Determining Optimal Selling Price and Lot Size When the Supplier Offers All-Unit Quantity Discounts*

This paper is concerned with finding the optimal price and lot size for a retailer purchasing a product for which the supplier offers all-unit quantity discounts. Demand for the product is assumed to be a decreasing function of price, and a procedure is developed for finding the optimal price and lot size for a class of demand functions. The procedure then is applied to two common demand functions: (1) the constant price-elasticity function, and (2) the linear demand function.     

A JOINT ECONOMIC-LOT-SIZE MODEL FOR PURCHASER AND VENDOR

In a typical purchasing situation, the issues of price, lot sizing, etc., usually are settled through negotiations between the purchaser and the vendor. Depending on the existing balance of power, the end result of such a bargaining process may be a near-optimal or optimal ordering policy for one of the parties (placing the other in a position of significant disadvantage) or, sometimes, inoptimal policies for both parties. This paper develops a joint economic-lot-size model for a special case where a vendor produces to order for a purchaser on a lot-for-lot basis under deterministic conditions. The focus of this model is the joint total relevant cost. It is shown that a jointly optimal ordering policy, together with an appropriate price adjustment, can be beneficial economically for both parties or, at the least, does not place either at a disadvantage.     

Integrated Procurement Planning in Multi‐division Firms

For large multi‐division firms, coordinating procurement policies across multiple divisions to leverage volume discounts from suppliers based on firm‐wide purchasing power can yield millions of dollars of savings in procurement costs. Coordinated procurement entails deciding which suppliers to use to meet each division's purchasing needs and sourcing preferences so as to minimize overall purchasing, logistics, and operational costs. Motivated by this tactical procurement planning problem facing a large industrial products manufacturer, we propose an integrated optimization model that simultaneously considers both firm‐wide volume discounts and divisional ordering and inventory costs. To effectively solve this large‐scale integer program, we develop and apply a tailored solution approach that exploits the problem structure to generate tight bounds. We identify several classes of valid inequalities to strengthen the linear programming relaxation, establish polyhedral properties of these inequalities, and develop both a cutting‐plane method and a sequential rounding heuristic procedure. Extensive computational tests for realistic problems demonstrate that our integrated sourcing model and solution method are effective and can provide significant economic benefits. The integrated approach yields average savings of 7.5% in total procurement costs compared to autonomous divisional policies, and our algorithm generates near‐optimal solutions (within 0.75% of optimality) within reasonable computational time.     

A Framework for Facilitating Sourcing and Allocation Decisions for Make‐to‐Order Items

This paper provides a fundamental building block to facilitate sourcing and allocation decisions for make‐to‐order items. We specifically address the buyer's vendor selection problem for make‐to‐order items where the goal is to minimize sourcing and purchasing costs in the presence of fixed costs, shared capacity constraints, and volume‐based discounts for bundles of items. The potential suppliers for make‐to‐order items provide quotes in the form of single sealed bids or participate in a dynamic auction involving open bids. A solution to our problem can be used to determine winning bids amongst the single sealed bids or winners at each stage of a dynamic auction. Due to the computational complexity of this problem, we develop a heuristic procedure based on Lagrangian relaxation technique to solve the problem. The computational results show that the procedure is effective under a variety of scenarios. The average gap across 2,250 problem instances is 4.65%.     

Measuring the Implications of Sales and Consumer Inventory Behavior

Temporary price reductions (sales) are common for many goods and naturally result in large increases in the quantity sold. Demand estimation based on temporary price reductions may mismeasure the long‐run responsiveness to prices. In this paper we quantify the extent of the problem and assess its economic implications. We structurally estimate a dynamic model of consumer choice using two years of scanner data on the purchasing behavior of a panel of households. The results suggest that static demand estimates, which neglect dynamics, (i) overestimate own‐price elasticities by 30 percent, (ii) underestimate cross‐price elasticities by up to a factor of 5, and (iii) overestimate the substitution to the no‐purchase or outside option by over 200 percent. This suggests that policy analysis based on static elasticity estimates will underestimate price–cost margins and underpredict the effects of mergers.     

