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

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

revenue management for a multiclass single server queue via a fluid model analysis motivated by the recent adoption of tactical pricing strategies in manufacturing settings this paper studies a problem of dynamic pricing for a multiproduct make to order system specifically for a multiclass mn m 1 queue with controllable arrival rates general demand curves and linear holding costs we study the problem of maximizing the expected revenues minus holding costs by selecting a pair of dynamic pricing and sequencing policies using a deterministic and continuous fluid model relaxation of this problem which can be justified asymptotically as the capacity and the potential demand grow large we show the following i greedy sequencing i e the c rule is optimal ii the optimal pricing and sequencing decisions decouple in finite time after which iii the system evolution and thus the optimal prices depend only on the total workload building on i iii we propose a one dimensional workload relaxation to the fluid pricing problem that is simpler to analyze and leads to intuitive and implementable pricing heuristics numerical results illustrate the near optimal performance of the fluid heuristics and the benefits from dynamic pricing

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

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

real time dynamic pricing with minimal and flexible price adjustment we study a standard dynamic pricing problem where the seller a monopolist possesses a finite amount of inventories and attempts to sell the products during a finite selling season despite the potential benefits of dynamic pricing many sellers still adopt a static pricing policy because of 1 the complexity of frequent reoptimizations 2 the negative perception of excessive price adjustments and 3 the lack of flexibility caused by existing business constraints in this paper we develop a family of pricing heuristics that can be used to address all these challenges our heuristic is computationally easy to implement it requires only a single optimization at the beginning of the selling season and automatically adjusts the prices over time moreover to guarantee a strong revenue performance the heuristic only needs to adjust the prices of a small number of products and do so infrequently this property helps the seller focus his effort on the prices of the most important products instead of all products in addition in the case where not all products are equally admissible to price adjustment due to existing business constraints such as contractual agreement strategic product positioning etc our heuristic can immediately substitute the price adjustment of the original products with the price adjustment of similar products and maintain an equivalent revenue performance this property provides the seller with extra flexibility in managing his prices

investment under uncertainty with price ceilings in oligopolies abstract we study the impact of price cap regulation on the level and timing of investment in an oligopolistic cournot industry facing stochastic demand we find that a price ceiling affects investment decisions in two mutually competing ways it makes the option to defer investment more valuable but at the same time it reduces the incentive for firms to strategically underinvest in order to raise prices we show that while sensible price cap regulation speeds up investment a low price cap can be a disincentive for investment there exists an optimal price cap independent of market concentration the competitive investment price trigger that maximizes investment incentives and in the long term increases industry installed capacity this optimal price cap becomes less effective and less robust as the market becomes more competitive and as demand volatility increases errors in estimation of the optimal price cap have asymmetric effects underestimation has more dire consequences than overestimation

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

performance of an lp based control for revenue management with unknown demand parameters we consider a standard network revenue management rm problem and study the performance of a linear program lp based control the probabilistic allocation control pac in the presence of unknown demand parameters we show that frequent re optimizations of pac without re estimation suffice to shrink the asymptotic impact of estimation error on revenue loss if in addition to re optimizations we also frequently re estimate the parameters we prove that the performance of pac in the unknown parameters setting is almost as good as the performance of pac in the known parameters setting our numerical experiments show that pac yields a revenue improvement of order 0 5 1 5 relative to lp based booking limit and bid price in most cases given the small margin in rm industries such as the airline industry about 2 this level of improvement can easily translate into a significant increase in profit

bundle pricing of inventories with stochastic demand we consider a retailer selling a fixed inventory of two perishable products over a finite horizon assuming poisson arrivals and a bivariate reservation price distribution we determine the optimal product and bundle prices that maximize the expected revenue our results indicate that the performances of mixed bundling pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels when the starting inventory levels are equal and in excess of average demand most of the benefits of bundling can be achieved through pure bundling however the mixed bundling strategy dominates the other two when the starting inventory levels are not equal we also observe that an incorrect modeling of the reservation prices may lead to significant losses the model is extended to allow for price changes during the selling horizon it is shown that offering price bundles mid season may be more effective than changing individual product prices

