Nonlinear pricing with consumer satiation

In various scenarios, consumers may become satiated with products, and the degree of satiation is directly associated with their prior experiences. Confronted with consumer satiation, the seller is unable to either identify consumers who have a higher likelihood of being satiated ex ante or distinguish satiated from non‐satiated consumers ex post. Therefore, the seller should address dynamic selling, valuation uncertainty, and quantity decisions, all of which are important operational issues. We consider a two‐period problem in which consumer types are influenced by their prior consumption experiences. Faced with these consumers, the seller intends to optimize quantities and adjust the prices of the products in each period to maximize revenue. We find that the seller may reduce ex ante production quantity as some consumers become satiated. Moreover, the ex ante quantity is first decreasing and then increasing with regard to the satiation rate. Furthermore, two‐period information asymmetries may provide a rationale for upward distortion in quantity when consumer preferences are highly sensitive to first‐period consumption. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 386–400, 2016     

Switching costs,dynamic uncertainty,and buyer–seller relationships

We analyze strategic relationships between buyers and sellers in markets with switching costs and dynamic uncertainty by investigating the scenario wherein a representative buyer trades with two foreign sellers located in the same foreign country. We show that, under exchange rate uncertainty, switching costs may lead to switching equilibria where both sellers co‐exist in the market with the buyer, or no‐switching equilibria where either seller captures the market. The presence of exchange rate uncertainty facilitates competition by allowing the sellers to co‐exist in the market with the buyer. However, if the level of uncertainty is beyond a threshold, the only viable equilibria are those where one of the sellers captures the market. Further, depending on the level of exchange rate uncertainty and the sellers' variable costs, switching costs may either raise or lower the level of prices in long‐term contracts between the buyer and the sellers. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A nonatomic‐game model for timing clearance sales under competition

We deal with dynamic revenue management (RM) under competition using the nonatomic‐game approach. Here, a continuum of heterogeneous sellers try to sell the same product over a given time horizon. Each seller can lower his price once at the time of his own choosing, and faces Poisson demand arrival with a rate that is the product of a price‐sensitive term and a market‐dependent term. Different types of sellers interact, and their respective prices help shape the overall market in which they operate, thereby influencing the behavior of all sellers. Using the infinite‐seller approximation, which deprives any individual seller of his influence over the entire market, we show the existence of a certain pattern of seller behaviors that collectively produce an environment to which the behavior pattern forms a best response. Such equilibrium behaviors point to the suitability of threshold‐like pricing policies. Our computational study yields insights to RM under competition, such as profound ways in which consumer and competitor types influence seller behaviors and market conditions. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 365–385, 2014     

A sequential dynamic pricing model and its applications

Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous‐time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Return policy: Hassle‐free or your money‐back guarantee?

This article compares the profitability of two pervasively adopted return policies—money‐back guarantee and hassle‐free policies. In our model, a seller sells to consumers with heterogeneous valuations and hassle costs. Products are subject to quality risk, and product misfit can only be observed post‐purchase. While the hassle‐free policy is cost advantageous from the seller's viewpoint, a money‐back guarantee allows the seller to fine‐tune the consumer hassle on returning the product. Thus, when the two return policies lead to the same consumer behaviors, the hassle‐free policy dominates. Conversely, a money‐back guarantee can be more profitable even if on average, high‐valuation consumers experience a lower hassle cost than the low‐valuation ones. The optimal hassle cost can be higher when product quality gets improved; thus, it is not necessarily a perfect proxy or signal of the seller's quality. We further allow the seller to adopt a mixture of these policies, and identify the concrete operating regimes within which these return policies are optimal among more flexible policies. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 403–417, 2014     