Assessing Antecedents of Socially Responsible Supplier Selection in Three Global Supply Chain Contexts

A number of highly publicized, controversial lapses in social responsibility within global supply chains have forced managers and scholars to reexamine long‐held perspectives on supplier selection. Extending Carter and Jennings’ department‐level study of purchasing social responsibility, our research assesses the role of supply managers’ ethical intentions and three key antecedents that drive socially responsible supplier selection. Comparing evidence from firms operating in China, the United States, and the United Arab Emirates, we identify three key drivers of supply managers’ ethical intentions and examine both their direct and indirect impacts on socially responsible supplier selection. We find differential support for the predictor relationships on supply manager ethical intentions across national contexts and mediated versus nonmediated models. These observations bear important implications for firms conducting global supply management.     

Generalizing the Announced Price Increase Problem*

This paper generalizes the announced price increase problem to consider a variety of practical concerns arising out of applications ranging from foreign exchange fluctuations to upper limits on the purchase of discounted supermarket items. These include limitations on the amount that can be purchased at the old price and/or on the length of the grace period, within which buyers may take advantage of this lower price. These constraints give rise to 16 possible situations. For each situation purchasing and inventory decision rules are developed. A numerical example is discussed to highlight the main features of the models.     

Lot-sizing decisions under limited-time price incentives: A review

The problem of determining the optimal order quantities for an inventoried item, when the vendor offers a limited-time price reduction is both interesting and important. It is interesting in that it has received continued attention of academic researchers for over four decades and it is important given its economic implication in a variety of practical settings. The extensive literature on this problem represents a fascinating confluence of: (1) economic significance and relevance to managerial practice, (2) continuing academic research interest directed at precise mathematical analysis leading to the development of rigorous and complex models and policies, and (3) elegance and adequacy of simple models and heuristic policies which are validated by the results of rigorous models and computational analysis. In this paper, we survey this literature using simple classification frameworks and then review some of the key studies. We highlight their key assumptions and findings, bring across key implications for policy implementation and academic research and identify avenues for further research.     

“Do as I Do and Not as I Say”: Exploring Price‐Oriented Maverick Buying During Supplier Selection

This article empirically examines the occurrence of price‐oriented maverick buying (MB) during supplier selection, in a direct purchasing process context. Drawing on agency theory, maverick buying, and total cost of ownership (TCO) literature, the statistically significant existence of price‐oriented MB is investigated and the purchasing manager (PM)‐related factors that influence such noncompliant behavior are determined. A discrete choice experiment is designed to simulate a TCO‐based supplier selection process in which an established purchasing framework agreement stipulates PMs not necessarily be price‐oriented (i.e., select suppliers primarily based on lowest price), and then models PM choice behavior in the supplier selection process (SSP), utilizing a conditional logit model (CLM) to determine PM compliance to the established purchasing framework agreement and identify if price‐oriented MB exists. Statistical tests utilizing comprehensive primary and secondary data are then conducted to determine if correlational relationships exist between PM‐related factors and PM price‐orientation. Results indicate that three PM‐related factors bear a significant correlational relationship to PM price‐orientation.     

Static and Dynamic Pricing of Excess Capacity in a Make‐to‐Order Environment

We consider a make‐to‐order manufacturer that serves two customer classes: core customers who pay a fixed negotiated price, and “fill‐in” customers who make submittal decisions based on the current price set by the firm. Using a Markovian queueing model, we determine how much the firm can gain by explicitly accounting for the status of its production facility in making pricing decisions. Specifically, we examine three pricing policies: (1) static, state‐independent pricing, (2) constant pricing up to a cutoff state, and (3) general state‐dependent pricing. We determine properties of each policy, and illustrate numerically the financial gains that the firm can achieve by following each policy as compared with simpler policies. Our main result is that constant pricing up to a cutoff state can dramatically outperform a state‐independent policy, while at the same time achieving most of the increase in revenue achievable from general state‐dependent pricing. Thus, we find that constant pricing up to a cutoff state presents an attractive tradeoff between ease of implementation and revenue gain. When the costs of policy design and implementation are taken into account, this simple heuristic may actually out‐perform general state‐dependent pricing in some settings.     