two period dynamic versus fixed ratio pricing in a capacity constrained duopoly this paper analyzes the impact of dynamic and fixed ratio pricing policies on firm profits and equilibrium prices under competition firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times in each period customers first purchase from the low price firm and then from the high price firm up to their inventories provided the prices are lower than the maximum they are willing to pay the main conclusions of this paper are as follows although dynamic pricing is a more sophisticated policy than fixed ratio pricing it may lead to decreased equilibrium profits under both pricing policies one firm assumes the role of a low cost high output firm while the other assumes the role of a high cost low output firm and the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices

on the minimax complexity of pricing in a changing environment we consider a pricing problem in an environment where the customers willingness to pay wtp distribution may change at some point over the selling horizon customers arrive sequentially and make purchase decisions based on a quoted price and their private reservation price the seller knows the wtp distribution pre and postchange but does not know the time at which this change occurs the performance of a pricing policy is measured in terms of regret the loss in revenues relative to an oracle that knows the time of change prior to the start of the selling season we derive lower bounds on the worst case regret and develop pricing strategies that achieve the order of these bounds thus establishing the complexity of the pricing problem our results shed light on the role of price experimentation and its necessity for optimal detection of changes in market response wtp our formulation allows for essentially arbitrary consumer wtp distributions and purchase request patterns

blind network revenue management we consider a general class of network revenue management problems where mean demand at each point in time is determined by a vector of prices and the objective is to dynamically adjust these prices so as to maximize expected revenues over a finite sales horizon a salient feature of our problem is that the decision maker can only observe realized demand over time but does not know the underlying demand function that maps prices into instantaneous demand rate we introduce a family of blind pricing policies that are designed to balance trade offs between exploration demand learning and exploitation pricing to optimize revenues we derive bounds on the revenue loss incurred by said policies in comparison to the optimal dynamic pricing policy that knows the demand function a priori and we prove that asymptotically as the volume of sales increases this gap shrinks to zero

rent seeking and tax competition abstract regional or local governments often appear to favour the interests of those who own land in the region here the implications of this sort of policy making are modelled formally people are assumed perfectly mobile between regions but are assumed to own land only in the region of their birth the nash equilibrium is shown to be efficient if and only if no migration of capital or labour is needed to achieve efficiency otherwise tax competition leads to too little migration voluntary inter regional transfers will never arise in equilibrium despite the inefficiency of the nash equilibrium when there is migration a higher level of government cannot alter the equilibrium if regional governments choose policies simultaneously after the federal government has committed to its policies

the investment effects of price caps under imperfect competition a note we examine the impact of price cap regulation on the capacity investments of oligopolistic suppliers facing time varying demand we find that binding price caps set above long run marginal cost increase rather than decrease aggregate capacity investment

analytical solutions to the dynamic pricing problem for time normalized revenue abstract in this work we consider dynamic pricing for the case of continuous replenishment an essential ingredient in such a formulation is the use of time normalized revenue or profit function in other words revenue or profit per unit time this provides the incentive to sell many items in the shortest time and of course at a high price moreover for most firms what matters most is how much revenue or profit is achieved in a certain time frame for example per year this changes the problem qualitatively and methodologically we develop a new dynamic pricing model for this formulation we derive an analytical solution to the pricing problem in the form of a simple to solve ordinary differential equation ode equation the trajectory of this ode gives the optimal pricing curve unlike many of the models existing in the literature that rely on computationally demanding dynamic programming type solutions our model is relatively simple to solve also we apply the derived equation to two commonly used price demand functions the exponential and the power functions and derive closed form pricing curves for these functions

