strategic capacity rationing to induce early purchases dynamic pricing offers the potential to increase revenues at the same time it creates an incentive for customers to strategize over the timing of their purchases a firm should ideally account for this behavior when making its pricing and stocking decisions in particular we investigate whether it is optimal for a firm to create rationing risk by deliberately understocking products then the resulting threat of shortages creates an incentive for customers to purchase early at higher prices but when does such a strategy make sense if it is profitable to create shortages what is the optimal amount of rationing risk to create we develop a stylized model to study this problem in our model customers have heterogeneous valuations for the firm s product and face declining prices over two periods customers are assumed to have identical risk preferences and know the price path and fill rate in each period via its capacity choice the firm is able to control the fill rate and hence the rationing risk faced by customers customers behave strategically and weigh the payoff of immediate purchases against the expected payoff of delaying their purchases we analyze the capacity choice that maximizes the firm s profits first we consider a monopoly market and characterize conditions under which rationing is optimal we examine how the optimal amount of rationing is affected by the magnitude of price changes over time and the degree of risk aversion among customers we then analyze an oligopoly version of the model and show that competition reduces the firms ability to profit from rationing indeed there exists a critical number of firms beyond which a rationing equilibrium cannot be supported

dynamic price competition with fixed capacities in this paper we study price competition for an oligopoly in a dynamic setting where each of the sellers has a fixed number of units available for sale over a fixed number of periods demand is stochastic and depending on how it evolves sellers may change their prices at any time this reflects the fact that firms constantly and almost costlessly change their prices reacting to updates in their estimates of market demand competitor prices or inventory levels in a setting with demand uncertainty we show that there is a unique subgame perfect equilibrium for a duopoly in which all states sellers engage in bertrand competition and the seller with the lower equilibrium reservation value sells a unit at a price equal to the competitor s equilibrium reservation value this structure therefore extends the marginal value concept of bid price control used in many revenue management implementations to a competitive model we give a closed form solution to the equilibrium price paths for a duopoly and extend all the results to an n firm oligopoly we then study extensions to multiple customer types uncertain valuations and differentiated products this paper was accepted by martin lariviere operations management

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

optimal dynamic price selection under attraction choice models abstract we present a single resource finite horizon markov decision process approach for a firm that seeks to maximize expected revenues by dynamically adjusting the menu of offered products and their prices to be selected from a finite set of alternative values predetermined as a matter of policy consumers choose among available products according to an attraction choice model a special but widely applied class of discrete choice models the fractional substructure inherent to attraction choice models enables the derivation of structural properties that significantly simplify the computation of an optimal policy we show that the more capacity or less time is remaining the lower are the optimal prices we develop an exact solution procedure for preprocessing and recursively solving price selection problems that clearly outperforms current revenue management approaches with respect to computational complexity furthermore we demonstrate that the potential revenue improvements from dynamic compared to fixed pricing can be significant ranging from 4 5 up to 149 for selected examples from the literature extensions to multiple resources and to related discrete choice models are discussed

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

will dynamic pricing outperform theoretical analysis and empirical evidence from o2o on demand food service market abstract this study attempts to identify the pricing strategy of three most commonly used on demand food service platforms in china based on detailed information of more than 240 000 orders and further evaluates the impact of pricing strategy on platform performance we find that some platforms adopt dynamic pricing strategies while other platforms adopt static pricing strategies considering the unique structure of the o2o on demand food service market in china we develop a dyadic two sided market theory and demonstrate that compared with static pricing strategies dynamic pricing strategies perform better consistent with our theory our empirical analysis also suggests that platforms adopting dynamic pricing strategies have a significantly higher level of demand compared with platforms adopting static strategies in addition our results indicate the importance of delivery speed red envelopes and ratings in promoting demand

the hidden information content of price movements dynamic patterns of prices in different markets may motivate strategic consumers who could be monitoring price movements over time to game vendors do past price movements carry information about the probability and magnitude of future price drops conducting empirical work in the airline industry on near 1000 us domestic routes we find that some price metrics carry information about future price swings these variables can assist in predicting the likelihood and magnitude of price drops these price metrics yield significantly different signals which also vary as the prediction horizon changes

optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices abstract consider a continuous time inventory problem in which a retailer sets the price on a fixed number of a perishable asset that must be sold prior to the time at which it perishes the retailer can dynamically adjust the price between any of a finite number of allowable prices demand for the product is poisson with an intensity that is inversely related to the price the optimal policy is piecewise constant the maximum expected revenue is nondecreasing and concave in both the remaining inventory and the time to go for a given inventory level the optimal price declines as the time at which the products perish approaches at any given time the optimal price is nonincreasing in the number of items remaining unsold these results are extended to i the case in which the prices and corresponding demand intensities depend on the time to go and ii the case in which the retailer can restock to meet demand at a unit cost after the initial inventory has been sold

retail pricing and clearance sales sellers of new products are faced with having to guess demand conditions to set price appropriately but sellers are able to adjustprice over time and to learn from past mistakes additionally it is not necessary that all goods be sold with certainty it is sometimes better to set a high price and to risk no sale this process is modeledto explain retail pricing behavior and the time distribution of transactions prices start high and fall as a function of time on theshelf the initial price and rate of decline can be predicted and depends on thinness of the market the proportion of customers who are window shoppers and other observable characteristics copyright 1986 by american economic association

the influence of production technology on risk and the cost of capital this paper uses a time state preference valuation model to examine how the firm s choice of technology and production method affects its equilibrium level of risk and as a result the firm s cost of capital a fixed and flexible method of production is analyzed for a firm using a cobb douglas production function in both cases it is found that risk and the cost of capital decrease with the level of capital intensity implications are drawn for the specification of empirical tests of the determinants of risk