A Methodology for Constructing Collective Causal Maps*

This article develops a new approach for constructing causal maps called the Collective Causal Mapping Methodology (CCMM). This methodology collects information asynchronously from a group of dispersed and diverse subject‐matter experts via Web technologies. Through three rounds of data collection, analysis, mapping, and interpretation, CCMM constructs a parsimonious collective causal map. The article illustrates the CCMM by constructing a causal map as a teaching tool for the field of operations management. Causal maps are an essential tool for managers who seek to improve complex systems in the areas of quality, strategy, and information systems. These causal maps are known by many names, including Ishikawa (fishbone) diagrams, cause‐and‐effect diagrams, impact wheels, issue trees, strategy maps, and risk‐assessment mapping tools. Causal maps can be used by managers to focus attention on the root causes of a problem, find critical control points, guide risk management and risk mitigation efforts, formulate and communicate strategy, and teach the fundamental causal relationships in a complex system. Only two basic methods for creating causal maps are available to managers today—brainstorming and interviews. However, these methods are limited, particularly when the subject‐matter experts cannot easily meet in the same place at the same time. Managers working with complex systems across large, geographically dispersed organizations can employ the CCMM presented here to efficiently and effectively construct causal maps to facilitate improving their systems.     

Efficient Heuristics for MRP Lot Sizing with Variable Production/Purchasing Costs*

Two heuristics based on branch and bound (B&B) are developed to solve closed-loop material requirements planning (MRP) lot-sizing problems that have general product structures and variable costs. A “look ahead method'’(LAM) heuristic allows for variable production/purchasing costs and uses a single-level B&B procedure to rapidly improve lower bound values; thus, LAM efficiently uses computer-storage capacity and allows solution of larger problems. The “total average modification'’(TAM) heuristic uses B&B, applied level by level, and modified setup and carrying costs to solve the variable production/purchasing costs MRP lot-sizing problem. LAM and TAM are tested on problems and compared to heuristics in the literature. TAM may be used to solve large MRP lot-sizing problems encountered in practice.     

Lot‐sizing Decisions Under Limited‐time Price Reduction*

We consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the “Early Purchase” (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.     

Managing Socially-Responsible Buying:: How to Integrate Non-economic Criteria into the Purchasing Process

Companies are increasingly scrutinized by various audiences and are made accountable not only for their internal practices, but also for their suppliers’ behavior. Many purchasing managers and executives are not accustomed to seeing the purchasing function receive so much attention from different parties. As a result, a number of them do not know how to embrace the trend toward socially responsible buying (SRB). The present paper offers a helping hand by (1) shedding some light on the nature of SRB and (2) explaining how companies can incorporate social responsibility criteria into their purchasing decisions.     

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.     

An Exploratory Study of Procurement Strategies for Multi‐Item RFQs in B2B Markets: Antecedents and Impact on Performance

This research explores procurement strategies for multi‐item requests for quotation (RFQs) in business‐to‐business (B2B) markets using responses from 825 purchasing professionals. The study first establishes procurement strategies that differ based on their level of strategic emphasis, i.e., the importance that is placed on the pursuit of four strategic objectives. Underlying objectives, which are obtained via factor analysis, include the focus on price, security of supply, internal procurement efficiencies, and bundle building. Next, cluster analysis is used to derive prototypical strategic approaches. The three cluster groups that emerge possess the same relative ranking of the four objectives, but differ based on the intensity with which these objectives are pursued. The clusters are labelled as the three strategic groups of strategists, opportunists, and responders. The research then explores, using an industrial buyer behavior lens, the impact of environmental antecedents in determining a particular strategy. Environmental variables include purchase importance, market uncertainty, supply base availability, buyer bargaining power, item experience, and supply base experience. Finally, the study tests the impact of procurement strategy on the buyer's perceived performance, suggesting that strategists, placing more emphasis on the pursuit of strategic sourcing objectives, achieve better performance than opportunists and responders.     