the d level nested logit model assortment and price optimization problems we consider assortment and price optimization problems under the d level nested logit model in the assortment optimization problem the goal is to find the revenue maximizing assortment of products to offer when the prices of the products are fixed using a novel formulation of the d level nested logit model as a tree of depth d we provide an efficient algorithm to find the optimal assortment for a d level nested logit model with n products the algorithm runs in o d n log n time in the price optimization problem the goal is to find the revenue maximizing prices for the products when the assortment of offered products is fixed although the expected revenue is not concave in the product prices we develop an iterative algorithm that generates a sequence of prices converging to a stationary point numerical experiments show that our method converges faster than gradient based methods by many orders of magnitude in addition to providing solutions for the assortment and price optimization problems

a nash tax game extending the generality of the henry george theorem abstract this paper analyzes a model of nash tax competition where jurisdictions can finance public goods with taxes on two types of mobile capital and a tax on land efficiency in public good provision results when the land tax becomes the single tax required to fund local government spending this conclusion affirms and extends the generality of the henry george theorem

optimality free mobility and the regional authority in a federation abstract this paper examines the efficiency properties of a federation characterized by strategically competing regions and freely mobile homogeneous individuals analyses of this economy have concluded that achieving a pareto optimal will require intervention by a national authority this paper makes one basic point the nash equilibrium of regional authority behavior is pareto optimal the implication is that there is no role for a national authority in either providing interregional transfers or correcting for decentralized provision of public goods the nash equilibrium involves samuelson public goods provision and regions purchasing preferred population distributions with optimal interregional transfers

interjurisdictional capital mobility fiscal externality and a corrective subsidy abstract recent studies emphasize that local property taxation may result in inefficiently small amounts of local public spending this paper shows that the inefficiency can be traced to a fiscal externality when one jurisdiction increases its taxes it causes a flow of capital to other jurisdictions that increases their tax revenues the inefficiency can be corrected with a subsidy that internalizes the externality key empirical parameters determining the magnitude of the externality are identified illustrative calculations indicate that subsidy rates on the order of 40 might be required to achieve efficiency

simple policies for dynamic pricing with imperfect forecasts we consider the classical single product dynamic pricing problem allowing the scale of demand intensity to be modulated by an exogenous market size stochastic process this is a natural model of dynamically changing market conditions we show that for a broad family of gaussian market size processes simple dynamic pricing rules that are essentially agnostic to the specification of this market size process perform provably well the pricing policies we develop are shown to compensate for forecast imperfections or a lack of forecast information altogether by frequent reoptimization and reestimation of the instantaneous market size

dynamic pricing with uncertain production cost an alternating move approach abstract this article studies a two firm dynamic pricing model with random production costs the firms produce the same perishable products over an infinite time horizon when production or operation costs are random in each period each firm determines its price and production levels based on its current production cost and its opponent s previous price level we use an alternating move game to model this problem and show that there exists a unique subgame perfect nash equilibrium in production and pricing decisions we provide a closed form solution for the firm s pricing policy finally we study the game in the case of incomplete information when both or one of the firms do not have access to the current prices charged by their opponents

reserve price lessons learned from brazilian electricity procurement auctions abstract auctions have been used in several formats in the electric energy industry in general regulators may be uncomfortable initiating a reverse auction at a higher than expected final price fearing that participants may sell their energy at an excess profitability nevertheless evidence from electricity procurement auctions conducted in brazil supports the findings that these types of auctions have the opposite effect by attracting a larger number of agents these auctions can trigger stronger competition and lead to lower settlement pricing accordingly the brazilian cases examined in this article present significant evidence to support this directional theory in fact there are some cases of electricity procurement auctions that show that inadequate auction reserve pricing leads to inefficient outcomes and may also cause the auction to fail on the other hand auctions with adequate price caps have led to lower final clearing prices thus contributing to reasonable final energy pricing