analysis of deterministic lp based booking limit and bid price controls for revenue management we study the performance of two popular and widely used heuristics for revenue management known as the booking limit and bid price controls in contrast to a recent result in the literature where frequent re solvings of a certain heuristic are shown to significantly reduce revenue loss we show that the asymptotic revenue loss of either booking limit or bid price control cannot be reduced regardless of the choice of re solving times and the frequency of re solving moreover we also show that further variations within the policy classes such as nested instead of partition booking limit or certainty equivalent instead of additive bid price are simply indistinguishable in terms of their order of revenue loss under frequent re solvings this negative result highlights the limitation of re solving deterministic linear programs when the solution is interpreted as either a booking limit or a bid price finally we briefly discuss how to modify the traditional booking limit control to make it more responsive

strategic and operational decisions in restaurant revenue management abstract the paper addresses restaurant revenue management from both a strategic and an operational point of view strategic decisions in restaurants are mainly related to defining the most profitable combination of tables that will constitute the restaurant we propose new formulations of the so called tables mix problem by taking into account several features of the real setting we compare the proposed models in a computational study showing that restaurants with the capacity of managing tables as renewable resources and of combining different sized tables can improve expected revenue performances operational decisions are mainly concerned with the more profitable assignment of tables to customers indeed the parties mix problem consists of deciding on accepting or denying a booking request from different groups of customers with the aim of maximizing the total expected revenue a dynamic formulation of the parties mix problem is presented together with a linear programming approximation whose solutions can be used to define capacity control policies based on booking limits and bid prices computational results compare the proposed policies and show that they lead to higher revenues than the traditional strategies used to support decision makers

adaptive ordering and pricing for perishable products we consider the combined problem of pricing and ordering for a perishable product with unknown demand distribution and censored demand observations resulting from lost sales faced by a monopolistic retailer we develop an adaptive pricing and ordering policy with the asymptotic property that the average realized profit per period converges with probability one to the optimal value under complete information on the distribution the pricing mechanism is modeled as a multiarmed bandit problem while the order quantity decision made after the price level is established is based on a stochastic approximation procedure with multiplicative updates

on optimal production and the market to book ratio given limited shareholder diversification our purpose is to examine a firm s optimal output decision and valuation when its shareholders hold a limited number of risky assets the primary theoretical result indicates that the market to book ratio is a function of the degree of shareholder diversification our theory suggests a negative relationship between a firm s market to book ratio and shareholder diversification

a new bid price approach to dynamic resource allocation in network revenue management abstract firms selling perishable products use a variety of techniques to maximize revenue through the dynamic control of their inventories one of the most powerful and simple approaches to address this issue consists of assigning threshold values bid prices to each resource and to accept requests whenever their revenue exceeds the sum of the bid prices associated with its constituent resources in this context we propose a new customer choice based mathematical program to estimate time dependent bid prices in contrast with most approaches from the current literature ours is characterized by its flexibility indeed it can easily embed technical and practical constraints that occur in most central reservation systems crs to solve the model we develop a column generation algorithm in which the np hard subproblem is addressed via an efficient heuristic procedure our computational results illustrate the performance of the method through comparisons with alternative proposals

revenue management for operations with urgent orders this article is motivated by the case of a company manufacturing industrial equipment that faces two types of demand on the one hand there are the so called regular orders for installations or refurbishing of existing facilities these orders have a relatively long lead time on the other hand there are urgent orders mostly related to spare parts when a facility has a breakdown the delay in such case is much shorter but higher margins can be obtained we study the order acceptance problem for a firm that serves two classes of demand over an infinite horizon the firm has to decide whether to accept a regular order or equivalently how much capacity to set aside for urgent orders in order to maximize its profit we formulate this problem as a multi dimensional markovian decision process mdp we propose a family of approximate formulations to reduce the dimension of the state space via aggregation we show how our approach can be used to compute bounds on the profit associated with the optimal order acceptance policy finally we show that the value of revenue management is commensurate with the operational flexibility of the firm

market structure uncertainty and the cost of equity capital the cost of capital plays a key role in the allocation of funds between different sectors of the economy the linkage between the cost of capital and market power has been hinted at by several authors however no rigorous development has been made this paper uses the simple static analysis of the capital asset pricing model to show that with more market power a firm s cost of equity capital declines hence firms with more market power will be able to raise equity capital at lower market rates than would the competitive firm if the product market had been perfectly competitive

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

integration of pricing and capacity allocation for perishable products abstract for years pricing and capacity allocation decisions in most revenue management models have been carried out independently this article presents a comprehensive model to integrate these two decisions for perishable products we assume that the supplier sells the same products to different micro markets at distinct prices throughout the sales season the supplier faces decisions as to which micro markets or customer classes should be served and at what prices we show that i at any time a customer class is active being served if and only if the price offered is over a threshold level but the optimal price may not be the highest one of the supplier s choice ii when the price decision is made in conjunction with inventory it is similar to the procedure shown in pure pricing models i e the optimal price comes from a subset of prices that forms a maximum increasing concave envelope iii because of dynamic changes in the optimal prices the nested price structure does not necessarily hold in general and needs to be redefined and iv the optimal pricing and capacity control policy is based on a sequence of threshold points that incorporate inventory price and demand intensity numerical examples are provided

