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

the hotel yield management with two types of room prices overbooking and cancellations abstract we consider a problem for hotel room allocations with early discount cancellations and overbooking in our model customers can book a room in discounted price if they reserve before a certain deadline the model takes overbooking into account we have expressed the expected total sale function proved it is unimodal on the number of allocated rooms for early discount and for overbooking respectively under a condition and clarified the range where the optimal solution exists we have derived an optimal allocation for early discount in a specified model without cancellations and overbooking

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

induced innovation in american agiculture a reconsideration this paper investigates the role of induced innovation in the development of american agriculture from 1880 to 1980 the induced innovation hypothesis most closely associated with the work of hayami and ruttan argues that successful economies develop technologies in accordance with market price signals to loosen constraints on growth imposed by factor scarcities our analysis employing new state and regional level data fails to find support for hayami and ruttan s hypothesis this paper suggests that many of the fundamental generalizations about american agricultural development need to be reconsidered and redirects attention to the role of settlement changing crop patterns and biological investments in explaining changes in factor utilization in american agriculture

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

pricing and capacity rationing for rentals with uncertain durations we consider a rental firm with two types of customers contract customers pay fixed prenegotiated rental fees and expect a high quality of service walk in customers have no contractual relations with the firm and are shopping for price given multiple contract and walk in classes the rental firm has to decide when to offer service to contract customers and what fees to charge walk in customers for service we formulate this rental management problem as a problem in stochastic control and characterize optimal policies for managing contract and walk in customers we also consider static myopic controls that are simpler to implement and we analytically establish conditions under which these policies perform optimally complementary numerical tests provide a sense of the range of systems for which myopic policies are effective

market structure and the value of overselling under stochastic demands in the operations management literature traditional revenue management focused on pricing and capacity allocation strategies in a two period model with stochastic demand inspired by travel and lodging industries we examine a two period model in which each seller may also adopt the overselling strategy to customers whose valuations are differentiated by timing of arrivals widely seen as a popular hedge against consumers skipping reservations we extend the stylized approaches of biyalogorsky carmon fruchter and gerstner 1999 and lim 2009 to understand the value of overselling under various market structures we find that contrary to existing literature the impact of period two pricing competition from overselling spills over to period one such that overselling may not always be a weakly dominant strategy once unlimited early demand ceases to hold in a duopoly regime we provide some numerical studies on the existence of multiple equilibria at the capacity allocation level which actually lead to different selling strategies at the equilibrium despite identical market conditions and firm characteristics

the effect of market segmentation with demand leakage between market segments on a firm s price and inventory decisions abstract in this paper we address the simultaneous determination of price and inventory replenishment in a newsvendor setting when the firm faces demand from two or more market segments in which the firm can set different prices we allow for demand leakage from higher priced segments to lower priced segments and assume that unsatisfied demand can be backlogged we examine the case where the demands occur concurrently without priority and are met from a single inventory we consider customer s buy down behavior explicitly by modeling demand leakage as a function of segment price differentiation and characterize the structure of optimal inventory and pricing policies

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

dynamic capacity management with substitution we examine a multiperiod capacity allocation model with upgrading there are multiple product types corresponding to multiple classes of demand and the firm purchases capacity of each product before the first period within each period after demand arrives products are allocated to customers customers who arrive to find that their product has been depleted can be upgraded by at most one level we show that the optimal allocation policy is a simple two step algorithm first use any available capacity to satisfy same class demand and then upgrade customers until capacity reaches a protection limit so that in the second step the higher level capacity is rationed we show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished in the latter case an order up to policy is optimal for replenishment although finding the optimal protection limits is computationally intensive we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems using these heuristics we examine numerically the relative value of strictly optimal capacity and dynamic rationing the value of perfect demand information and the impact of demand and economic parameters on the value of optimal substitution

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

the induced innovation hypothesis and u s public agricultural research applicability of the induced innovation hypothesis that a change in relative input prices induces innovation to economize use of the increasingly expensive input hicks 1932 is examined for u s public agricultural research a reduced form test is developed using input prices from the agricultural production sector expenditures from the public research sector aimed at developing new technology to save specific agricultural inputs and variables to control for innovation marginal cost differences and nonhomotheticity unlike recent demand side studies that soundly reject the induced innovation hypothesis for agriculture support for the hypothesis is found for several input pairings through these tests of public agricultural research using state level panel data

optimal dynamic auctions for revenue management we analyze a dynamic auction in which a seller withc units to sell faces a sequence of buyers separated intot time periods each group of buyers has independent private values for a single unit buyers compete directly against each other within a period as in a traditional auction and indirectly with buyers in other periods through the opportunity cost of capacity assessed by the seller the number of buyers in each period as well as the individual buyers valuations are random the model is a variation of the traditional single leg multiperiod revenue management problem in which consumers act strategically and bid for units of a fixed capacity over time for this setting we prove that dynamic variants of the first price and second price auction mechanisms maximize the seller s expected revenue we also show explicitly how to compute and implement these optimal auctions the optimal auctions are then compared to a traditional revenue management mechanism in which list prices are used in each period together with capacity controls and to a simple auction heuristic that consists of allocating units to each period and running a sequence of standard multiunit auctions with fixed reserve prices in each period the traditional revenue management mechanism is proven to be optimal in the limiting cases when there is at most one buyer per period when capacity is not constraining and asymptotically when the number of buyers and the capacity increases the optimal auction significantly outperforms both suboptimal mechanisms when there are a moderate number of periods capacity is constrained and the total volume of sales is not too large the benefit also increases when variability in the dispersion in buyers valuations or in the number of buyers per period increases