Evergreening and operational risk under price competition

“Evergreening” is a strategy wherein an innovative pharmaceutical firm introduces an upgrade of its current product when the patent on this product expires. The upgrade is introduced with a new patent and is designed to counter competition from generic manufacturers that seek to imitate the firm's existing product. However, this process is fraught with uncertainty because the upgrade is subject to stringent guidelines and faces approval risk. Thus, an incumbent firm has to make an upfront production capacity investment without clarity on whether the upgrade will reach the market. This uncertainty may also affect the capacity investment of a competing manufacturer who introduces a generic version of the incumbent's existing product but whose market demand depends on the success or failure of the upgrade. We analyze a game where capacity investment occurs before uncertainty resolution and firms compete on prices thereafter. Capacity considerations that arise due to demand uncertainty introduce new factors into the evergreening decision. Equilibrium analysis reveals that the upgrade's estimated approval probability needs to exceed a threshold for the incumbent to invest in evergreening. This threshold for evergreening increases as the intensity of competition in the generic market increases. If evergreening is optimal, the incumbent's capacity investment is either decreasing or nonmonotonic with respect to low end market competition depending on whether the level of product improvement in the upgrade is low or high. If the entrant faces a capacity constraint, then the probability threshold for evergreening is higher than the case where the entrant is not capacity constrained. Finally, by incorporating the risk‐return trade‐off that the incumbent faces in terms of the level of product improvement versus the upgrade success probability, we can characterize policy for a regulator. We show that the introduction of capacity considerations may maximize market coverage and/or social surplus at incremental levels of product improvement in the upgrade. This is contrary to the prevalent view of regulators who seek to curtail evergreening involving incremental product improvement. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 71–89, 2016     

Sensitivity analysis on responsive pricing and production under imperfect demand updating

This paper examines three types of sensitivity analysis on a firm's responsive pricing and responsive production strategies under imperfect demand updating. Demand has a multiplicative form where the market size updates according to a bivariate normal model. First, we show that both responsive production and responsive pricing resemble the classical pricing newsvendor with posterior demand uncertainty in terms of the optimal performance and first‐stage decision. Second, we show that the performance of responsive production is sensitive to the first‐stage decision, but responsive pricing is insensitive. This suggests that a “posterior rationale” (ie, using the optimal production decision from the classical pricing newsvendor with expected posterior uncertainty) allows a simple and near‐optimal first‐stage production heuristic for responsive pricing. However, responsive production obtains higher expected profits than responsive pricing under certain conditions. This implies that the firm's ability to calculate the first‐stage decision correctly can help determine which responsive strategy to use. Lastly, we find that the firm's performance is not sensitive to the parameter uncertainty coming from the market size, total uncertainty level and information quality, but is sensitive to uncertainty originating from the procurement cost and price‐elasticity.     

Strategic outsourcing under technology spillovers

We study a supply chain in which an original equipment manufacturer (OEM) and a contract manufacturer (CM) compete in the finished goods market. The OEM can decide whether to outsource the intermediate good, a critical component for producing the finished good, from the CM or make in‐house production. Technology transition improves the CM's production efficiency, and it can take two different forms: a direct technology transfer from the OEM to the CM or technology spillovers through outsourcing from the OEM to the CM. We document the possibility of strategic outsourcing, that is, the CM supplies the intermediate good to the OEM when she is less efficient than the OEM's in‐house production. We find that technology spillovers can strengthen the incentive for strategic outsourcing. Furthermore, compared with direct technology transfers, outsourcing coupled with technology spillovers may generate more technology transition. Outsourcing is a particularly appropriate channel for implicit collusion when the OEM is not very efficient with the production of the intermediate good. Our results suggest that ex post competition on the finished goods can create room for ex ante collaboration and provide some implications on the OEM's outsourcing strategies when facing a competitive CM.© 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 501–514, 2014     

Commitment decisions with partial information updating

In this paper, we extend the results of Ferguson M. Naval Research Logistics 8 . on an end‐product manufacturer's choice of when to commit to an order quantity from its parts supplier. During the supplier's lead‐time, information arrives about end‐product demand. This information reduces some of the forecast uncertainty. While the supplier must choose its production quantity of parts based on the original forecast, the manufacturer can wait to place its order from the supplier after observing the information update. We find that a manufacturer is sometimes better off with a contract requiring an early commitment to its order quantity, before the supplier commits resources. On the other hand, the supplier sometimes prefers a delayed commitment. The preferences depend upon the amount of demand uncertainty resolved by the information as well as which member of the supply chain sets the exchange price. We also show conditions where demand information updating is detrimental to both the manufacturer and the supplier. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Impacts of sequential acquisition,market competition mode,and confidentiality on information flow