optimal minimum bids and inventory scrapping in sequential single unit vickrey auctions with demand learning abstract retailers often conduct sequential single unit auctions and need to decide the minimum bid in each auction to reduce inventory costs it may be optimal to scrap some of the inventory rather than holding it until it is auctioned off in some auctions the seller may be uncertain about the market response and hence may want to dynamically learn the demand by observing the number of posted bids we formulate a markov decision process mdp to study this dynamic auction design problem under the vickrey mechanism we first develop a clairvoyant model where the seller knows the demand distribution we prove that it is optimal to scrap all inventory above a certain threshold and then auction the remaining units we derive a first order necessary condition whereby the bidders virtual value at an optimal minimum bid equals the seller s marginal profit this is a generalization of riley and samuelson s result from the one single unit auction case when the virtual value is strictly increasing this necessary condition is also sufficient and leads to a structured value iteration algorithm we then assume that the number of bidders is poisson distributed but the seller does not know its mean the seller uses a mixture of gamma prior on this mean and updates this belief over several auctions this results in a high dimensional bayesian mdp whose exact solution is intractable we therefore propose and compare two approximation methods called certainty equivalent control cec and q function approximation numerical experiments suggest that q function approximation can attain higher revenues than cec

a minmax regret price control model for managing perishable products with uncertain parameters abstract conventional revenue management assumes that demand parameters used in the models are known the control policy derived based on such a premise however guarantees no optimality as the real parameters can significantly deviate from their estimates this article proposes a robust price control model for managing perishable products it attempts to find a policy that minimizes the worst case regret due to imperfect information distribution of each uncertain parameter is assumed arbitrary with only the lower and upper bound available we formulate the dynamic price control problem as a continuous time model under fairly mild conditions we derive the optimality condition for the control policy and develop a recursive procedure for the optimal solution our analysis shows that the proposed minmax regret price control model is equivalent to conventional rm models when demand parameters are deterministic we examine structural properties of the solution and managerial insights they imply numerical results show that the proposed robust model outperforms the conventional rm model when parameters are unknown in particular it significantly reduces the variation in revenues without sacrificing the average revenue

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

gender awareness in modeling structural adjustment abstract the macroeconomic models underpinning the design of structural adjustment programs are gender blind this paper discusses strategies for introducing gender analysis into these models and evaluates the strengths and weaknesses of the models from a gender perspective it concludes that besides being blind to gender the models are also blind to the waste of resources and impoverishment that stems from deficient aggregate demand undemocratic decision making and directly unproductive expenditures that buttress male power this waste is however likely to be diminished by moves to more egalitarian systems of gender relations entailing changes in the structure of entitlements and the social matrix in which macroeconomic processes are embedded

price discrimination through refund contracts in airlines this paper shows how an airline monopoly uses refundable and non refundable tickets to screen consumers who are uncertain about their travel our theoretical model predicts that the difference between these two fares diminishes as individual demand uncertainty is resolved using an original data set from u s airline markets we find strong evidence supporting our model price discrimination opportunities through refund contracts decline as the departure date nears and individuals learn about their demand

optimal inventory policies when purchase price and demand are stochastic in this paper we consider the problem of a firm that faces a stochastic poisson demand and must replenish from a market in which prices fluctuate such as a commodity market we describe the price evolution as a continuous stochastic process and we focus on commonly used processes suggested by the financial literature such as the geometric brownian motion and the ornstein uhlenbeck process it is well known that under variable purchase price a price dependent base stock policy is optimal using the single unit decomposition approach we explicitly characterize the optimal base stock level using a series of threshold prices we show that the base stock level is first increasing and then decreasing in the current purchase price we provide a procedure for calculating the thresholds which yields closed form solutions when price follows a geometric brownian motion and implicit solutions under the ornstein uhlenbeck price model in addition our numerical study shows that the optimal policy performs much better than inventory policies that ignore future price evolution because it tends to place larger orders when prices are expected to increase

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

perishable asset revenue management with markovian time dependent demand intensities 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 items with long procurement lead times given a sunk investment in seats rooms or winter 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 expected revenues in this paper we address the problem of deciding the optimal timing of price changes within a given menu of allowable possibly time dependent price paths each of which is associated with a general poisson process with markovian time dependent predictable intensities we show that a set of variational inequalities characterize the value functions and the optimal possibly random time changes in addition we develop an efficient algorithm to compute the optimal value functions and the optimal pricing policy

a competitive dynamic pricing model when demand is interdependent over time abstract in this study we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels customers can purchase and store the products even if they do not need them at the time in order to use them in future the stockpile of the products generated by customers affects the demand in future periods therefore the demand for each product not only is a function of prices and quality levels but also of the products stockpile levels in addition the stockpile levels change the customers consumption behavior more product in a stockpile leads to more consumption therefore we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment the decision variable of each firm at the beginning of each period is its unit sale price we use a deterministic dynamic program to calculate the equilibrium prices at the beginning of each period by assuming that the market stockpile is public information we show the existence of a unique nash equilibrium we next consider the case when the firms do not know the market stockpile we then develop appropriate heuristics to calculate the optimal prices in each case a numerical study is also provided to calculate the price levels in different scenarios and compare their performances

transformation of optimization problems in revenue management queueing system and supply chain management abstract for revenue optimization problems in the literature on revenue management supply chain management and queueing systems some assumptions such as concavity of revenue functions or increasing generalized failure rate are often needed to ensure the problems to be analytically tractable we show that these assumptions are not necessary for this we present and study a parametric revenue maximization problem to unify some problems in the literature without the usual assumptions we transform the problem into an equivalent one where the revenue function is increasing continuous and concave we then apply the transformation method to a continuous time revenue management problem and conclude that the monotone results are robust to demand function and allowable price set also we apply the transformation method to study a parametric cost minimization problem we further apply our method to two optimal control problems in queueing systems and an inventory control problem in a supply chain with price only contract

