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239
Management: Research Overview and Prospects
 Transportation Science
"... This survey reviews the fortyyear history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The surv ..."
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Cited by 150 (5 self)
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This survey reviews the fortyyear history of research on transportation revenue management (also known as yield management). We cover developments in forecasting, overbooking, seat inventory control, and pricing, as they relate to revenue management, and suggest future research directions. The survey includes a glossary of revenue management terminology and a bibliography of over 190 references. In the forty years since the first publication on overbooking control, passenger reservations systems have evolved from low level inventory control processes to major strategic information systems. Today, airlines and other transportation companies view revenue management systems and related information technologies as critical determinants of future success. Indeed, expectations of revenue gains that are possible with expanded revenue management capabilities are now driving the acquisition
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 62 (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 55 (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.
Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case
, 2002
"... We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the produ ..."
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Cited by 55 (11 self)
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We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s, S, p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical (s, S) policy and price is determined based on the inventory position at the beginning of each period. 1
The Dynamic and Stochastic Knapsack Problem with Deadlines
 Operations Research
, 1996
"... In this paper a dynamic and stochastic model of the wellknown knapsack problem is developed and analyzed. The problem is motivated by a wide variety of realworld applications. Objects of random weight and reward arrive according to a stochastic process in time. The weights and rewards associated w ..."
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Cited by 54 (0 self)
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In this paper a dynamic and stochastic model of the wellknown knapsack problem is developed and analyzed. The problem is motivated by a wide variety of realworld applications. Objects of random weight and reward arrive according to a stochastic process in time. The weights and rewards associated with the objects are distributed according to a known probability distribution. Each object can either be accepted to be loaded into the knapsack, of known weight capacity, or be rejected. The objective is to determine the optimal policy for loading the knapsack within a fixed time horizon so as to maximize the expected accumulated reward. The optimal decision rules are derived and are shown to exhibit surprising behavior in some cases. It is also shown that if the distribution of the weights is concave, then the decision rules behave according to intuition. Keywords: dynamic programming, sequential stochastic resource allocation This research was supported by the National Science Foundati...
Airline yield management with overbooking, cancellations and noshows
 Transportation Science
, 1999
"... We formulate and analyze a Markov decision process (dynamic programming) model for airline seat allocation (yield management) on a singleleg flight with multiple fare classes. Unlike previous models, we allow cancellation, noshows, and overbooking. Additionally, we make no assumptions on the arriv ..."
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Cited by 53 (0 self)
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We formulate and analyze a Markov decision process (dynamic programming) model for airline seat allocation (yield management) on a singleleg flight with multiple fare classes. Unlike previous models, we allow cancellation, noshows, and overbooking. Additionally, we make no assumptions on the arrival patterns for the various fare classes. Our model is also applicable to other problems of revenue management with perishable commodities, such as arise in the hotel and cruise industries. We show how to solve the problem exactly using dynamic programming. Under realistic conditions, we demonstrate that an optimal booking policy is characterized by state and timedependent booking limits for each fare class. Our approach exploits the equivalence to a problem in the optimal control of admission to a queueing system, which has been well studied in the queueingcontrol literature. Techniques for efficient implementation of the optimal policy and numerical examples are also given. In contrast to previous models, we show that 1) the booking limits need not be monotonic in the time remaining until departure; 2) it may be optimal to accept a lowerfare class and simultaneously reject a higherfare class because of differing cancellation refunds, so that the optimal booking limits may not always be nested according to fare class; and 3) with the possibility of cancellations, an optimal policy
The Dynamic and Stochastic Knapsack Problem
 Operations Research
, 1998
"... The Dynamic and Stochastic Knapsack Problem #DSKP# is de#ned as follows: Items arrive according toaPoisson process in time. Each item has a demand #size# for a limited resource #the knapsack# and an associated reward. The resource requirements and rewards are jointly distributed according to a kn ..."
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Cited by 49 (1 self)
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The Dynamic and Stochastic Knapsack Problem #DSKP# is de#ned as follows: Items arrive according toaPoisson process in time. Each item has a demand #size# for a limited resource #the knapsack# and an associated reward. The resource requirements and rewards are jointly distributed according to a known probability distribution and become known at the time of the item's arrival. Items can be either accepted or rejected. If an item is accepted, the item's reward is received, and if an item is rejected, a penalty is paid. The problem can be stopped at any time, at which time a terminal value is received, whichmay depend on the amount of resource remaining. Given the waiting cost and the time horizon of the problem, the objective is to determine the optimal policy that maximizes the expected value #rewards minus costs# accumulated. Assuming that all items have equal sizes but random rewards, optimal solutions are derived for a variety of cost structures and time horizons, and recursive algorithms for computing them are developed. Optimal closedform solutions are obtained for special cases. The DSKP has applications in freight transportation, in scheduling of batch processors, in selling of assets, and in selection of investment projects.
Dynamic Pricing Strategies for Multiproduct Revenue Management Problems
, 2006
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Optimal dynamic auctions for revenue management
 Management Science
, 2002
"... We analyze a dynamic auction, in which a seller with C units to sell faces a sequence of buyers separated into T time periods. Eachgroup of buyers has independent, private values for a single unit. Buyers compete directly against each other within a period, as in a traditional auction, and indirectl ..."
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Cited by 39 (4 self)
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We analyze a dynamic auction, in which a seller with C units to sell faces a sequence of buyers separated into T time periods. Eachgroup of buyers has independent, private values for a single unit. Buyers compete directly against each other within a period, as in a traditional auction, and indirectly with buyers in other periods through the opportunity cost of capacity assessed by the seller. The number of buyers in each period, as well as the individual buyers ’ valuations, are random. The model is a variation of the traditional singleleg, multiperiod revenue management problem, in which consumers act strategically and bid for units of a fixed capacity over time. For this setting, we prove that dynamic variants of the firstprice and secondprice auction mechanisms maximize the seller’s expected revenue. We also show explicitly how to compute and implement these optimal auctions. The optimal auctions are then compared to a traditional revenue management mechanism—in which list prices are used in each period together with capacity controls—and to a simple auction heuristic that consists of allocating units to eachperiod and running a sequence of standard, multiunit auctions withfixed reserve prices in each period. The traditional revenue management mechanism is proven to be optimal in the limiting cases when there is at most one buyer per period, when capacity is not constraining, and asymptotically when the number of buyers and the capacity increases. The optimal auction significantly outperforms both suboptimal mechanisms when there are a moderate number of periods, capacity is constrained, and the total volume of sales is not too large. The benefit also increases when variability in the dispersion in buyers ’ valuations or in the number of buyers per period increases.
A partially observed markov decision process for dynamic pricing
 Management Science
, 2002
"... In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework, to study a dynamic pricing problem faced by sellers of fashionlike goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer i ..."
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Cited by 38 (1 self)
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In this paper, we develop a stylized partially observed Markov decision process (POMDP) framework, to study a dynamic pricing problem faced by sellers of fashionlike goods. We consider a retailer that plans to sell a given stock of items during a finite sales season. The objective of the retailer is to dynamically price the product in a way that maximizes expected revenues. Our model brings together various types of uncertainties about the demand, some of which are resolvable through sales observations. We develop a rigorous upper bound for the seller’s optimal dynamic decision problem and use it to propose an activelearning heuristic pricing policy. We conduct a numerical study to test the performance of four different heuristic dynamic pricing policies, in order to gain insights into several important managerial questions that arise in the context of revenue management.