Vendor Selection with Bundling: A Comment*

In a recent article by Rosenthal, Zydiak, and Chaudhry (1995), a mixed integer linear programming model was introduced to solve the vendor selection problem for the case in which the vendor can sell items individually or as part of a bundle. Each vendor offered only one type of bundle, and the buyer could purchase at most one bundle per vendor. The model employed n(m+ 1) binary variables, where n is the number of vendors and m is the number of products they sell. The existing model can lead to a purchasing paradox: it may force the buyer to pay more to receive less. We suggest a reformulation of the same problem that (i) eliminates this paradox and reveals a more cost-effective purchasing strategy; (ii) uses only n integer variables and significantly reduces the computational workload; and (iii) permits the buyer to purchase more than one bundle per vendor.     

Coordinated Replenishments from a Common Supplier

Coordinated replenishment strategies may be implemented by jointly ordering multiple items from a common supplier. A major benefit of coordinated replenishment is that it increases the size of shipments, permitting the buyer to enjoy transportation economies without a major increase in average inventory levels. The coordinated replenishment problem is complex because side constraints govern the attainment of transportation rate breaks. The problem is further complicated by the presence of purchase quantity discount opportunities. Thus, the buyer must decide which items to order independently, which items to include in a group order, and the order quantities of each item, governed by the frequency of independent or group orders. We present a mathematical model and a heuristic solution procedure that provide analytical support to the buyer seeking to minimize total costs of replenishing multiple items from a common supplier. The relevant costs are purchase prices, ordering costs, holding costs, and transportation costs. Coordinated replenishment provides nearly a 30 percent reduction in controllable costs relative to independent control. Experimentation with the heuristic has yielded optimal solutions over 88 percent of the time. When optimality was not obtained, the mean penalty was much less than one percent. The average heuristic search was more than two orders of magnitude faster than branch and bound, even for small problems, and possessed a much tighter distribution around the mean search time.     

A Generalized Framework for Quantity Discount Pricing Schedules

The use of price to influence a buyer's purchasing behavior and thus improve supply chain coordination has received considerable attention. The vendor and buyer are independent economic entities, each maximizing its own profit. We consider the case of a buyer with fixed annual demand, independent of cost. The vendor's objective is to set a price schedule that encourages the buyer to raise its order quantity, increasing the vendor's profits. We present a unified treatment of the problem, categorize different variations, and provide a common solution procedure for all cases.     

Strong Duality for a Multiple‐Good Monopolist

We characterize optimal mechanisms for the multiple‐good monopoly problem and provide a framework to find them. We show that a mechanism is optimal if and only if a measure μ derived from the buyer's type distribution satisfies certain stochastic dominance conditions. This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types. As a corollary, we characterize the optimality of grand‐bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived. As an application, we show that the optimal mechanism for n independent uniform items each supported on [c,c+1] is a grand‐bundling mechanism, as long as c is sufficiently large, extending Pavlov's result for two items Pavlov, 2011. At the same time, our characterization also implies that, for all c and for all sufficiently large n, the optimal mechanism for n independent uniform items supported on [c,c+1] is not a grand‐bundling mechanism.     

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.     

On revenue maximization with sharp multi-unit demands

We consider markets consisting of a set of indivisible items, and buyers that have sharp multi-unit demand. This means that each buyer \(i\) wants a specific number \(d_i\) of items; a bundle of size less than \(d_i\) has no value. We consider the objective of setting prices and allocations in order to maximize the total revenue of the market maker. The pricing problem with sharp multi-unit demand buyers has a number of properties that the unit-demand model does not possess, and is an important question in algorithmic pricing. We consider the problem of computing a revenue maximizing solution for two solution concepts: competitive equilibrium and envy-free pricing. For unrestricted valuations, these problems are NP-complete; we focus on a realistic special case of “correlated values” where each buyer \(i\) has a valuation \(v_iq_j\) for item \(j\), where \(v_i\) and \(q_j\) are positive quantities associated with buyer \(i\) and item \(j\) respectively. We present a polynomial time algorithm to solve the revenue-maximizing competitive equilibrium problem. For envy-free pricing, if the demand of each buyer is bounded by a constant, a revenue maximizing solution can be found efficiently; the general demand case is shown to be NP-hard.     

Will More Purchasing Options Benefit Customers?