the impact of macroeconomic adjustment on poverty in the presence of wage rigidities abstract the paper examines the effects of macro economic policy on poverty when the labour market is subject to partial wage rigidity it shows that the orothodox assumption of a perfect labour market ignores a number of important conflicts arising from macro economic policy specifically it demonstrates that an expenditure switching policy will have greater adverse effects on the formal sector compared with the informal sector and this has implications for poverty under reasonable assumptions about the incidence of poverty in these sectors the paper suggests that more confident predictions about poverty outcomes are possible although in the last analysis theoretical ambiguity is always present whether the rigid wage case gives significantly different predictions from the orthodox model is shown to depend critically on the poverty level among the unemployed if this is similar to that found in the formal sector the difference between the two models is only quantitatively important when the share of formal sector employment is large in this case the rigid wage model indicates less favourable poverty outcomes however if poverty levels are high among the unemployed the rigid wage model predicts more favourable effects

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

quantity premiums and discounts in dynamic pricing we consider a dynamic pricing problem for a monopolistic company selling a perishable product when customer demand is both uncertain and occurs in batches that must be fulfilled as a whole the seller can price discriminate between different sized batches by setting different unit prices the problem is modeled as a stochastic optimal control problem to find an inventory contingent dynamic pricing policy that maximizes the expected total revenues we find the optimal pricing policy and prove several monotonicity results first we establish stochastic order conditions on the unit willingness to pay distributions that determine when quantity discounts or premiums take place for a batch purchase compared to a rapid sequence of purchases with the same total size second we give sufficient conditions for prices to be monotonically decreasing or increasing in inventory third we characterize the conditions for the perceived quantity discounts and premiums that result from comparing unit prices for different batch sizes under a particular inventory level

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

revenue management under a general discrete choice model of consumer behavior customer choice behavior such as buy up and buy down is an important phenomenon in a wide range of revenue management contexts yet most revenue management methodologies ignore this phenomenon or at best approximate it in a heuristic way in this paper we provide an exact and quite general analysis of this problem specifically we analyze a single leg reserve management problem in which the buyers choice behavior is modeled explicitly the choice model is very general simply specifying the probability of purchase for each fare product as a function of the set of fare products offered the control problem is to decide which subset of fare products to offer at each point in time we show that the optimal policy for this problem has a quite simple form namely it consists of identifying an ordered family of efficient subsets s 1 s m and at each point in time opening one of these sets s k where the optimal index k is increasing in the remaining capacity x and decreasing in the remaining time that is the more capacity or less time available the further the optimal set is along this sequence we also show that the optimal policy is a nested allocation policy if and only if the sequence of efficient sets is nested that is s 1 s 2 s m moreover we give a characterization of when nesting by fare order is optimal we also develop an estimation procedure for this setting based on the expectation maximization em method that jointly estimates arrival rates and choice model parameters when no purchase outcomes are unobservable numerical results are given to illustrate both the model and estimation procedure

an analysis of bid price controls for network revenue management bid prices are becoming an increasingly popular method for controlling the sale of inventoryin revenue management applications in this form of control threshold or bid prices are set for the resources or units of inventory seats on flight legs hotel rooms on specific dates etc and a product a seat in a fare class on an itinerary or room for a sequence of dates is sold only if the offered fare exceeds the sum of the threshold prices of all the resources needed to supply the product this approach is appealing on intuitive and practical grounds but the theory underlying it is not well developed moreover the extent to which bid price controls represent optimal or near optimal policies is not well understood using a general model of the demand process we show that bid price control is not optimal in general and analyze why bid price schemes can fail to produce correct accept deny decisions however we prove that when leg capacities and sales volumes are large bid price controls are asymptotically optimal provided the right bid prices are used we also provide analytical upper bounds on the optimal revenue in addition we analyze properties of the asymptotically optimal bid prices for example we show they are constant over time even when demand is nonstationary and that they may not be unique

union firm bargaining and the influence of product market power and production technology on systematic risk the relationship between the capm firm beta and the firm s microeconomic decisions is studied by a model under uncertainty which combines the feature of an ex ante inputs substituable production technology and the existence of a union which bargains over various economic dimensions of the firm it is shown that the earlier findings of a relationship between the firm beta the firm product market power and the labor capital ratio may be reinforced through the indirect channel of labor market bargaining but the relationship becomes more complex and heavily depends on the scope of the union firm bargaining process this yields the empirical prediction confirmed for a panel of belgian firms that any proper estimation of the determinants of firm beta must control for firms in the sample being unionized

mathematical programming for network revenue management revisited mathematical programming models for airline seat inventory control provide booking limits and bid prices for all itineraries and fare classes e l williamson airline network seat inventory control methodologies and revenue impacts ph d thesis massachusetts institute of technology cambridge ma 1992 finds that simple deterministic approximation methods based on average demand often outperform more advanced probabilistic heuristics we argue that this phenomenon is due to a booking process that includes nesting of the fare classes which is ignored in the modeling phase the differences in the performance between these approximations are studied using a stochastic programming model that includes the deterministic model as a special case our study carefully examines the trade off between computation time and the aggregation level of demand uncertainty with examples of a multi leg flight and a single hub network