Marketing Is from Mars,IT Is from Venus: Aligning the Worldviews for Firm Performance

A typical firm is operated by multiple functional managers who may collaborate as well as compete to achieve firm performance. In the digital age, firm performance is essentially customer‐dependent and technology‐dependent, with both marketing and information technology (IT) playing key roles. Unfortunately the two functions often have very different worldviews. We show how these differences can damage firm performance, and suggest ways to mitigate this damage. We build a worldview difference model, synthesized from multiple disciplines. The model is tested using both matched and nonmatched observations from marketing and IT managers, and is analyzed with hierarchical linear models using both perceptual and objective firm performance data over a 4‐year period. We find that differences between the beliefs and perceptions of marketing managers and IT managers generate a negative impact on firm performance, and suggest appropriate technology‐culture associations to effectively align their worldviews for firm performance. To improve firm performance, a cross‐functional appreciation for market and technology drivers can be achieved by making marketing managers more learning‐oriented and by providing IT managers a culture that is congruent with technology.     

考虑消费者网购体验滞后的产品定价研究

随着电子商务技术的发展，网络购物越来越便利。与此同时，网络购物带来的产品体验滞后也导致了消费者对产品的认知不确定性。而这种不确定性正在成为消费者策略性退货行为的主要原因，如消费者同时购买多件具有横向差异的产品，在收到货物后经亲身体验后保留一件而将其他产品退货。本文通过构建Hotelling模型，探讨了企业在考虑此种影响情况下的最优定价策略，分析得出：当消费者的退货成本增加时，企业最优定价也随之增加；消费者对产品的先验效用差异化越小，企业的最优定价也越低。同时发现，若某种产品无消费者单独购买，企业的最优定价会随消费者偏好的增加而增加；而当两种产品均有消费者单独购买且消费者退货成本较大时，企业的最优定价不但不会随消费者偏好的增加而提高，反而会随消费者偏好增加而减少。此外，本文给出了消费者策略性退货行为存在的临界条件，当消费者的退货成本高于这一临界条件时消费者的策略退货行为将消失。     

Branch‐and‐Price Methods for Prescribing Profitable Upgrades of High‐Technology Products with Stochastic Demands*

This paper develops a model that can be used as a decision support aid, helping manufacturers make profitable decisions in upgrading the features of a family of high‐technology products over its life cycle. The model integrates various organizations in the enterprise: product design, marketing, manufacturing, production planning, and supply chain management. Customer demand is assumed random and this uncertainty is addressed using scenario analysis. A branch‐and‐price (B&P) solution approach is devised to optimize the stochastic problem effectively. Sets of random instances are generated to evaluate the effectiveness of our solution approach in comparison with that of commercial software on the basis of run time. Computational results indicate that our approach outperforms commercial software on all of our test problems and is capable of solving practical problems in reasonable run time. We present several examples to demonstrate how managers can use our models to answer “what if” questions.     

Efficient Multi‐Attribute Multi‐Unit Auctions for B2B E‐Commerce Logistics

This study is the first proposing allocatively efficient multi‐attribute auctions for the procurement of multiple items. In the B2B e‐commerce logistics problem (ELP), the e‐commerce platform is the shipper generating a large number of online orders between product sellers and buyers, and third‐party logistics (3PL) providers are carriers that can deliver these online orders. This study focuses on the ELP with multiple attributes (ELP‐MA), which is generally the problem of matching the shipper's online orders and 3PL providers given that price and other attributes are jointly evaluated. We develop a one‐sided Vickrey–Clarke–Groves (O‐VCG) auction for the ELP‐MA. The O‐VCG auction leads to incentive compatibility (on the sell side), allocative efficiency, budget balance, and individual rationality. We next introduce the concept of universally unsatisfied set to construct a primal‐dual algorithm, also called the primal‐dual Vickrey (PDV) auction. We prove that the O‐VCG auction can be viewed as a single‐attribute multi‐unit forward Vickrey (SA‐MFV) auction. Both PDV and SA‐MFV auctions realize VCG payments and truthful bidding for general valuations. This result reveals the underlying link not only between single‐attribute and multi‐attribute auctions, but between static and dynamic auctions in a multi‐attribute setting.