optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

dynamic pricing of perishable assets under competition we study dynamic price competition in an oligopolistic market with a mix of substitutable and complementary perishable assets each firm has a fixed initial stock of items and competes in setting prices to sell them over a finite sales horizon customers sequentially arrive at the market make a purchase choice and then leave immediately with some likelihood of no purchase the purchase likelihood depends on the time of purchase product attributes and current prices the demand structure includes time variant linear and multinomial logit demand models as special cases assuming deterministic customer arrival rates we show that any equilibrium strategy has a simple structure involving a finite set of shadow prices measuring capacity externalities that firms exert on each other equilibrium prices can be solved from a one shot price competition game under the current time demand structure taking into account capacity externalities through the time invariant shadow prices the former reflects the transient demand side at every moment and the latter captures the aggregate supply constraints over the sales horizon this simple structure sheds light on dynamic revenue management problems under competition which helps capture the essence of the problems under demand uncertainty we show that the equilibrium solutions from the deterministic game provide precommitted and contingent heuristic policies that are asymptotic equilibria for its stochastic counterpart when demand and supply are sufficiently large this paper was accepted by yossi aviv operations management

hotel room rate pricing strategy for market share in oligopolistic competition eight year longitudinal study of super deluxe hotels in seoul abstract this paper examines pricing strategies and business performances of super deluxe hotels in seoul to achieve this purpose empirical research is conducted on the basis of data from 1989 when the formation of the present product life cycle stage and the market structure began to 1996 through quick cluster and regression analysis a separation of the price competition between groups of hotels is identified by anova pricing strategies and market shares of selected leading hotels are compared as a longitudinal study the same research design is applied based on four two year periods the final part of the paper evaluates the results of the statistical analysis and discusses important findings and implications of the four two year periods respectively

simulation study of the price differentiation effect in a stochastic deteriorating inventory with heterogeneous consumers freshness sensitivity a fixed price policy regardless of expiration date may result in unsold inventory and sales loss price reduction over time as the expiration date approaches motivates customers to purchase all items including the ones that are left with only a short interval until their expiration we conduct a discrete event simulation that captures the main characteristics of this phenomenon results show that a moderate differentiation of price increases profits by 6 a larger differentiation reduces profits profits are the highest for freshness oriented customers a fixed price policy is preferred in an environment of large variance and expected near term expirations

dynamic pricing of inventory capacity with infrequent price changes we consider a problem of dynamically pricing a single product sold by a monopolist over a short time period if demand characteristics change throughout the period it becomes attractive for the company to adjust price continuously to respond to such changes i e price discriminate intertemporally however in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes if that is the case instead of a continuous pricing rule the company might want to establish a piece wise constant pricing policy in order to limit the number of price adjustments such a pricing policy which involves optimal choice of prices and timing of price changes is the focus of this paper we analyze the pricing problem with a limited number of price changes in a dynamic deterministic environment in which demand depends on the current price and time and there is a capacity inventory constraint that may be set optimally ahead of the selling season the arrival rate can evolve in time arbitrarily allowing us to model situations in which prices decrease increase or neither we consider several plausible scenarios where pricing and or timing of price changes are endogenized various notions of complementarity single crossing property supermodularity and total positivity are explored to derive structural results conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period furthermore we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results additional insights are obtained directly from the solutions of various special cases

joint inventory allocation and pricing decisions for perishable products abstract we jointly determine the price and the inventory allocation for a perishable product with a predetermined lifetime we assume that the price of the product increases as the time when it perishes approaches as in the airline industry demand for the product is price sensitive to maximize the expected revenue we developed a discrete time dynamic programming model to obtain the optimal prices and the optimal inventory allocations for the product with a two period lifetime we then proposed three heuristics when the lifetime is longer than two periods the computational results showed that the expected revenues from the proposed heuristics were very close to that of the optimal solution we extended these results to i the case where the price for the product consistently decreases and ii the case where the price for the product first increases and later decreases

optimal price markup policy for an inventory model with random price fluctuations and option for additional purchase abstract in this paper based on the analysis of empirical data of dealer and retailer prices and sales of cement as a prototype of functional products we develop a probabilistic inventory model for the situation when dealer s selling price fluctuates and affects the retailer s selling price demand is a function of price markup and retailer s purchase price dynamic price markup policy is proposed and optimal length of replenishment cycle and order quantity is obtained concavity of the profit function with respect to price markup is discussed a procurement policy which considers opportunity of purchase at a low price before the end of the optimal replenishment cycle is proposed and compared with other policies algorithm numerical examples sensitivity analysis and managerial insights are presented

demand uncertainty and sales a study of fashion and markdown pricing the theory of clearance sales is expanded and applied to explain why markups markdowns and the frequency of sales of merchandise sold by department stores have increased dramatically in recent years and why they differ across merchandise groups tha major theme of the paper is that the growing role of fashion and product variety is an important reason for these increases and for the differences between merchandise groups the growing importance of fashion is illustrated by documenting the declining use of whites and the increasing use of colors and prints estimates of the effects of imports and technological and demographic changes on markups and markdowns are presented copyright 1988 by american economic association