doing the right thing or doing the thing right allocating resources between marketing research and manufacturing matching production with sales potential is essential for survival in volatile markets manufacturing and marketing managers compete for staff space cash and other assets as they struggle both to determine what and how many products ought to be produced and to actually produce them we develop an analytical framework to answer one simple question how much marketing research should a firm do when it takes resources away from manufacturing the goods that generate revenue to understand the costs and benefits of marketing research we account for the lost opportunities to produce these goods some analytical findings are striking firms without initial knowledge of their potential customers should allocate one third of the firm s resources to marketing research the model suggests a host of issues to be more deeply studied by management scientists

simultaneous capacity and price control based on fuzzy controllers abstract analyzing the basic conditions of modern service and production processes the strengthened competition constraints and unpredictable demand fluctuations are obvious to cause an intense pressure to on the one hand reduce costs through an efficient process control and on the other hand optimize revenue through an adequate capacity and price control demand sided revenue optimization the objective of this article is to identify the revenue potential of a rule based implementation of revenue management as a method for simultaneous capacity and price control first the general conduction of this integrated method is described based on the available literature second the limitations and constraints in the use of the underlying model especially in terms of the applicability in practice and the impreciseness of information are illustrated third a solution concept is established that is able to cope with these limitations one crucial part will be the use of a fuzzy expert controller to handle the rule based approach after the description of the general use of fuzzy expert controllers an application for cases of fixed prices based on an example of the waste incineration industry is illustrated

booming sector and de industrialisation in a small open economy this paper presents a theoretical analysis of the dutch disease the phenomenon whereby a boom in one traded goods sector squeezes porfitability in other traded goods sectors both by directly bi

stolper samuelson rybczynski in the pacific real wages and real exchange rates in the philippines 1956 1978 abstract the paper attempts to explain movements of real wages in the philippines in terms of the standard trade theoretic stolper samuelson rybczynski model in view of the factor intensities in the philippines commodities are aggregated into two composite goods traded and non traded whose relative price the so called real exchange rate is shown to have been an important determinant with changes in relative factor supplies of less importance in determining real wages a conventional two sector model is set out which distinguishes between the short and long run effects in terms of the quasi fixity of sector specific capital a simple regression model is estimated and seems to provide a fairly good explanation of what has hitherto appeared to be a puzzling feature of post war philippines economic performance high growth rates of output and employment accompanied by declining real wages in turn being associated with a rising incidence of poverty in at least two periods

competitive strategies for two firms with asymmetric production cost structures we model joint production marketing strategies for two firms with asymmetric production cost structures in competition the first firm called the production smoother faces a convex production cost and a linear inventory holding cost the second firm called the order taker faces a linear production cost and holds no inventory each firm is assumed to vary continuously over time both its production rate and its price in view of an unstable surge pattern of demand the underlying theoretical motivation is to investigate the temporal nature of the equilibrium policies of two competing firms one operating at or near capacity the production smoother and one operating significantly below capacity the order taker we characterize and compare the equilibrium strategies of the two competing firms among our results we show that if the duopolistic production smoother finds it optimal to hold inventory then he will begin the season by building up inventory continue by drawing down inventory until i

dynamic pricing of multiple home delivery options abstract online grocers accept delivery bookings and have to deliver groceries to consumers residences grocery stores operate on very thin margins therefore a critical question that an online grocery store needs to address is the cost of home delivery operations in this paper we develop a markov decision process based pricing model that recognizes the need to balance utilization of delivery capacity by the grocer and the need to have the goods delivered at the most convenient time for the customer the model dynamically adjusts delivery prices as customers arrive and make choices the optimal prices have the following properties first the optimal prices are such that the online grocer gains the same expected payoff in the remaining booking horizon regardless of the delivery option independently chosen by a consumer second with unit order sizes delivery prices can increase due to dynamic substitution effects as there is less time left in the booking horizon

systematic peak load pricing congestion premia and demand diverting empirical evidence abstract this paper finds empirical support to systematic peak load pricing in airlines higher fares in ex ante known congested periods it estimates a congestion premia and supports the main empirical prediction in gale and holmes gale i holmes t 1993 advance purchase discounts and monopoly allocation of capacity american economic review 83 135 146 less discount seats on peak flights

beta firm size and concentration the asset beta of a firm is defined as the uncertainty about the firm s future value scaled by its current value empirically beta is negatively related to a firm s size and concentration in its major product market this relation has been interpreted as evidence that monopoly power affects beta this paper shows that this empirical result is also consistent with competitive product markets where greater firm size and concentration are due to greater efficiency in production thus the correlation between beta firm size and concentration is not prima facie evidence of widespread monopoly power

a price directed approach to stochastic inventory routing we consider a new approach to stochastic inventory routing that approximates the future costs of current actions using optimal dual prices of a linear program we obtain two such linear programs by formulating the control problem as a markov decision process and then replacing the optimal value function with the sum of single customer inventory value functions the resulting approximation yields statewise lower bounds on optimal infinite horizon discounted costs we present a linear program that takes into account inventory dynamics and economics in allocating transportation costs for stochastic inventory routing on test instances we find that these allocations do not introduce any error in the value function approximations relative to the best approximations that can be achieved without them also unlike other approaches we do not restrict the set of allowable vehicle itineraries in any way instead we develop an efficient algorithm to both generate and eliminate itineraries during solution of the linear programs and control policy in simulation experiments the price directed policy outperforms other policies from the literature