This paper considers the sale of a seasonal product in the face of strategic customers. At the beginning of the selling season, the retailer announces both the price p_h at which the product will be sold during the selling season and the post‐season clearance price p<p_h for unsold items. We analyze two operating regimes: The “no reservation regime” allows a buyer either to purchase the product at price p_h when he arrives or to enter a lottery to purchase at price p if the product remains unsold. The “reservation regime” offers each buyer one extra option than the no reservation regime: reserve the product for purchase at the clearance price p. If the buyer reserves the product under the reservation regime and if it remains unsold at the end of the selling season, then he is obligated to purchase it at price p. We consider a situation in which heterogeneous customers with probabilistic valuation arrive in accord with a Poisson process. We characterize the rational purchasing behavior wherein each arriving customer is strategic; each customer takes other customers' purchasing behavior into consideration. By considering the Nash equilibrium of this game, we show that strategic customer behavior can render the customer to be worse off and the retailer to be better off under the reservation regime, despite the fact that this regime offers one extra option (reservation) to a customer. Hence, more purchasing options do not necessarily benefit customers.     

Toward a Typology of Buyer–Supplier Relationships: A Study of the Computer Industry*

Buyer–supplier relationship typologies are useful analytical tools for purchasing managers in managing exchange relationships with suppliers and monitoring their purchasing portfolios. Existing buyer–supplier relationship typologies are mainly focused on either relational contents or power‐dependence and have limited empirical support for their performance implications. In this study, we developed an alternative buyer–supplier relationship typology that integrates both relational content and power‐dependence dimensions, resulting in four generic relationship types: market, power, autonomous‐link, and constrained‐link relationships. We then performed a longitudinal exploratory investigation of eight leading firms in the U.S. computer industry to explore the performance implications of the typology, using a combinatorial qualitative approach that leverages the strengths of case study research, content analysis, and quasi‐experimental design. The results suggest three theoretical propositions. First, the association between the type of buyer–supplier relationships and buyer firm performance varies such that constrained‐link relationships are superior in terms of operational efficiency while autonomous‐link relationships are superior in terms of product innovation. Second, the positive association between buyer–supplier relational contents (i.e., relationalism) and buyer firm operational efficiency is strengthened as the suppliers' dependence on the buyer firm increases. And finally, the positive association between buyer–supplier relationalism and buyer firm product innovation is weakened as the suppliers' dependence on the buyer firm increases.     

Strategic Purchases of Bundled Products in a Health Care Supply Chain Environment*

Recent articles in the Wall Street Journal summarize the state of business practice in American hospitals by shedding light on the state of supply chain management practices and foci in today's health care supply chains. In health care, the single largest cost after labor is materials, and it has been documented that health care facilities can reduce the environmental impacts of the products and services they consume before regulatory problems arise or waste disposal costs increase by focusing on their upstream activities. Health care systems around the country consume significant quantities and varieties of products within the health delivery processes. Solving these environmental problems requires a much broader view involving collaborative efforts of professionals from different areas of health care to meet these challenges. The purchasing function bridges the gaps by providing a healthy dialogue on key environmental attributes within the health care supply chain. The concept of bundling new with refurbished products is gaining a lot of attention in the health care supply chain. This research describes a health care purchasing problem for bundling new and refurbished products of the type facing a growing number of large health care providers, and then proposes a methodology for evaluating the complex tradeoffs involved in bundling decisions for refurbished health care products. By exploiting some useful properties of the problem structure, our results provide buyers with useful insights for examining and selecting suppliers who are willing to offer bundles of new and refurbished products.     

基于提前订购策略的供需双方动态博弈模型研究

在两级供应链环境下,相对于传统的即时订购策略,通过以较低批发价提供一个提前订购的机会,给予购买商两次订货机会,那么供应商和购买商的利润可以实现帕累托改进.同时如果供应商在提供提前订购机会的同时收取一个固定费用,则可以进一步优化模型.建立了一个具体的模型,用逆向归纳法计算出了均衡解,并对不同策略下的均衡结果进行了对比分析.     

The Purchasing Performance of Organizations Using e-Marketplaces

We apply transaction cost economic theory and perspectives in an empirical test regarding purchasing performance using electronic marketplaces. Basically, buyers can purchase products either by hopping across multiple electronic marketplaces or maintaining close relationships with a particular electronic marketplace. We investigate which is more beneficial for a buyer organization's purchasing performance in terms of price reduction and purchasing efficiency. We undertake this task by developing hypotheses and a research model and subjecting them to testing and analysis using the purchase of maintenance, repair and operations products in a large and important market, South Korea.     

