uniform Pricing Strategy of a Service Firm When Facing Two Classes of Customers

When facing heterogeneous customers, how should a service firm make its pricing decision to maximize revenue? If discrimination is allowed, then priority schemes and differentiated pricing are often used to achieve that. In many applications, however, the firm cannot or is not allowed to set discriminatory prices, for example, list price in retail stores, online shopping, and gas stations; thus a uniform price must be applied to all customers. This study addresses the optimal uniform pricing problem of a service firm using a queueing system with two classes of customers. Our result shows that the potential pool of customers plays a central role in the firm's optimal decision. Depending on the range of system parameters, which are determined explicitly by the primitive data, the firm's optimal strategy may choose to serve only one class of customers, a subset of a class of customers, or a combination of different classes of customers. In addition, the optimal price is in general not monotonic with respect to the potential market sizes because their changes may lead to a major shift in the firm's decision on which customer class to serve. However, unless such a shift occurs, the optimal price is weakly decreasing in the potential market sizes.     

Flexibility or Cost Saving? Sourcing Decisions with Two Suppliers

This article studies a decentralized supply chain in which there are two suppliers and a single buyer. One supplier offers the quantity flexibility (QF) contract to the buyer, while the other offers the cheaper price. Under the QF contract, the buyer does not assume full responsibility for the forecast, yet the supplier guarantees the availability of the forecasted quantity with additional buffer inventory. On the other hand, the price‐only contract places full inventory burden on the buyer, but with a cheaper price. We study this problem from the buyer's perspective and solve for the buyer's optimal procurement and forecasting decisions. We identify areas where flexibility and cheaper price have an advantage, one over the other. Our results indicate that the buyer significantly benefits from having multiple sources of supply. We also find that, from the system's standpoint, a multisupplier system may outperform a single‐supplier supply chain under certain conditions. Interestingly, we observe that providing too much flexibility may benefit the low‐price supplier rather than benefiting the QF supplier. We discuss the managerial implications and provide directions for future research opportunities.