cargo capacity management with allotments and spot market demand we consider a problem faced by an airline that operates a number of parallel flights to transport cargo between a particular origin to destination pair the airline can sell its cargo capacity either through allotment contracts or on the spot market where customers exhibit choice behavior between different flights the goal is to simultaneously select allotment contracts among available bids and find a booking control policy for the spot market to maximize the sum of the profit from the allotments and the total expected profit from the spot market we formulate the booking control problem on the spot market as a dynamic program and construct approximations to its value functions which can be used to estimate the total expected profit from the spot market we show that our value function approximations provide upper bounds on the optimal total expected profit from the spot market and they allow us to solve the allotment selection problem through a sequence of linear mixed integer programs with a special structure furthermore the value function approximations are useful for constructing a booking control policy for the spot market with desirable monotonic properties computational experiments show that the proposed approach can be scaled to realistic problems and provides well performing allotment allocation and booking control decisions

sectoral conflict over stabilisation policies in small open economies a small open economy is characterized by a two sector model with tradables and non tradables stabilization policies typically have unequal effects on these two sectors and expansion of total output often requires contraction in one sector such situations make difficult obtaining effective consensus on the appropriate stabilization policy expansionary fiscal policy requires a contraction in one sector after the labour market adjusts to the disturbance monetary policy is ineffective under fixed exchange rates and may not have sectoral conflict under flexible exchange rates sectoral conflict can be eliminated by designing policy combinations that maintain a given relative price of nontradables this abstract was borrowed from another version of this item

optimal pricing strategies for new products in dynamic oligopolies this paper deals with the determination of optimal pricing policies for firms in oligopolistic markets the problem is studied as a differential game and optimal pricing policies are established as nash open loop controls cost learning effects are assumed such that unit costs are decreasing with cumulative output discounting of future profits is also taken into consideration initially the problem is addressed in a general framework and we proceed to study some specific cases that are related to models presented in recent literature three basic classes of sales dynamics are analyzed competition with price effects only competition with price as well as adoption effects and competition with adoption effects only in some cases it turns out that results which hold for the monopoly case carry over to the multi firm case in the sense that the qualitative structure of optimal pricing strategies is the same in the monopoly and the oligopoly cases however due to competitive interdependencies differences certainly exist in the levels as well as the rates of change of optimal prices

demand fluctuation and chaotic behaviour by interaction between customers and suppliers this paper presents an investigation on simulation of interaction between customers and suppliers in a three tier supply chain system in the simulation customers respond to the price discount offer made by the supplier and the supplier makes adjusts the price according to stock held the simulation shows that the behaviour of such interaction exhibits deterministic chaos it is found that the attractors of the model move with the environment and the initial states thus the bifurcating points in such a system are unable to provide a guideline in system design to avoid chaos

why are products sold on sale explanations of pricing regularities this paper reports on interesting changes in markdown pricing practices over time and differences in the pricing within a product line the price discrimination and the uncertainty hypotheses appear to better explain the data than the peak load hypothesis fashion has become more important over time and appears to explain the greater seasonal variation in retail apparel prices in recent years differences in uncertainty also explains differences in the pricing of different types of men s dress shirts

dynamic advertising and pricing with constant demand elasticities in this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand the state space is discrete time is continuous and the planing horizon is allowed to be finite or infinite a dynamic version of the dorfman steiner identity will be derived explicit expressions of the optimal advertising and pricing policies of the value function and of the optimal advertising expenditures will be given the general results will be used to analyze the case of impatient customers furthermore particular time inhomogeneous models and homogeneous ones with and without discounting will be examined we will study the social efficiency of a monopolist s optimal policies and the consequences of specific subsidies from a buyer s perspective our analysis reveals that waiting when looking at immediate expected prices is never profitable should two or more units be available but we will also prove that the sequence of average sales prices is monotone decreasing moreover the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space

fairness efficiency and flexibility in organ allocation for kidney transplantation we propose a scalable data driven method for designing national policies for the allocation of deceased donor kidneys to patients on a waiting list in a fair and efficient way we focus on policies that have the same form as the one currently used in the united states in particular we consider policies that are based on a point system that ranks patients according to some priority criteria e g waiting time medical urgency etc or a combination thereof rather than making specific assumptions about fairness principles or priority criteria our method offers the designer the flexibility to select his desired criteria and fairness constraints from a broad class of allowable constraints the method then designs a point system that is based on the selected priority criteria and approximately maximizes medical efficiency i e life year gains from transplant while simultaneously enforcing selected fairness constraints among the several case studies we present employing our method one case study designs a point system that has the same form uses the same criteria and satisfies the same fairness constraints as the point system that was recently proposed by u s policy makers in addition the point system we design delivers an 8 increase in extra life year gains we evaluate the performance of all policies under consideration using the same statistical and simulation tools and data as the u s policy makers use other case studies perform a sensitivity analysis for instance demonstrating that the increase in extra life year gains by relaxing certain fairness constraints can be as high as 30 and also pursue the design of policies targeted specifically at remedying criticisms leveled at the recent point system proposed by u s policy makers

a simple framework for analysing various real aspects of stabilisation and structural adjustment policies this article shows how a simple geometric framework containing a real model based on the standard two good three factor trade theoretic model and a monetary model of the domestic banking system can be used to analyse the changes in the real and nominal values of various economic variables of concern resulting from stabilisation and structural adjustment policies

optimal pricing for information goods with piracy and saturation effect we analyze the pricing decision of a firm selling a product for which there is a significant and continuous saturation effect over time and that can be pirated assuming that the firm uses a skimming strategy we solve three profit maximization models given demand that is linearly decreasing in price few prices can be used over the life of the product the effects of both piracy and saturation are combined in the first model in the second model the firm can invest in technology or copyright enforcement to reduce piracy the third model describes the case in which piracy leads to increased awareness of the product and increased demand numerical sensitivity analysis and examples are used to illustrate the results the results indicate that under strong piracy and saturation effects a skimming strategy is suboptimal