Organizational Learning in Global Purchasing: A Model and Test of Internal Users and Corporate Buyers*

This research examines a model centered on organizational learning in purchasing. Two different studies are conducted to test the hypotheses among purchasing users (Study 1) and buyers (Study 2). The user sample consists of users representing 355 strategic business units of a Fortune 500 multinational corporation. The buyer sample consists of corporate buyers of 200 multinational corporations drawn from the membership directory of the National Association of Purchasing Management (NAPM). In each study, the focus is on the learning relationships between corporate buyers and internal users in the purchasing organization. Based on the two studies, the results suggest that organizational learning in the purchasing process is influenced by the organizational culture factors of localness, transformational leadership, and openness. Organizational learning has a positive effect on information processing in the purchasing system, which, in turn, has a positive influence on the cycle time of the purchasing process.     

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.     

BUNDLING ELECTRONIC JOURNALS AND COMPETITION AMONG PUBLISHERS

Site licensing of electronic journals has revolutionized the way academic information is distributed. However, many librarians are concerned about the possibility that commercial publishers might abuse site licensing by the practice of bundling. In this paper, we analyze how bundling affects journal pricing in the market of scientific, technical, and medical electronic journals and offer a novel insight on the bundling of a large number of information goods. We find that (i) when bundling is prohibited, surprisingly, industry concentration does not affect prices; (ii) when bundling is allowed, each publisher finds bundling profitable and bundling increases industry profits while reducing social welfare; and (iii) any merger among publishers already active in the market is profitable but reduces social welfare. (JEL: D4, K21, L41, L82)     

考虑信用销售的改良品联合采购决策

信用销售能够提升生产企业竞争力、扩大经营规模,帮助销售企业缓解资金压力,对供应链的运作效率有较大影响,成为供应链管理研究的重要课题之一。考虑在单一供应商和多个零售商组成的二级改良品供应链中,供应商提供延迟支付作为信用销售手段,分别建立零售商独立采购和联合采购的最小单位时间总成本函数,通过比较最小单位时间总成本函数得到联合采购优于独立采购的条件。将改良品联合采购的成本分配问题构造为改良品联合采购博弈,给出博弈具有的基本性质,并设计一种基于博弈核心的成本分配方法。通过数值算例和敏感性分析验证了文中所构建模型的正确性。     

Competitive Bundling

This paper proposes a framework for studying competitive (pure) bundling in an oligopoly market. We find that under fairly general conditions, relative to separate sales, bundling raises market prices, benefits firms, and harms consumers when the number of firms is above a threshold (which can be small). This is in contrast to the findings in the duopoly case on which the existing literature often focuses. Our analysis also sheds new light on how consumer valuation dispersion affects price competition more generally.     

在弹性需求和物品易变质条件下数量折扣定价模型

研究在弹性需求和易变质物品条件下,当供应商和零售商独自决策时,供应商如何确定最优数量折扣问题。基于Stackelberg博奕建立了数学模型,证明了零售商的出售价格随供应商出售价格的降低而降低,从而需求量增大。当供应商给予价格折扣时,零售商的利润是增加的。在此基础上,给出了最优数量折扣的计算方法。对供应商和零售商单独决策时,供应商利用数量折扣对供应链进行协调产生的系统利润与供应商和零售商联合决策时的系统利润做了数值分析和比较。结果表明,供应商采用数量折扣的方法使供应链协调是有效的;价格折扣随价格敏感系数的增大而增大,随变质率的增大而减小。     

非瞬时补货下改良品联合采购决策

联合采购往往使订货批量成倍增加,从而更易享受供应商提供的价格折扣,因此联合采购受到零售商们的青睐。考虑由单供应商与多零售商组成的二级改良品供应链中,供应商对零售商提供非瞬时补货,分别建立零售商独立采购与联合采购的单位时间成本函数,求解出两种采购模式的最小单位时间成本并对之进行比较,得到联合采购优于独立采购的必要条件。同时,以联合采购的联盟成本作为分摊对象,应用多人合作博弈理论,将联合采购的成本分摊问题构造成多人合作博弈问题,给出最小核心法的成本分摊思路。通过数值算例演示成本分摊过程,给出净改良率对订货参数及成本参数的敏感性分析,并对四种成本分摊算法的分摊结果作出比较。     

Configuration of flexibility strategies under supply uncertainty

In this paper, we study a buyer׳s configuration of flexibility strategies under supply uncertainty. His main supplier׳s production process is uncertain, and he can either choose pricing flexibility (setting prices depending on the available supply) or operational flexibility (requesting a contingent order from a backup supplier). As the buyer may or may not find a suitable contingent supplier ex post, we study two scenarios that the backup supplier׳s supply is infinite, and that this supply is random. We also include the factor that the main supplier may determine the wholesale price. We demonstrate that the adoption of flexibility strategies is controlled by threshold policies in different scenarios whether the main supplier determines the wholesale price or not. We also investigate how the buyer׳s attribute (finding a suitable contingent supplier) affects the configuration of flexibility strategies.     

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.