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95
Optimal pricing of seasonal products in the presence of forwardlooking consumers.Manufacturing Service Oper
 Management
, 2008
"... We study the optimal pricing of fashionlike seasonal goods, in the presence of forwardlooking (strategic) customers, characterized by heterogeneous valuations that decline over the course of the season. We distinguish between two classes of pricing strategies: Inventorycontingent discounting stra ..."
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Cited by 63 (0 self)
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We study the optimal pricing of fashionlike seasonal goods, in the presence of forwardlooking (strategic) customers, characterized by heterogeneous valuations that decline over the course of the season. We distinguish between two classes of pricing strategies: Inventorycontingent discounting strategies, and announced fixeddiscount strategies. For the first class, we find a subgameperfect Nash equilibrium for the game between the seller and the customers. For the second class, we develop an optimization problem for the seller, taking into account the consumers ’ response to any feasible precommitted price path. When inventory is limited, strategic consumers need to consider not only future prices, but the likelihood of stockouts, which depends on other customers ’ behavior. Under both classes of pricing strategies, we show that it is optimal for the consumers to purchase according to individual thresholds that depend on personal base valuations and arrival times to the store. We conducted a numerical study to explore the way by which strategic consumer behavior impacts pricing policies and expected revenue performance, and to examine the way by which it interferes with the drivers of the benefits of price segmentation. We discuss the way by which equilibrium in the contingent pricing case is affected by various key factors. We also examine the performance of announced fixeddiscount strategies, and argued that precommitment can bring an advantage to the seller, of up to 8.32% increase in expected revenues. Unlike the case of myopic customers, under strategic consumer behavior, inventory has a significant impact on the announced depth of discounts, particularly when the rate of decline in valuations is lowtomodest. Finally, we considered the case in which the seller incorrectly assumes that strategic customers are myopic in their purchasing decisions. This misperception can be quite costly, reaching a loss of 20 % in expected revenues.
Intertemporal Pricing with Strategic Customer Behavior
 Management Science
, 2005
"... This paper develops a model of dynamic pricing with endogenous customer behavior. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically in order to maximize revenue. Customers arrive continually over the duration of the sel ..."
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Cited by 60 (3 self)
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This paper develops a model of dynamic pricing with endogenous customer behavior. In the model, there is a monopolist who sells a finite inventory over a finite time horizon. The seller adjusts prices dynamically in order to maximize revenue. Customers arrive continually over the duration of the selling season. At each point in time, customers may purchase the product at current prices, remain in the market at a cost in order to purchase later, or exit, and they wish to maximize individual utility. The customer population is heterogeneous along two dimensions: they may have different valuations for the product and different degrees of patience (waiting costs). We study this continuoustime game between the seller and the customers, show that it can be reduced into a singlevariable nonlinear program, and characterize the equilibrium that maximizes revenue for the seller. We demonstrate that heterogeneity in both valuation and patience is important because they jointly determine the structure of optimal pricing policies. In particular, when highvalue customers are proportionately less patient, markdown pricing policies are effective because the highvalue customers would still buy early at high prices while the lowvalue customers are willing to wait (i.e. they are not lost). On the other hand, when the highvalue customers are more patient than the lowvalue customers, prices should increase over time in order to discourage inefficient waiting. Our results also shed light on how the composition of the customer population affects optimal revenue, consumer surplus, and social welfare. Finally, we consider the long run problem of selecting the optimal initial stocking quantity.
A Dynamic NearOptimal Algorithm for Online Linear Programming
, 2009
"... A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) where the constraint matrix is revealed column by column along with the objective function. We provide a nearoptimal algorithm for this surprisingly general ..."
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Cited by 35 (7 self)
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A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) where the constraint matrix is revealed column by column along with the objective function. We provide a nearoptimal algorithm for this surprisingly general class of online problems under the assumption of random order of arrival and some mild conditions on the size of the LP righthandside input. Our learningbased algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from revealed columns in the previous period are used to determine the sequential decisions in the current period. Our algorithm has a feature of “learning by doing”, and the prices are updated at a carefully chosen pace that is neither too fast nor too slow. In particular, our algorithm doesn’t assume any distribution information on the input itself, thus is robust to data uncertainty and variations due to its dynamic learning capability. Applications of our algorithm include many online multiresource allocation and multiproduct revenue management problems such as online routing and packing, online combinatorial auctions, adwords matching, inventory control and yield management.
Customer Behavior Modeling in Revenue Management and Auctions: A Review and New Research Opportunities
"... Invited Paper for Production and Operations Management Customer behavior modeling has been gaining increasing attention in the operations management community. In this paper we review current models of customer behavior in the revenue management and auction literatures and suggest several interesti ..."
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Cited by 28 (0 self)
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Invited Paper for Production and Operations Management Customer behavior modeling has been gaining increasing attention in the operations management community. In this paper we review current models of customer behavior in the revenue management and auction literatures and suggest several interesting research directions in this area. 1
Dynamic pricing for nonperishable products with demand learning
"... Abstract A retailer is endowed with a finite inventory of a nonperishable product. Demand for this product is driven by a pricesensitive Poisson process that depends on an unknown parameter, θ; a proxy for the market size. If θ is high then the retailer can take advantage of a large market chargi ..."
