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

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 pricing for perishable assets with nonhomogeneous demand we consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon customers whose reservation price distribution changes over time arrive according to a nonhomogeneous poisson process we show that at any given time the optimal price decreases with inventory we also identify a sufficient condition under which the optimal price decreases over time for a given inventory level this sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time in addition to shedding managerial insight these structural properties enable efficient computation of the optimal policy numerical studies are conducted to show the revenue impact of dynamic price policies price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price for the former our examples show that using optimal dynamic optimal policies achieves 2 4 7 3 revenue improvement over the optimal single price policy for the latter the revenue increase can be as high as 100 these results explain why yield management has become so essential to fashion retailing and travel service industries

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

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

a survey on risk averse and robust revenue management abstract many industries use revenue management to balance uncertain stochastic demand and inflexible capacity popular examples include airlines hotels car rentals retailing and manufacturing the classical revenue management approaches considered in theory and practice are based on two assumptions first demand as the only uncertain variable follows a known distribution and second risk neutrality justifies the maximization of expected revenue recently two related streams of literature emerged that do not need these assumptions research on risk averse revenue management acknowledges that in practice many decision makers are risk averse research on robust revenue management focuses worst case scenarios without a known demand distribution which is especially relevant for new and extremely unstable businesses this paper motivates the consideration of risk averse and robust revenue management we briefly introduce revenue managements two main methods capacity control and dynamic pricing in the classical risk neutral setting then we provide an exhaustive review of the literature on risk averse and robust capacity control and dynamic pricing in doing so the relevant decision criteria are briefly introduced finally possible avenues for future research are outlined

new evidence on targets for monetary policy monetary policy involves the federal reserve s use of select policy instruments to influence general economic conditions of the major policy instruments required reserve ratios the discount rate and open market operations open market operations are commonly manipulated to affect economic conditions open market purchases and sales are employed to achieve the operational targets i e levels of free reserves and or the monetary base the operational targets influence market interest rates the monetary aggregates and or credit aggregates the so called indicators or intermediate targets of monetary policy the intermediate targets then impact upon the general economic policy goals e g real growth gnp the aggregate price level fellner 8 and davidson hafer 6 argue that a variable is appropriate as an intermediate target if it is closely related to the objectives considered of substantial importance is causally prior to such objectives or goals and follows changes in the policy instruments in a predictable manner i e it is controllable the appropriate choice of a variable as the intermediate target is the source of great debate 20 19 1 16 this debate involves the ability of the federal reserve to control the target variable as well as the relation of the target with the goal variables time series techniques are now utilized to examine both aspects of this debate timeseries examinations of the control problem appear in bomhoff 4 johannes rasche 15 and davidson hafer 6 time series examinations of the target goal relationship are presented in davidson hafer 6 friedman 10 and mcmillin fackler 18 with the exception of the vector autoregressive var procedures reported in friedman 10 and mcmillin fackler 18 all researchers employ single equation procedures bivariate techniques fail to permit possible feedback from a wide array of sources many of which are believed to be important this research employs a multiple autoregressive moving average marma technique to examine the appropriateness of several intermediate target candidates the marma procedure is more general than and hence generally preferred to var or univariate procedures see section iii equally important however is our simultaneous examination of

some evidence on selecting an intermediate target for monetary policy the purpose of monetary policy is to influence the evolution of the economy this influence may be expressed in the oft heard phrases of reducing inflation promoting real economic growth and lowering unemployment these are the goals of policy action how are these goals to be achieved the federal reserve is limited in its power in that there are only a few policy vehicles over which it exercises dominance although the main policy instrument of the fed has differed over time during the past few decades fed policy has been exerted primarily through its control of the banking system s reserves via open market operations the difficulty faced by the policymaker is to know just what effect the changes in the instruments are having on the economy since data on the goal variables generally are received with a lag it is useful to find an intermediate variable that is more timely in its availability and that acts as a good proxy for the goal variable in other words changes in the intermediate variable should reliably predict changes in the goal measure if however a measure is unduly influenced by the goal variable then its usefulness in policy decisions is diminished greatly this is because movements in the intermediate measure might emanate from policy actions from changes in the goal measure or both for a measure to be useful as an intermediate target therefore it should have the feature of being exogenous or causally prior to the goal variable in addition to having minimal feedback from the goal measure the intermediate target measure also should respond predictably to changes in the direction of policy for example an intermediate target that responds randomly to changes in the policy instrument