china s changing energy intensity trend a decomposition analysis china experienced a dramatic decline in energy intensity from the onset of economic reform in the late 1970s until 2000 but since then the rate of decline slowed and energy intensity actually increased in 2003 most previous studies found that most of the decline was due to technological change but disagreed on the role of structural change to the best of our knowledge no decomposition study has investigated the role of inter fuel substitution in the decline in energy intensity or the causes of the rise in energy intensity since 2000 in this paper we use logarithmic mean divisia index lmdi techniques to decompose changes in energy intensity in the period 1980 2003 we find that 1 technological change is confirmed as the dominant contributor to the decline in energy intensity 2 structural change at the industry and sector sub industry level actually increased energy intensity over the period of 1980 2003 although the structural change at the industry level was very different in the 1980s and in the post 1990 period 3 structural change involving shifts of production between sub sectors however decreased overall energy intensity 4 the increase in energy intensity since 2000 is explained by negative technological progress 5 inter fuel substitution is found to contribute little to the changes in energy intensity

optimal selling strategies when to haggle when to hold firm a seller encountering risk neutral buyers one at a time should if commitments are feasible quote a single take it or leave it price to each this strategy is superior to any other for finite or infinite buyer populations whether there is learning or the distribution of buyer prices is known at the outset with one object for sale or many although haggling may offer advantages in terms of price discrimination these gains are more than offset by the losses it generates by encouraging buyers to refuse purchases at high prices

dynamic pricing through discounts for optimizing multiple class demand fulfillment in a multiple customer class model of demand fulfillment for a single item we consider the use of dynamic price discounts to encourage backlogging of demand for customer classes denied immediate service customers are assumed to arrive over several stages in a period and customer classes are distinguished by their contractual price and sensitivity to discounts through dynamic programming we determine the optimal discounts to offer assuming a linear model for the sensitivity of customers to such inducements we show that customers are served in class order and allocation of inventory to demand is determined by considering the current number of customers backlogged as well as the current inventory position through comparison to a naive supplier allocating inventory first come first served with no discounting we show that profits are primarily influenced by the allocation of capacity and the use of price discounts primarily benefits the second class customers overall fill rate heuristics for implementation of the solution in real time settings are given

technical note dynamic pricing and demand learning with limited price experimentation in a dynamic pricing problem where the demand function is not known a priori price experimentation can be used as a demand learning tool existing literature usually assumes no constraint on price changes but in practice sellers often face business constraints that prevent them from conducting extensive experimentation we consider a dynamic pricing model where the demand function is unknown but belongs to a known finite set the seller is allowed to make at most m price changes during t periods the objective is to minimize the worst case regret i e the expected total revenue loss compared with a clairvoyant who knows the demand distribution in advance we demonstrate a pricing policy that incurs a regret of ologmt or m iterations of the logarithm furthermore we describe an implementation of this pricing policy at groupon a large e commerce marketplace for daily deals the field study shows significant impact on revenue and bookings the e companion is available at https doi org 10 1287 opre 2017 1629

dynamic pricing when consumers are strategic analysis of posted and contingent pricing schemes abstract we study dynamic pricing policies for a monopolist selling perishable products over a finite time horizon to strategic buyers buyers are strategic in the sense that they anticipate the firm s price policies it is expensive and administratively difficult for most brick and mortar retailers to change prices placing limits on the number of price changes and the types of pricing policies they can adopt the simplest policy is to commit to a set of price changes a more complex alternative is to let the price depend on sales history we investigate two pricing schemes that we call posted and contingent pricing using the posted pricing scheme the firm announces a set of prices at the beginning of the horizon in the contingent pricing scheme price evolution depends upon demand realization our focus is on the posted pricing scheme because of its ease of implementation counter to intuition we find that neither a posted pricing scheme nor a contingent pricing scheme is dominant and the difference in expected revenues of these two schemes is small limiting the number of price changes will result in a decrease in expected revenues we show that a multi unit auction with a reservation price provides an upper bound for expected revenues for both pricing schemes numerical examples suggest that a posted pricing scheme with two or three price changes is enough to achieve revenues that are close to the upper bound dynamic pricing is only useful when strategic buyers perceive scarcity we study the impact of scarcity and derive the optimal stocking levels for large markets finally we investigate whether or not it is optimal for the seller to conceal inventory or sales information from buyers a firm benefits if it does not reveal the number of units it has available for sale at the beginning of the season or subsequently withholds information about the number of units sold

clearance pricing and inventory policies for retail chains clearance pricing and end of season inventory management are challenging and important problems in retailing sales rates depend upon price seasonal effects and the remaining assortment of items available to customers there is little time to react to observed sales and pricing errors result in either loss of potential revenue or excess inventory to be liquidated this paper develops optimal clearance prices and inventory management policies that take into account the impact of reduced assortment and seasonal changes on sales rates versions of these policies have been tested and implemented at three major retail chains and these applications are summarized and discussed