We investigate information flow in a setting in which 2 retailers order from a supplier and sell to a market with uncertain demand. Each retailer has access to a signal. The retailers can disclose signals to each other (horizontal information sharing), while the supplier can solicit signals by offering retailers differential payments as incentives for signal disclosure (vertical information acquisition). In the base setting, market competition is in quantity, and a retailer can fully infer the signal that the other retailer discloses to the supplier. We show that the supplier prefers to sequentialize the procedure for information acquisition. Moreover, vertical information acquisition by the supplier is a strategic complement to horizontal information sharing between the retailers to establish information flow. In the equilibrium, the retailers have no incentive to exchange signals, but system wide information transparency can be realized through a combination of information acquisition and inference. We further study the signaling effect, whereby the supplier utilizes wholesale pricing as an instrument to affect the retailers' inference of the shared signals, and price competition to explore their impacts on the supplier's preference for sequential acquisition and the sustainability of information flow.     

Impact of transfer pricing methods for tax purposes on supply chain performance under demand uncertainty

Transfer pricing refers to the pricing of an intermediate product or service within a firm. This product or service is transferred between two divisions of the firm. Thus, transfer pricing is closely related to the allocation of profits in a supply chain. Motivated by the significant impact of transfer pricing methods for tax purposes on operational decisions and the corresponding profits of a supply chain, in this article, we study a decentralized supply chain of a multinational firm consisting of two divisions: a manufacturing division and a retail division. These two divisions are located in different countries under demand uncertainty. The retail division orders an intermediate product from the upstream manufacturing division and sets the retail price under random customer demand. The manufacturing division accepts or rejects the retail division's order. We specifically consider two commonly used transfer pricing methods for tax purposes: the cost‐plus method and the resale‐price method. We compare the supply chain profits under these two methods. Based on the newsvendor framework, our analysis shows that the cost‐plus method tends to allocate a higher percentage of profit to the retail division, whereas the resale‐price method tends to achieve a higher firm‐wide profit. However, as the variability of demand increases, our numerical study suggests that the firm‐wide and divisional profits tend to be higher under the cost‐plus method than they are under the resale‐price method. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

The value of losing control: Competition in markets for complements

When selling complementary products, manufacturers can often benefit from considering the resulting cross‐market interdependencies. Although using independent retailers makes it difficult to internalize these positive externalities, the ensuing double marginalization can mitigate within‐market competition. We use standard game theoretic analysis to determine optimal distribution channel strategies (through independent retailers or integrated) for competing manufacturers who participate in markets for complements. Our results suggest that a firm's optimal channel choice is highly dependent on its competitive positioning. A firm with a competitive advantage in terms of product characteristics (customer preferences) or production capabilities (cost) might benefit from selling through company‐controlled stores, allowing coordinated pricing across the two markets, whereas a less competitive firm might be better off using independent channel intermediaries to mitigate price competition. We consider two scenarios depending on whether the two firms make their distribution channel decisions sequentially or simultaneously. Although firms are unlikely to make such decisions at exactly the same instant, the simultaneous model also serves as a proxy for the scenario where firms decide sequentially, but where they cannot observe each other's strategic channel choices. For the sequential case, we find that the sequence of entry can have tremendous impact on the two firms'profits; whereas in some cases, the first mover can achieve substantially higher profits, we find that when the two markets are of sufficiently different size and only loosely related, a firm with a competitive advantage might be better off as a follower. Interestingly, our results suggest that, when the markets are of rather similar size, both firms are better off if they enter the industry sequentially. In those cases, the first entrant has incentive to reveal its planned channel strategies, and the follower has incentive to seek out and consider this information. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal pricing and scheduling control of product shipping