price trends and dynamic pricing in perishable product market consisting of superior and inferior firms abstract we consider the problem of a firm that sells perishable products with a dynamic pricing scheme in the presence of a firm offering a superior product we provide a probabilistic characterization of the optimal price process under the existence of such a firm for an aggregate demand model and for a multinomial logit demand model our results demonstrate that if the seller takes the price of the other firm into account in their optimal policy then the optimal price process tends to increase over time before the inventory level falls to one after which it decreases otherwise the price process decreases and then increases this path is called a j shaped curve before the inventory level falls to one if the price of the other firm is relatively low and the customer s valuation remains unchanged over time early in the sales period we also demonstrate numerically that when the firm uses a monopolistic policy and the difference in service quality between the two firms is large the switching time between the downward and upward trends takes place in the early stage of the sales period and in particular this j shaped phenomenon is strongly observed

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

lag length selection and tests of granger causality between money and income one of the most widely accepred relationships in macroeconomics is the positive relationship between the rate of growth of the money supply and the rate of growth of income a diversity of opinion arises however with the attempt to identify a causal relationship between these variables while friedman and schwartz 1963 initiated the empirical investigation of money income causality sims 1972 made the most significant contribution to this literature with a practical application of the criterion developed by granger 1969 for identifying a causal relationship since the appearance of sims s approach and an alternative one advanced by sargent 1976 many researchers have applied these techniques to the investigation of the causal relationship between money and income l with two exceptions hsiao 1981 and mcmillin and fackler 1984 these researchers have arbitrarily chosen the lengths of their distributed lags the purpose of this paper is to test for granger causality between money and income this paper differs from previous work in that considerably more attention is focused on the effect of the lag specification on the test results in particular we investigate the extent to which rules of thumb arbitrary lag specifications and

the competitive newsboy we consider a competitive version of the classical newsboy problem in which a firm must choose an inventory or production level for a perishable good with random demand and the optimal solution is a fractile of the demand distribution and investigate the impact of competition upon industry inventory a splitting rule specifies how initial industry demand is allocated among competing firms and how any excess demand is allocated among firms with remaining inventory we examine the relation between equilibrium inventory levels and the splitting rule and provide conditions under which there is a unique equilibrium our most general result is that if all excess demand is reallocated i e there is perfect substitutability then competition never leads to a decrease in industry inventory

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

optimal policies of yield management with multiple predetermined prices it is a common practice for industries to price the same products at different levels for example airlines charge various fares for a common pool of seats seasonal products are sold at full or discount prices during different phases of the season this article presents a model that reflects this yield management problem the model assumes that 1 products are offered at multiple predetermined prices over time 2 demand is price sensitive and obeys the poisson process and 3 price is allowed to change monotonically i e either the markup or markdown policy is implemented to maximize the expected revenue management needs to determine the optimal times to switch between prices based on the remaining season and inventory major results in this research include 1 an exact solution for the continuous time model 2 piecewise concavity of the value function with respect to time and inventory and 3 monotonicity of the optimal policy the implementation of optimal policies is fairly facile because of the existence of threshold points embedded in the value function the value function and time thresholds can be solved with a reasonable computation effort numerical examples are provided

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

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

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

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

diversification strategy and r d intensity in multiproduct firms this study provides empirical evidence that choice of diversification strategy systematically affects r d intensity in large multiproduct firms research and development intensity in dominant busin

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

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

can the reserves approach to monetary control really work on october 6 1979 the board of governors bog of the federal reserve system announced that the federal open market committee fomc was abandoning its historical preoccupation with an interest rate approach to monetary control in favor of a reserve aggregate approach 1 underlying this new approach is the fact that at time t any money stock concept m is the product of a money multiplier m and a reserve aggregate r that is