nonparametric advertising budget allocation with inventory constraint abstract in this paper we study the optimization problem of the advertising budget allocation for revenue management faced by a marketer besides the advertising budget the marketer is subject to an inventory constraint during the promotion season the marketer can affect sales by spending on advertising but does not initially know the relationship between the advertising expense and consequent sales we propose a nonparametric learning while doing budget allocation policy for the problem specifically we first conduct a sequence of advertising experiments to learn predict the market sales response through observing realized sales exploration then based on the learned sales function determine the following budget allocation planning exploitation in particular during the exploration and exploitation phases we need to balance the advertising and inventory budgets simultaneously we show that our policy is asymptotically optimal as the size of the market increases by constructing a worst case example we show that our policy achieves near best asymptotic performance we also provide numerical illustrations to show how our policy works and discuss how its performance changes as the system parameters vary we also glen some managerial implications of our model and policy from the numerical results

a taxonomy and research overview of perishable asset revenue management yield management overbooking and pricing this paper proposes the term perishable asset revenue management to denote the field that combines the areas of yield management overbooking and pricing for perishable assets after summarizing the characteristics common to problems in this field the paper discusses the objectives and constraints faced by decision makers then it offers a comprehensive taxonomy with 14 different elements and reviews the research that has been done related to each element finally it suggests some important areas of future research that can help bridge the gap between theory and application

repeated auctions with budgets in ad exchanges approximations and design ad exchanges are emerging internet markets where advertisers may purchase display ad placements in real time and based on specific viewer information directly from publishers via a simple auction mechanism advertisers join these markets with a prespecified budget and participate in multiple second price auctions over the length of a campaign this paper studies the competitive landscape that arises in ad exchanges and the implications for publishers decisions the presence of budgets introduces dynamic interactions among advertisers that need to be taken into account when attempting to characterize the bidding landscape or the impact of changes in the auction design to this end we introduce the notion of a fluid mean field equilibrium fmfe that is behaviorally appealing and computationally tractable and in some important cases it yields a closed form characterization we establish that an fmfe approximates well the rational behavior of advertisers in these markets we then show how this framework may be used to provide sharp prescriptions for key auction design decisions that publishers face in these markets in particular we show that ignoring budgets a common practice in this literature can result in significant profit losses for the publisher when setting the reserve price this paper was accepted by dimitris bertsimas optimization

note the role of returns policies in pricing and inventory decisions for catalogue goods manufacturers often use returns policies to encourage retailers to stock and price items more aggressively we focus on the effect that such policies have on both a retailer s and a manufacturer s profits when the retailer must commit prior to the selling season to both a stocking quantity and a price at which to sell an item such a commitment is often necessary for retailers who sell primarily through catalogues

airline seat allocation with multiple nested fare classes this paper addresses the problem of determining optimal booking policies for multiple fare classes that share the same seating pool on one leg of an airline flight when seats are booked in a nested fashion and when lower fare classes book before higher ones we show that a fixed limit booking policy that maximizes expected revenue can be characterized by a simple set of conditions on the subdifferential of the expected revenue function these conditions are appropriate for either the discrete or continuous demand cases these conditions are further simplified to a set of conditions that relate the probability distributions of demand for the various fare classes to their respective fares the latter conditions are guaranteed to have a solution when the joint probability distribution of demand is continuous characterization of the problem as a series of monotone optimal stopping problems proves optimality of the fixed limit policy over all admissible policies a comparison is made of the optimal solutions

pricing and manufacturing decisions when demand is a function of prices in multiple periods in most deterministic manufacturing decision models demand is either known or induced by pricing decisions in the period that the demand is experienced however in more realistic market scenarios consumers make purchase decisions with respect to price not only in the current period but also in past and future periods we model a joint manufacturing pricing decision problem accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods we formulate a mathematical programming model and develop solution techniques we identify structural properties of our models and develop closed form solutions and effective heuristics for various special cases of our models finally we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights

a multiproduct dynamic pricing problem and its applications to network yield management a firm has inventories of a set of components that are used to produce a set of products there is a finite horizon over which the firm can sell its products demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered the problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon an upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem the solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity several applications of the model to network yield management are given numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics the results provide several fundamental insights into the performance of yield management systems

price versus production postponement capacity and competition this article presents a comparative analysis of possible postponement strategies in a two stage decision model where firms make three decisions capacity investment production inventory quantity and price typically investments are made while the demand curve is uncertain the strategies differ in the timing of the operational decisions relative to the realization of uncertainty we show how competition uncertainty and the timing of operational decisions influence the strategic investment decision of the firm and its value in contrast to production postponement price postponement makes the investment and production inventory decisions relatively insensitive to uncertainty this suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility under price postponement additional postponement of production has relatively small incremental value therefore it may be worthwhile to consider flexible ex post pricing before production postponement reengineering while more postponement increases firm value it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty we highlight the different impact of more timely information which leads to higher investment and inventories and of reduced demand uncertainty which decreases investment and inventories our analysis suggests appropriateness conditions for simple make to stock and make to order strategies we also present technical sufficiency and uniqueness conditions under price postponement these results extend to oligopolistic and perfect competition for which pure equilibria are derived interestingly the relative value of operational postponement techniques seems to increase as the industry becomes more competitive

discrete order admission atp model with joint effect of margin and order size in a mto environment abstract swarming demands and seasonality periodically induce a stringent capacity problem in the made to order mto b2b environment desirable order admission is a tactic with minimal application cost for handling this problem a real time order admission problem with limited major customer population and batch size demand with heterogeneous distributions is modeled as a dynamic and stochastic knapsack problem the optimality of the markovian deterministic reward threshold policy is verified optimal policy basic policy and the capacity rationing method are compared in the designed experiment the numerical results suggest great potential for increasing profit using the optimal order admission policy for mto businesses