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

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

price caps and investment long run effects in the electric generation industry abstract this paper utilizes a dynamic framework to determine the long run effects of price caps on electricity generation investment and spot prices the results show that the effects of spot market price caps differ significantly based upon the market structure in a social welfare maximization scenario price caps will not reduce average electricity prices and may actually raise them due to the dynamic affect of price caps on investment in addition price caps may reduce overall investment levels and result in welfare losses if the independent system operator is forced to shed load therefore since social welfare maximization will approximate a competitive outcome the results imply that price caps should be avoided in competitive markets in contrast for the monopoly producer price caps produce an indeterminate effect on overall investment and unequivocally lower average prices which are otherwise unbounded therefore price caps are necessary to prevent unlimited price markups

the persistence and inefficiency of property tax finance of local public expenditures abstract i both characterize and evaluate equilibrium outcomes in multiple jurisdiction economies with property and land taxation but where direct taxation of residents is not possible the model contains perfectly mobile capital and population and competitive entrepreneurial governments that choose local taxes and expenditures to maximize after tax land rent when the cost of public goods is proportional to population the property tax emerges as the sole source of local finance even though the land tax has no deadweight loss it is shown that equilibria are not constrained efficient in general hence decentralized decision making is not consistent with the best use of the available tax instruments

efficient decentralized fiscal and environmental policy a dual purpose henry george tax abstract one consequence of decentralized responsibility to set tax policy and environmental standards is that local governments might try to attract industry and jobs by underproviding local public goods with lower taxes or lax environmental standards or both but if local authorities exploit fixed property site i e land taxation to fund local public goods affect firm migration and internalize potential local emission rents herein we find decentralized efficiency is supported this result reflects a dual form of the classic henry george theorem previously overlooked

tax competition with two types of capital abstract we examine a tax competition model in which two types of mobile capital are taxed to fund local public goods when taxing land is not feasible we derive optimal tax rules and we find it is possible for localities to subsidize one type of capital

optimal dynamic pricing and ordering decisions for perishable products abstract in this paper we determine the order quantity and the prices for a perishable product with a multiple period lifetime demands for products of different ages are dependent on the prices of mutually substitutable products the problem for a product with lifetime of two periods is first analyzed and the stochastic dynamic programming model is developed given the inventory level for the old product product of age 2 the expected profit is a concave function of the order quantity the price of the new product product of age 1 and the discounted price of the old product product of age 2 the computational results show that the total profit significantly increases when demand transfers between products of different ages are considered for a product with lifetime of longer than two periods a heuristic based on the optimal solution for a single period problem is proposed for a multiple period problem

design and evaluation of a dynamic capacity apportionment procedure abstract deploying a decision theory based approach we develop a heuristic for short term constrained capacity allocation to multiple product classes in make to order manufacturing attempting to maximize profit by discriminating between product classes efficacy of the heuristic is evaluated by comparing its performance to a base case and an upper bound under a wide variety of operational conditions such as variations in profit attractiveness capacity tightness customer order size structure customer order rate structure and demand coefficient of variation considering three different scenarios of time variant order rate of products the results indicate that the heuristic is effective in obtaining increased profit when capacity is very tight and products are well differentiated on average it yields an increase of 9 38 in total profit with a concomitant decrease of 0 85 in capacity utilization the results of this study serve to highlight the value of proactively seeking to differentiate products particularly when demand exceeds capacity

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

dynamic pricing with a prior on market response we study a problem of dynamic pricing faced by a vendor with limited inventory uncertain about demand and aiming to maximize expected discounted revenue over an infinite time horizon the vendor learns from purchase data so his strategy must take into account the impact of price on both revenue and future observations we focus on a model in which customers arrive according to a poisson process of uncertain rate each with an independent identically distributed reservation price upon arrival a customer purchases a unit of inventory if and only if his reservation price equals or exceeds the vendor s prevailing price we propose a simple heuristic approach to pricing in this context which we refer to as decay balancing computational results demonstrate that decay balancing offers significant revenue gains over recently studied certainty equivalent and greedy heuristics we also establish that changes in inventory and uncertainty in the arrival rate bear appropriate directional impacts on decay balancing prices in contrast to these alternatives and we derive worst case bounds on performance loss we extend the three aforementioned heuristics to address a model involving multiple customer segments and stores and provide experimental results demonstrating similar relative merits in this context