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

turnover statistics and federal government balances in money supply targets in the middle of the last decade congress mandated that the federal reserve announce its goals for monetary aggregates this increased emphasis on aggregates combined with the more recent financial innovations and deregulation has led to considerable discussion about the best monetary aggregate today arguments abound for every conceivable money stock or credit aggregate ranging from davidson and hafer s support of m i 5 to friedman s support of total net credit 7 given such a range of disagreement one can empathize with the frustration that prompted a congressional committee to ask can we identify a particular conception of money ml m2 or whatever with sufficient precision to allow its use as a proxy for economic performance a promising approach to the resolution of this problem has been the substitution of weighted sum monetary aggregates for the conventional simple sum aggregates in a simple sum aggregate each component is assigned a weight of one for instance one dollar of currency carries the same weight as one dollar of passbook savings but in the divisia aggregate approach 2 each component is assigned a weight which is proportional to the opportunity cost of holding that financial asset consequently a dollar of currency which earns no interest carries greater weight than a dollar of passbook savings the higher cost of holding currency directly reflects the value of its services as a medium of exchange the basic function of money a study by spindt 19 uses a second weighting system based on turnover statistics the basic assumption is that the more often a financial asset changes hands the greater its services as a medium of exchange using a st louis type reduced form model spindt discovered that his turnover weighted aggregate bore a closer relationship to gnp than did the federal reserve s mi in his detailed analysis spindt estimates some time series that are not directly measured for example the turnover of currency as a result he does not advocate the substitution of his aggregate index for the conventional aggregates nevertheless he does point out that the integration of the turnover statistics may be helpful in explaining certain anomalies in the behavior of the conventional aggregates 19 24

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

a continuous time yield management model with multiple prices and reversible price changes this article studies a continuous time yield management model in which reversible price changes are allowed we assume that perishable assets are offered at a set of discrete price levels demand at each level is a poisson process to maximize the expected revenue management controls the price dynamically as sales evolve we show that a subset of these prices that form a concave envelope is potentially optimal we formulate the problem into an intensity control model and derive the optimal solution in closed form properties of the optimal solution and their policy implementations are discussed numerical examples are provided

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

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

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

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

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

revenue management for low cost providers low cost providers have emerged as important players in many service industries the most predominant being low cost or the so called discount airlines this paper presents models and results leading toward understanding the revenue management outlook for a discount pricing firm a framework and model is formulated specifically for the airline industry but is generalizable to low cost providers in similar revenue management settings we formulate an optimal pricing control model for a firm that must underprice to capture a segment of exogenous demand two specific model formulations are considered a continuous deterministic version and a discrete stochastic version structural results are derived for the deterministic case providing insight into the general form of optimal underpricing policies the stochastic results support the structural insight from the deterministic solution and illuminate the effect of randomness on the underpricing policies

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

general managers control new and existing products differently abstract this article presents some initial findings from an ongoing research project on the way that divisional general managers of targe organizational units control new product innovations control in this instance refers to the set of procedures systems and actions that general managers use to monitor evaluate influence or define what subordinates are doing the research presented here focuses on three broad questions 1 1 do divisional general managers of large organizational units control their new product activities differently from their more established operations 2 2 is a new product s innovation strategy related to the nature and degree of divisional general manager control and if so in what way 3 3 is a divisional general manager s choice of control methods related to his her unit s new product output the results were based on in depth interviews with the general managers of 26 large canadian based divisions in 12 firms all the firms were significant competitors in the north american market and all were actively engaged in new product activities firm size ranged from 210 million to 5 billion in sales the following is a summary of the study s principal findings and conclusions 1 1 control varies among dimensions the study measured the degree of control exercised by divisional general managers over new and established products on 14 control variables it was found that none of the new products relative to established brands was controlled in the same fashion by the managers instead new products were always managed through a variety of loose and tight controls in so doing it appeared that the divisional general managers were trying to balance the control and freedom required by subordinates with new products 2 2 control varies with strategy both theory and empirical research generally support the notion of linkage between a unit s strategy and its organizational eg design reward placement information etc practices the results of this study strengthen this line of thinking the data show that both the nature and degree of divisional general manager control vary with three dimensions of product strategy i e familiarity uniqueness and advancement 3 3 control varies with output the analysis highlighted the pivotal relationship between divisional general manager control and new product output both the nature and degree of control were found to be associated with new product output in each strategic category although there does not appear to be one best way to control all types of new products some divisional general management approaches to control were more preferred than others 4 4 loose formal tight informal the general managers control patterns showed that formal control dimensions were usually managed more loosely than informal ones that tighter informal controls were used to off set or balance the more relaxed formal dimensions and that the observed reduction in formal control should not be interpreted to mean either the absence of bureaucracy or the absence of formal control indeed some formal bureaucratic control was always found in the high output strategic categories thus rather than being considered or labeled as typically bad bureaucracy may in fact be beautiful provided of course that it is appropriately used the article concludes by arguing that a divisional general manager s approach to controlling new products seems to make a difference in terms of performance as such the control approach chosen should not be made haphazardly or with abandon