improved bid prices for choice based network revenue management one of the latest developments in network revenue management rm is the incorporation of customer purchase behavior via discrete choice models many authors presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories however in many implemented rm systems most notably in the hotel industry bid price control is being used and this entails the problem that the recommended combination of products as identified by these policies might not be representable through bid price control if demand were independent from available product alternatives an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network but under dependent demand this is not necessarily the case in fact it seems that these bid prices are typically not restrictive enough and result in buy down effects we propose 1 a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector this first guess could be for example dynamic estimates of the marginal value of capacity moreover 2 we demonstrate that using these dynamic marginal capacity values directly as bid prices can lead to significant revenue loss as compared to using our heuristic to improve them finally 3 we investigate numerically how much revenue performance is lost due to the confinement to product combinations that can be represented by a bid price the heuristic is not restricted to a particular choice model and can be combined with any method that provides us with estimates of the marginal values of capacity in our numerical experiments we test the heuristic on some popular networks examples taken from peer literature we use a multinomial logit choice model which allows customers from different segments to have products in common that they consider to purchase in most problem instances our heuristic policy results in significant revenue gains over some currently available alternatives at low computational cost

optimal inventory policy for a perishable item with demand function sensitive to price and time abstract we formulate a model for determining the optimal pricing order quantity and replenishment period for perishable items with price dependent and time dependent demand the items have a fixed shelf life and the demand rate decreases linearly in the selling price and polynomially over the time after replenishment until it vanishes either at the reservation price or at expiration time we prove that the three variable profit maximization problem can be reduced into a single variable problem in which the variable is the duration of the replenishment period we show that the profit function is strictly pseudo concave and provide means of obtaining the optimal policy three numerical examples are presented to demonstrate the model accompanied by a sensitivity analysis

comments on pricing research in marketing the state of the art rao s paper provides an account of recent research published in the marketing literature on the subject of pricing the paper contains an impressive bibliographic survey however the formal model proposed by the author as a framework for classifying and assessing the advances and needs in this area of marketing science is rather limited a major shortcoming of this model which appears to epitomize the marketing literature on pricing is the treatment of prices and quantities as unidimensional in other words the model implicitly assumes that purchases of the product under consideration can be characterized by a scalar quantity denoting the number of units purchased while the pricing of any such purchase is determined by a uniform unit price this restriction severely limits the pricing strategies and product types that can be addressed within such a framework for example it excludes two part tariffs and important classes of products involving metered usage service contracts etc in spite of these deficiencies i found the paper very educational its primary value is in highlighting the main research directions of pricing in the marketing literature and in conveying the importance of various pricing issues from the perspective of a leading marketing scientist taking rao s survey as a reference point i will attempt in the remainder of this discussion to examine the marketing perspective on pricing versus the approach prevailing in the economics literature dealing with pricing issues in particular i will try to identify some strengths and weaknesses of these approaches and to suggest possibilities for cross fertilization between the two disciplines with a few possible exceptions it is fair to say that the marketing literature on pricing typically focuses on developing pricing strategies for the firm and therefore treats prices as control variables the economics literature on the other hand approaches pricing from the perspective of industrial organization theory its primary objectives are to

yield optimization of display advertising with ad exchange it is clear from the growing role of ad exchanges in the real time sale of advertising slots that web publishers are considering a new alternative to their more traditional reservation based ad contracts to make this choice the publisher must trade off in real time the short term revenue from ad exchange with the long term benefits of delivering good spots to the reservation ads in this paper we formalize this combined optimization problem as a multiobjective stochastic control problem and derive an efficient policy for online ad allocation in settings with general joint distribution over placement quality and exchange prices we prove the asymptotic optimality of this policy in terms of any arbitrary trade off between the quality of delivered reservation ads and revenue from the exchange and we show that our policy approximates any pareto optimal point on the quality versus revenue curve experimental results on data derived from real publisher inventory confirm that there are significant benefits

dynamic pricing with loss averse consumers and peak end anchoring we study the dynamic pricing implications of a new behaviorally motivated reference price mechanism based on the peak end memory mode this model suggests that consumers anchor on a reference price that is a weighted average of the lowest and most recent prices loss averse consumers are more sensitive to perceived losses than gains relative to this reference price we find that a range of constant pricing policies is optimal for the corresponding dynamic pricing problem this range is wider the more consumers anchor on lowest prices and it persists when buyers are loss neutral in contrast with previous literature in a transient regime the optimal pricing policy is monotone and converges to a steady state price which is lower the more extreme and salient the low price anchor is our results suggest that behavioral regularities such as peak end anchoring and loss aversion limit the benefits of varying prices and caution that the adverse effects of deep discounts on the firm s optimal prices and profits might be more enduring than previous models predict

dynamic pricing and ordering decisions by a monopolist this paper considers the relationship between pricing and ordering decisions for a monopolistic retailer facing a known demand function where over the inventory cycle the product may exhibit i physical decay or deterioration of inventory called wastage and ii decrease in market value called value drop associated with each unit of inventory on hand the retailer is allowed to continuously vary the selling price of the product over the cycle we introduce a notion of instantaneous margin and use it to derive profit maximizing conditions for the retailer the model explains the markdown of retail goods subject to decay it also provides guidance in determining when price changes during the cycle are worthwhile due to product aging how often such changes should be made and how such changes affect ordering intervals and quantities