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

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

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

revenue management through dynamic cross selling in e commerce retailing we consider the problem of dynamically cross selling products e g books or services e g travel reservations in the e commerce setting in particular we look at a company that faces a stream of stochastic customer arrivals and may offer each customer a choice between the requested product and a package containing the requested product as well as another product what we call a packaging complement given consumer preferences and product inventories we analyze two issues 1 how to select packaging complements and 2 how to price product packages to maximize profits we formulate the cross selling problem as a stochastic dynamic program blended with combinatorial optimization we demonstrate the state dependent and dynamic nature of the optimal package selection problem and derive the structural properties of the dynamic pricing problem in particular we focus on two practical business settings with the emergency replenishment model and without the lost sales model the possibility of inventory replenishment in the case of a product stockout for the emergency replenishment model we establish that the problem is separable in the initial inventory of all products and hence the dimensionality of the dynamic program can be significantly reduced for both models we suggest several packaging pricing heuristics and test their effectiveness numerically

combined pricing and inventory control under uncertainty this paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty more specifically we analyze the following single item periodic review model demands in consecutive periods are independent but their distributions depend on the item s price in accordance with general stochastic demand functions the price charged in any given period can be specified dynamically as a function of the state of the system a replenishment order may be placed at the beginning of some or all of the periods stockouts are fully backlogged we address both finite and infinite horizon models with the objective of maximizing total expected discounted profit or its time average value assuming that prices can either be adjusted arbitrarily upward or downward or that they can only be decreased we characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models we also develop an efficient value iteration method to compute these optimal strategies finally we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values

reoptimization and self adjusting price control for network revenue management we consider a standard dynamic pricing problem with finite inventories finite selling horizon and stochastic demands where the objective of the seller is to maximize total expected revenue we introduce a simple improvement of the popular static price control known in the literature the proposed heuristic only requires a single optimization at the beginning of the selling horizon and does not require any reoptimization at all this provides an advantage over the potentially heavy computational burden of reoptimization especially for very large applications with frequent price adjustments in addition our heuristic can be implemented in combination with a few reoptimizations to achieve a high level revenue performance this hybrid of real time adjustment and reoptimization allows the seller to enjoy the benefit of reoptimization without overdoing it

the inverse newsvendor problem choosing an optimal demand portfolio for capacitated resources the classical newsvendor problem is one of optimally choosing a level of capacity to respond to a known demand distribution the inverse newsvendor problem is one of optimally choosing a demand distribution with fixed capacity the applications of the inverse problem include industrial settings where demand management is relatively less costly than capacity adjustments demand distributions are chosen from an opportunity set which reflects the set of market opportunities for the firm we analyze the firm s profit as a function of these demand alternatives provide solution methods and insights and identify inefficient and dominated distributions we provide results when the opportunity set is known or only partially known we extend the results to cases in which there are multiple prioritized customer classes that share the firm s productive capacity this paper was motivated by an industrial application in a firm selling a semicommodity product into three prioritized industrial sectors we review the application of our methods to this setting

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

dynamic capacity management with general upgrading this paper studies a capacity management problem with upgrading a firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time a general upgrading rule is considered i e unmet demand can be satisfied using multistep upgrade no replenishment is allowed and the firm has to make the allocation decisions without observing future demand we first characterize the structure of the optimal allocation policy which consists of parallel allocation and then sequential rationing specifically the firm first uses capacity to satisfy the same class demand as much as possible then considers possible upgrading decisions in a sequential manner we also propose a heuristic based on certainty equivalence control to solve the problem numerical analysis shows that the heuristic is fast and delivers close to optimal profit for the firm finally we conduct extensive numerical studies to derive insights into the problem it is foun