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Cited by 21 (0 self)
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Abstract A retailer is endowed with a finite inventory of a nonperishable product. Demand for this product is driven by a pricesensitive Poisson process that depends on an unknown parameter, θ; a proxy for the market size. If θ is high then the retailer can take advantage of a large market charging premium prices, but if θ is small then price markdowns can be applied to encourage sales. The retailer has a prior belief on the value of θ which he updates as time and available information (prices and sales) evolve. We also assume that the retailer faces an opportunity cost when selling this nonperishable product. This opportunity cost is given by the longterm average discounted profits that the retailer can make if he switches and starts selling a different assortment of products. The retailer's objective is to maximize the discounted longterm average profits of his operation using dynamic pricing policies. We consider two cases. In the first case, the retailer is constrained to sell the entire initial stock of the nonperishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the nonperishable product at any time to switch to a different menu of products. In both cases, the retailer's pricing policy tradesoff immediate revenues and future profits based on active demand learning. We formulate the retailer's problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution which we use to propose a simple approximated solution. This solution combines a pricing policy and a stopping rule (if stopping is an option) depending on the inventory position and the retailer's belief about the value of θ. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed solution.
Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach
, 2008
"... We study the revenue maximizing allocation of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson process. There is a deadline after which no more objects can be allocated. We first characterize implem ..."
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Cited by 20 (4 self)
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We study the revenue maximizing allocation of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson process. There is a deadline after which no more objects can be allocated. We first characterize implementable allocation schemes, and compute the expected revenue for any implementable, deterministic and Markovian allocation policy. The revenuemaximizing policy is obtained by a variational argument which sheds more light on its properties than the usual dynamic programming approach. In particular, we show that this policy does not depend on the characteristics of the available objects at each point in time. Finally, we use our main result in order to: a) establish a comparison with the welfare maximizing policy; b) derive the optimal inventory choice; c) explain empirical regularities about pricing in clearance sales.
Online auction and list price revenue management
 Management Science
, 2007
"... We analyze a revenue management problem in which a seller facing a Poisson arriving stream of customers operates an online multiunit auction. Customers have an alternative list price channel where to get the product from. We consider two variants of this problem: In the first one, the list price is ..."
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Cited by 19 (2 self)
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We analyze a revenue management problem in which a seller facing a Poisson arriving stream of customers operates an online multiunit auction. Customers have an alternative list price channel where to get the product from. We consider two variants of this problem: In the first one, the list price is an external channel run by another firm. In the second variant, the seller manages simultaneously both the auction and the list price channels. Each consumer, trying to maximize his own surplus, must decide either to buy at the posted price and get the item at no risk, or to join the auction and wait until its end, where the winners are revealed and the auction price is disclosed. Our approach consists of two parts. First, we study structural properties of the problem, and show that the equilibrium strategy for both versions of this game is of the threshold type, meaning that a consumer will join the auction only if his arrival time is above a function of his own valuation. This consumer’s strategy can be computed using an iterative algorithm in a function space, provably convergent under some conditions. Unfortunately, this procedure is computationally intensive. To overcome this, we formulate an asymptotic version of the problem, in which the demand rate and the initial number of units grow proportionally large. We get a simple closed form for the equilibrium strategy in this regime, which is then used as an approximated solution for the original problem. Numerical computations show that this heuristic is very accurate. The asymptotic solution culminates then in simple and precise recipes for how bidders should behave, and how the seller should structure the auction, and price the product in the dual channel case. Key words: revenue management, online auction, dual channel, strategic behavior, asymptotic analysis
The optimality of two prices: Maximizing revenue in a stochastic network
 Proc. of 45th Annual Allerton Conference on Communication, Control, and Computing (invited paper
, 2007
"... Abstract — This paper considers the problem of pricing and transmission scheduling for an Access Point (AP) in a wireless network, where the AP provides service to a set of mobile users. The goal of the AP is to maximize its own timeaverage profit. We first obtain the optimum timeaverage profit of ..."
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Cited by 15 (11 self)
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Abstract — This paper considers the problem of pricing and transmission scheduling for an Access Point (AP) in a wireless network, where the AP provides service to a set of mobile users. The goal of the AP is to maximize its own timeaverage profit. We first obtain the optimum timeaverage profit of the AP and prove the “Optimality of Two Prices ” theorem. We then develop an online scheme that jointly solves the pricing and transmission scheduling problem in a dynamic environment. The scheme uses an admission price and a business decision as tools to regulate the incoming traffic and to maximize revenue. We show the scheme can achieve any average profit that is arbitrarily close to the optimum, with a tradeoff in average delay. This holds for general Markovian dynamics for channel and user state variation, and does not require apriori knowledge of the Markov model. The model and methodology developed in this paper are general and apply to other stochastic settings where a single party tries to maximize its timeaverage profit.