In this article, we seek to understand how a capacity‐constrained seller optimally prices and schedules product shipping to customers who are heterogeneous on willingness to pay (WTP) and willingness to wait (WTW). The capacity‐constrained seller does not observe each customer's WTP and WTW and knows only the aggregate distributions of WTP and WTW. The seller's problem is modeled as an M/M/N_s queueing model with multiclass customers and multidimensional information screening. We contribute to the literature by providing an optimal and efficient algorithm. Furthermore, we numerically find that customers with a larger waiting cost enjoys a higher scheduling priority, but customers with higher valuation do not necessarily get a higher scheduling priority. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 215–227, 2015     

Quality risk in outsourcing: Noncontractible product quality and private quality cost information

This article addresses the concept of quality risk in outsourcing. Recent trends in outsourcing extend a contract manufacturer's (CM's) responsibility to several functional areas, such as research and development and design in addition to manufacturing. This trend enables an original equipment manufacturer (OEM) to focus on sales and pricing of its product. However, increasing CM responsibilities also suggest that the OEM's product quality is mainly determined by its CM. We identify two factors that cause quality risk in this outsourcing relationship. First, the CM and the OEM may not be able to contract on quality; second, the OEM may not know the cost of quality to the CM. We characterize the effects of these two quality risk factors on the firms' profits and on the resulting product quality. We determine how the OEM's pricing strategy affects quality risk. We show, for example, that the effect of noncontractible quality is higher than the effect of private quality cost information when the OEM sets the sales price after observing the product's quality. We also show that committing to a sales price mitigates the adverse effect of quality risk. To obtain these results, we develop and analyze a three‐stage decision model. This model is also used to understand the impact of recent information technologies on profits and product quality. For example, we provide a decision tree that an OEM can use in deciding whether to invest in an enterprise‐wide quality management system that enables accounting of quality‐related activities across the supply chain. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

A model for geographically distributed combat interactions of swarming naval and air forces

This article describes the Distributed Interaction Campaign Model (DICM), an exploratory campaign analysis tool and asset allocation decision‐aid for managing geographically distributed and swarming naval and air forces. The model is capable of fast operation, while accounting for uncertainty in an opponent's plan. It is intended for use by commanders and analysts who have limited time for model runs, or a finite budget. The model is purpose‐built for the Pentagon's Office of Net Assessment, and supports analysis of the following questions: What happens when swarms of geographically distributed naval and air forces engage each other and what are the key elements of the opponents’ force to attack? Are there changes to force structure that make a force more effective, and what impacts will disruptions in enemy command and control and wide‐area surveillance have? Which insights are to be gained by fast exploratory mathematical/computational campaign analysis to augment and replace expensive and time‐consuming simulations? An illustrative example of model use is described in a simple test scenario. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 562–576, 2016     

Competing with channel partners: Supply chain conflict when retailers introduce store brands

Private‐label products are of increasing importance in many retail categories. While national‐brand products are designed by the manufacturer and sold by the retailer, the positioning of store‐brand products is under the complete control of the retailer. We consider a scenario where products differ on a performance quality dimension and we analyze how retailer–manufacturer interactions in product positioning are affected by the introduction of a private‐label product. Specifically, we consider a national‐brand manufacturer who determines the quality of its product as well the product's wholesale price charged to the retailer. Given the national‐brand quality and wholesale price, the retailer then decides the quality level of its store brand and sets the retail prices for both products. We find that a manufacturer can derive substantial benefits from considering a retailer's store‐brand introduction when determining the national brand's quality and wholesale price. If the retailer has a significant cost disadvantage in producing high‐quality products, the manufacturer does not need to adjust the quality of the national‐brand product, but he should offer a wholesale price discount to ensure its distribution through the retailer. If the retailer is competitive in providing products of high‐quality, the manufacturer should reduce this wholesale price discount and increase the national‐brand quality to mitigate competition. Interestingly, we find the retailer has incentive to announce a store‐brand introduction to induce the manufacturer's consideration of these plans in determining the national‐brand product quality and wholesale price. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Bayesian strategies for dynamic pricing in e‐commerce