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

pricing in revenue management for multiple firms competing for customers abstract we consider the pricing strategies of multiple firms providing the same service in competition for a common pool of customers in a revenue management context the firms have finite capacity and the demand at each firm depends on the selling prices charged by all firms each of which satisfies demand up to a given capacity limit we use game theory to analyze the systems when firms face either a deterministic demand or a general stochastic demand the existence and uniqueness conditions of a nash equilibrium are derived and we calculate the explicit nash equilibrium point when the demand at each firm is a linear function of price we also conduct sensitivity analysis of the equilibrium prices with respect to cost and capacity parameters

a pricing model for clearing end of season retail inventory the problem of setting prices for clearing retail inventories of fashion goods is a difficult task that is further exacerbated by the fact that markdowns enacted near the end of the selling season have a smaller impact on demand in this article we present discrete time models for setting clearance prices in such an environment when demand is deterministic we compute optimal prices and show that decreasing reservation prices lead to declining optimal prices when demand is stochastic and arbitrarily correlated across planning periods we obtain bounds on the optimal expected revenue and on optimal prices we also develop a heuristic procedure for finding near optimal prices and test its accuracy through numerical experiments these experiments reveal new insights for practitioners for example the penalty for choosing clearance price once and keeping it unchanged for the remainder of the selling season is found to be small when either the mean reservation prices do not change appreciably over time or when they drop sharply after the first period

optimal bundle formation and pricing of two products with limited stock abstract in this study we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm one of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit product demands follow a poisson process with a price dependent rate customer reservation prices are assumed to have a joint distribution we study the impact of reservation price distributions initial inventory levels product prices demand arrival rates and cost of bundling we observe that the expected profit decreases as the correlation between the reservation prices of two products increases with negative correlation bundling cost has a significant impact on the number of bundles formed when the product prices are low the retailer sells individual products as well as the bundle mixed bundling when they are high the retailer sells only bundles pure bundling the expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases for high starting inventory levels the retailer reduces bundle price and offers more bundles the number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases impacts of substitutability and complementarity of products are also investigated the retailer forms more bundles or charges higher prices for the bundle or both as the products become more complementary and less substitutable

list pricing versus dynamic pricing impact on the revenue risk abstract we consider the problem of a firm selling multiple products that consume a single resource over a finite time period the amount of the resource is exogenously fixed we analyze the difference between a dynamic pricing policy and a list price capacity control policy the dynamic pricing policy adjusts prices steadily resolving the underlying problem every time step whereas the list pricing policy sets static prices once but controls the capacity by allowing or preventing product sales as steady price changes are often costly or unachievable in practice we investigate the question of how much riskier it is to apply a list pricing policy rather than a dynamic pricing policy we conduct several numerical experiments and compare expected revenue standard deviation and conditional value at risk between the pricing policies the differences between the policies show that list pricing can be a useful strategy when dynamic pricing is costly or impractical

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

capacity management in order driven production networks a flexibility oriented approach to determine the size of a network capacity pool abstract assuming heterarchical production networks capacity management is faced with uncertainties of both network orders and network capacity in order to deal with these uncertainties we propose a flexible approach that combines capacity oriented pricing with two modes of providing network capacity capacity on demand and network capacity pool flexibility of this approach arises from additional degrees of freedom for matching capacity supply and demand the central problem of sizing the network capacity pool is solved iteratively by a decentralised planning process applying the top down bottom up principle in this paper we present the underlying formal models of the corporate level and the network level as well as the coordination procedure in order to illustrate the approach we provide a continued numerical example

on interjurisdictional competition and environmental federalism herein we construct a competitive interjurisdictional model that reconciles two recent exceptions to the race to the bottom j publ econ 35 1988 333 354 j urban econ 37 1995 290 310 our results suggest that since environmental rents from local production are likely not captured 100 percent by local residents devolved command and control environmental regulation is inefficient moreover faced with the reality of fiscal constraints local governments adopt property tax structures that serve to compound inefficiencies within such a second best setting if a jurisdiction underprovides non environmental public goods and jurisdictional capital productivity and emissions are strong complements a race to the bottom equilibrium is supported