optimal starting times for end of season sales and optimal stopping times for promotional fares many industries face the problem of selling a fixed stock of items over a finite horizon these industries include airlines selling seats before planes depart hotels renting rooms before midnight theaters selling seats before curtain time and retailers selling seasonal goods such as air conditioners or winter coats before the end of the season given a fixed number of seats rooms or coats the objective for these industries is to maximize revenues in excess of salvage value when demand is price sensitive and stochastic pricing is an effective tool to maximize revenues in this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price under mild conditions we show that it is optimal to decrease resp to increase the initial price as soon as the time to go falls below resp above a time threshold that depends on the number of yet unsold items

dynamic and targeted bundle pricing of two independently valued products abstract bundling is when two or more products are offered as a single unit and at a price lower than the sum of the individual prices of the products we study a multi segment market in which a retailer aims to clear the inventory of an item by bundling it with a second product which is independently valued we investigate the question of how dynamic and segment specific bundle pricing impacts retailer s revenue we develop a revenue model that integrates the dynamic and segment specific aspects of the pricing decisions and present a computational study to analyze their revenue impact relative to a price promotion for the individual item only the computational results indicate that the bundle offers are most effective when the initial inventory of the item under consideration is high the results also demonstrate that dynamic pricing is beneficial when the initial inventory of the item is low an additional revenue improvement is observed when the price of the bundle is dynamically optimized in the computational study segment specific pricing is observed to have no direct impact on revenue when prices are static segment specific and dynamic pricing however can bring about substantial revenue improvements that are an increasing function of the initial inventory level of the item we consider the correlation in consumers valuations of the bundled products and show that dynamically priced and segment specific bundle offers yield a robust revenue performance mitigating the potentially revenue diminishing impact of positive correlation in consumers valuations of the products

periodic pricing of seasonal products in retailing this paper studies intertemporal pricing policies when selling seasonal products in retail stores we first present a continuous time model where a seller faces a stochastic arrival of customers with different valuations of the product for this model we characterize the optimal pricing policies as functions of time and inventory we use this model as a benchmark against which we compare more realistic models that consider periodic pricing reviews we show that the structure of the optimal pricing policies in this case is consistent with the procedures observed in practice retail stores successively discount the product during the season and promote a liquidation sale at the end of the planning horizon we also show that the loss experienced when implementing periodic pricing reviews instead of continuous policies is small when the appropriate number of reviews is chosen several interesting economic insights emerge from our analysis for example uncertainty in the demand for new products leads to higher prices larger discounts and more unsold inventory finally we study the effect of announced discount policies on prices and profits we show that stores that have adopted this type of strategy usually set prices such that with high probability the merchandise is sold during the first periods and the largest discounts rarely take place

tacit collusion in repeated auctions uniform versus discriminatory within an infinitely repeated game i compare the level and conduct of collusion under uniform and discriminatory auctions for this purpose i characterize the optimal collusive schemes and sets of sustainable profits under these auction formats i show that uniform auctions facilitate collusion more than discriminatory auctions the optimal penal code is equally severe under the two formats but bidders deviation incentives are weaker in uniform auctions given that the payoff irrelevant bids can be used to relax the enforcement problem this discussion is particularly relevant after the recent reforms in the electricity industry in england wales and elsewhere

optimal price skimming by a monopolist facing rational consumers this paper considers the intertemporal pricing problem for a monopolist marketing a new product the key feature differentiating this paper from the extant management science literature on intertemporal pricing is the assumption that consumers are intertemporal utility maximizers a subgame perfect nash equilibrium pricing policy is characterized and shown to involve intertemporal price discrimination we compare this policy to the optimal policy for a monopolist facing myopic consumers and find that for any given state prices are always lower with rational consumers than with myopic consumers for plausible parameter values the assumption of consumer rationality can be shown to lead to large differences in optimal prices moreover if a monopolist facing rational consumers implements the optimal myopic consumer pricing policy profits can be significantly less than if the monopolist follows the equilibrium pricing policy for rational consumers

a partially observed markov decision process for dynamic pricing in this paper we develop a stylized partially observed markov decision process pomdp framework to study a dynamic pricing problem faced by sellers of fashion like 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 active learning heuristic pricing policy we conduct a numerical study to test the performance of four different heuristic dynamic pricing policies in order to gain insight into several important managerial questions that arise in the context of revenue management

monopolist pricing with dynamic demand and production cost this paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream the interdependency of cost and demand on cumulative production makes the problem inherently dynamic cost is assumed to be declining with cumulative production learning curve effect while demand is a function of price and cumulative sales representing word of mouth and saturation effects the paper addresses this problem in a general framework that includes several previous results as special cases and provides new insights in other situations while the learning curve and word of mouth effect cause prices to be lower than the price that maximizes immediate revenues the saturation factor has the opposite effect the price path over time is affected by these factors and the interest rate we characterize the price path under several different situations and interpret the results for policy guidelines