E‐commerce platforms afford retailers unprecedented visibility into customer purchase behavior and provide an environment in which prices can be updated quickly and cheaply in response to changing market conditions. This study investigates dynamic pricing strategies for maximizing revenue in an Internet retail channel by actively learning customers' demand response to price. A general methodology is proposed for dynamically pricing information goods, as well as other nonperishable products for which inventory levels are not an essential consideration in pricing. A Bayesian model of demand uncertainty involving the Dirichlet distribution or a mixture of such distributions as a prior captures a wide range of beliefs about customer demand. We provide both analytic formulas and efficient approximation methods for updating these prior distributions after sales data have been observed. We then investigate several strategies for sequential pricing based on index functions that consider both the potential revenue and the information value of selecting prices. These strategies require a manageable amount of computation, are robust to many types of prior misspecification, and yield high revenues compared to static pricing and passive learning approaches. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Should firms conceal information when dealing with common suppliers?

A firm making quantity decision under uncertainty loses profit if its private information is leaked to competitors. Outsourcing increases this risk as a third party supplier may leak information for its own benefit. The firm may choose to conceal information from the competitors by entering in a confidentiality agreement with the supplier. This, however, diminishes the firm's ability to dampen competition by signaling a higher quantity commitment. We examine this trade‐off in a stylized supply chain in which two firms, endowed with private demand information, order sequentially from a common supplier, and engage in differentiated quantity competition. In our model, the supplier can set different wholesale prices for firms, and the second‐mover firm could be better informed. Contrary to what is expected, information concealment is not always beneficial to the first mover. We characterize conditions under which the first mover firm will not prefer concealing information. We show that this depends on the relative informativeness of the second mover and is moderated by competition intensity. We examine the supplier's incentive in participating in information concealment, and develop a contract that enables it for wider set of parameter values. We extend our analysis to examine firms' incentive to improve information. © 2014 Wiley Periodicals, Inc. 62:1–15, 2015     

Synchronizing pricing and replenishment to serve forward-looking customers

We incorporate strategic customer waiting behavior in the classical economic order quantity (EOQ) setting. The seller determines not only the timing and quantities of the inventory replenishment, but also the selling prices over time. While similar ideas of market segmentation and intertemporal price discrimination can be carried over from the travel industries to other industries, inventory replenishment considerations common to retail outlets and supermarkets introduce additional features to the optimal pricing scheme. Specifically, our study provides concrete managerial recommendations that are against the conventional wisdom on “everyday low price” (EDLP) versus “high-low pricing” (Hi-Lo). We show that in the presence of inventory costs and strategic customers, Hi-Lo instead of EDLP is optimal when customers have homogeneous valuations. This result suggests that because of strategic customer behavior, the seller obtains a new source of flexibility—the ability to induce customers to wait—which always leads to a strictly positive increase of the seller's profit. Moreover, the optimal inventory policy may feature a dry period with zero inventory, but this period does not necessarily result in a loss of sales as customers strategically wait for the upcoming promotion. Furthermore, we derive the solution approach for the optimal policy under heterogeneous customer valuation setting. Under the optimal policy, the replenishments and price promotions are synchronized, and the seller adopts high selling prices when the inventory level is low and plans a discontinuous price discount at the replenishment point when inventory is the highest.     

Information disclosure with endogenous channel structure

This article investigates the firms' optimal quality information disclosure strategies in a supply chain, wherein the supplier may encroach into the retail channel to sell products directly to end consumers. We consider two disclosure formats, namely, retailer disclosure (R-C) and supplier disclosure (S-C), and examine the optimal disclosure format from each firm's perspective. We show that either firm prefers to delegate the disclosure option to its partner when the supplier cannot encroach. However, the threat of supplier encroachment dramatically alters the firm's preference of disclosure. The supplier may prefer the S-C format to the R-C format when the entry cost is low and the disclosure cost is high to achieve a higher quality information transparency. Meanwhile, the retailer may prefer the R-C format to the S-C format when the entry cost is intermediate to deter the possible encroachment of the supplier. In this sense, the firms' preferences of disclosure format can be aligned due to the threat of supplier encroachment. The consumer surplus is always higher under the S-C format while either disclosure format can lead to a higher social welfare. We also consider an alternative scenario under which the supplier encroaches after the product quality information is disclosed. An interesting observation appears that the supplier may encroach when the product quality is low but foregoes encroachment when the product quality gets higher.