inventory competition under dynamic consumer choice we analyze a model of inventory competition among n firms that provide competing substitutable goods each firm chooses initial inventory levels for their good in a single period newsboy like inventory model customers choose dynamically based on current availability so the inventory levels at one firm affect the demand of all competingfirms this creates a strategic interaction amongthe firms inventory decisions our work extends earlier work on variations of this problem by karjalainen 1992 lippman and mccardle 1997 and parlar 1988 specifically we model demand in a more realistic way as a stochastic sequence of heterogeneous consumers who choose dynamically from amongthe available goods or choose not to purchase based on a utility maximization criterion we also use a sample path analysis so minimal assumptions are imposed on this demand process we characterize the nash equilibrium of the resulting stocking game and prove it is unique in the symmetric case we show there is a bias toward overstocking caused by competition specifically reducing the quantity stocked at any equilibrium of the game increases total system profits and at any joint optimal set of stocking levels each firm has an individual incentive to increase its own stock for the symmetric case we show that as the number of competing firms increases the overstockingbecomes so severe that total system and individual firm profits approach zero finally we propose a stochastic gradient algorithm for computing equilibria and provide several numerical examples

money income and causality the japanese case sims 20 provided evidence of a unidirectional causal relationship running from the money supply to nominal income with u s data by a statistical test now called sims s test however williams goodhart and gowland 21 derived an ambiguous result using u k data namely the possibility of a weak unidirectional causal relationship running from income to money to resolve these apparently inconsistent findings putnam and wilford 18 considered the role of the pound and the dollar in the world market that is the u s can control its own money supply since the dollar serves as a reserve currency under a fixed exchange rate regime while the u k cannot since the price level in the u k is determined in the world market and the u k money supply is adjusted accordingly as individuals in the u k seek to maintain their equilibrium money balances thus according to their analysis it is only in the u s that money can cause income while in other countries money and income are simultaneously determined further testing mundell s theoretical implication 12 that monetary policy cannot affect income but rather income fluctuations produce accommodating monetary flows 11 24 mills and wood found a unidirectional causal relationship running from income to money for the u k for the gold standard period 1870 1914 1 on the other hand mehra 9 examined the causal relationship among the variables of the money demand equation while real money demand is exogenously explained by distributed lags of real income and interest rates the results indicate no conclusive relationship among nominal money demand nominal income interest rates and price as a result he reaffirms the usual practice of inferring the causal structure between two variables within the bivariate distributed lag framework 6 228

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

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

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

a methodology for competitive advantage analysis and strategy formulation an example in a transitional economy industrial competitiveness has become the focal point of study in recent years as global competition has intensified although many studies are devoted to the topic they remain largely conceptual and descriptive and thus it is difficult to make them operational very recently several studies were conducted to model industrial competitiveness through quantitative analysis but few consider how to combine the degree and scope of determinant factors of competitive advantages dfcas and competitive strategic goals csgs to maximize a firm s competitiveness or how to analyze the main problems of creating competitive advantage the present study proposes a model based approach to competitive analysis and discusses its multi phased implementation in a large electronic plant in china the proposed model can provide a comprehensive analytical tool for industrial competitiveness and can yield useful insights for competitive strategy formulation

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

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

dynamic pricing in the presence of inventory considerations research overview current practices and future directions the benefits of dynamic pricing methods have long been known in industries such as airlines hotels and electric utilities where the capacity is fixed in the short term and perishable in recent years there has been an increasing adoption of dynamic pricing policies in retail and other industries where the sellers have the ability to store inventory three factors contributed to this phenomenon 1 the increased availability of demand data 2 the ease of changing prices due to new technologies and 3 the availability of decision support tools for analyzing demand data and for dynamic pricing this paper constitutes a review of the literature and current practices in dynamic pricing given its applicability in most markets and its increasing adoption in practice our focus is on dynamic intertemporal pricing in the presence of inventory considerations

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

a continuous time dynamic pricing model knowing the competitor s pricing strategy abstract in this paper we consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy we establish a continuous time model to analyze the effect of dynamic pricing on the improvement in expected revenue in the duopoly we assume that customers arrive to purchase tickets in accordance with a geometric brownian motion we derive an explicit closed form expression for an optimal pricing policy to maximize the expected revenue it is shown that when the competitor adopts a static pricing policy dynamic pricing is not always effective in terms of maximizing expected revenue compared to a fixed pricing strategy moreover we show that the size of the reduction in the expected revenue depends on the competitor s pricing strategy numerical results are presented to illustrate the dynamic pricing policy

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