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

effects of sourcing structure on performance in a multiple product assemble to order supply chain abstract this paper addresses the strategic pricing decisions of a decentralized assemble to order system and the effects of sourcing structure on system performance we consider an assemble to order system consisting of two substitute products and three components manufactured by different suppliers demand for the products is price sensitive the selling prices for the products are jointly determined by firms in the system we study the system under both centralized and decentralized decision making situations for the centralized system we demonstrate that there exists a unique optimal pricing solution for the decentralized system we show that there exists a unique nash equilibrium in the players pricing game we further analyze the effects of different sourcing structures on the system performance and the assembler s performance we find that reduction of suppliers in the system does not guarantee improvement of system performance different sourcing structures have different impacts on performance when the two dedicated components are sourced from a single supplier and the common component is sourced from another independent supplier the system and the assembler s performance become worse we show that the decentralized system can be effectively coordinated and the system performance can be improved with a simple profit sharing contract finally we provide comprehensive numerical examples to demonstrate some important managerial insights

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

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

pricing non storable perishable goods by using a purchase restriction with an application to airline fare pricing abstract the aim of this paper is to address the pricing problem of non storable perishable goods or services such as airline seats and hotel rooms by incorporating the use of purchase restrictions such as the advance booking requirement that is commonly used by airlines and hotels we will show that there exists an optimal pricing policy of at most three prices which can be obtained by solving a series of linear programming problems we will demonstrate that when applied to airline fare pricing the monotonicity condition of the model is equivalent to the requirement that business travelers are less price elastic than leisure travelers we will further illustrate the applicability of the model through a numerical example in the context of airline fare pricing by incorporating the impact of various fences

dynamic price competition with discrete customer choices abstract for many years dynamic pricing has proven to be an effective tool to increase revenue in the airline and other service industries most studies however focused on monopolistic models and ignored the fact that nowadays consumers can easily compare prices on the internet in this paper we develop a game theoretic model to describe real time dynamic price competition between firms that sell substitutable products by assuming the real time inventory levels of all firms are public information we show the existence of nash equilibrium we then discuss how a firm can adapt if it knows only the initial but not the real time inventory levels of its competitors we compare a firm s expected revenue under different information structures through numerical experiments

technical note personalized dynamic pricing of limited inventories prior work has investigated time and inventory level dependent pricing of limited inventories with finite selling horizons we consider a third dimension in addition to time and inventory level that the firms can use in setting their prices the information that the firm has at the individual customer level an arriving customer provides a signal to the firm which is an imperfect indicator of the customer s willingness to pay and the firm makes a personalized price offer depending on the signal inventory level and time we consider two different models full personalization and partial personalization in the full personalization model the firm charges any price it wishes given the customer signal while in the partial personalization model the firm can charge one of two prices we find that a mere correlation between the signals and customers willingness to pay is not sufficient to ensure intuitive relationships between the signal and the optimal prices we determine a stronger condition which leads to several structural properties including the monotonicity of the optimal price with respect to the signal in the full personalization model for the partial personalization model we show that the optimal pricing policy is of threshold type and that the threshold is monotonic in the inventory level and time

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

the stochastic knapsack revisited switch over policies and dynamic pricing the stochastic knapsack has been used as a model in wide ranging applications from dynamic resource allocation to admission control in telecommunication in recent years a variation of the model has become a basic tool in studying problems that arise in revenue management and dynamic flexible pricing and it is in this context that our study is undertaken based on a dynamic programming formulation and associated properties of the value function we study in this paper a class of control that we call switch over policies start by accepting only orders of the highest price and switch to including lower prices as time goes by with the switch over times optimally decided via convex programming we establish the asymptotic optimality of the switch over policy and develop pricing models based on this policy to optimize the price reductions over the decision horizon