multiperiod airline overbooking with a single fare class consider a multiperiod airline overbooking problem that relates to a single leg flight and a single service class passengers may cancel their reservations at any time including being no shows at flight time at that time the airline bumps passengers in excess of flight capacity and pays a penalty for so doing we give conditions on the fares refunds and distributions of passenger demand for reservations and cancellations in each period and on the bumping penalty function that ensure that a booking limit policy is optimal i e in each period the airline accepts reservation requests up to a booking limit if the number of initial reservations is less than that booking limit and declines reservation requests otherwise the optimal booking limits are easily computed we give conditions under which the optimal booking limits are monotone in the time to flight departure the model is applied to the discount allocation problem in which lower fare classes book prior to higher fare classes

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

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

optimal 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

supply and demand functions for multiproduct u s cash grain farms biases caused by research and other policies this study presents new estimates of supply and demand elasticities for u s multiproduct cash grain farms and estimates of input and output bias effects caused by public and private crop research extension and farmers schooling the study also shows that the social rate of return to public crop research is large about 62 percent

hiring and leasing with nonlinear prices this paper examines the problem of a monopolist setting an optimal nonlinear pricing schedule in the face of consumers of unknown type who arrive randomly over time and self select a choice of hire period the major determinant of pricing policy is the customer arrival distribution with the overall level of price higher than in the atemporal yield management nonuniform pricing solution by a margin which increases with the average frequency with which potential customers arrive by contrast the solution is generally fairly insensitive to variations in the time rate of discount although there is a tendency for the rate of price discount to increase with increases in the time discount rate

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

asset selling problems with holding costs abstract sequential stochastic assignment problems now comprise a significant literature that includes such important economical applications as the classical asset selling problem and labor market analysis job search in this type of problems there is a stream of bidders to whom several identical units at the disposal of the decision maker have to be sold in this paper we incorporate holding costs to be incurred on the units say assets at hand into the classical model optimal strategies are defined as selling decision rules which maximize the total expected net reward from the units we take advantage of the specific structure offered by the framework of sequential stochastic assignment to get explicit results for the optimal strategies it is further shown how to implement these results for important specific bid distributions

revenue management by sequential screening abstract using a mechanism design approach we consider a firm s optimal pricing policy when consumers are heterogeneous and learn their valuations at different times we show that by offering a menu of advance purchase contracts that differ in when and for how much the product can be returned a firm can more easily price discriminate between privately informed consumers in particular we show that screening on when the return option can be exercised increases firm profits relative to screening on the size of the refund alone only if the expected gains from trade are higher for consumers who learn later we show that in some settings mean preserving spread the firm can achieve the complete information profits and analyze the optimal contract in other settings first order stochastic dominance in which the first best allocation is not always feasible

an optimal dynamic policy for hotel yield management abstract most research into the yield management problem has generated variations on the marginal seat revenue models that are based on simplifying assumptions about the demand process and heuristic decision rules in this paper a dynamic programming formulation of the problem is given allowing for general demand patterns and a policy that is based on time and the number of vacancies furthermore this policy incorporates both revealed price and hidden price market behavior it is shown that this formulation has a simple closed form solution that can be efficiently computed as a result a more general formulation of the problem with an optimal solution is available to hotels and airlines the particular application that motivated this model development is that of yield management for small hotels

geographic aggregation and induced innovation in american agriculture the induced innovation hypothesis is tested for the usa and western regions using cointegration procedures an error correction model separates short run and long run effects of relative price changes a significant difference in the elasticities of factor substitution along the isoquant and the innovation possibility curve implies induced innovation the estimated results support the hypothesis for washington the pacific northwest and the western region but not for the nation corroborative tests of weak exogeneity fail to support the hypothesis in any of the geographic units changes in output level and research investment do not significantly bias agricultural technology in the usa

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

securitization and loan performance ex ante and ex post relations in the mortgage market this study examines the relation between securitization and loan performance using a comprehensive dataset from a major national mortgage lender loans remaining on the bank s balance sheet ex post incurred higher delinquency rates than sold loans contrasting the negative relation between screening efforts and ex ante probability of loan sale explored by prior studies moreover the performance gap between sold and retained loans was wider among the subsample of loans that were perceived as easier to resell the investors seeming advantage over the originating bank can mostly be explained by information revealed during the time between loan origination and sale

robustness of capacity rationing policies a recent paper discusses a capacity rationing policy that allows make to order manufacturing firms encountering expected total demand in excess of available capacity to discriminate between two classes of products one yielding a higher profit contribution per unit of capacity allocated to it than the other the result is a selective rejection of orders for the class with lower unit contribution yielding an increase in total profit when compared to a base case that implements no capacity rationing implementation of the policy requires forecasts of demand parameters for both product classes in this paper we test the sensitivity of the capacity rationing policy to forecast errors in these parameters the results indicate that on average the rationing policy is quite robust in improving profit even when actual demands are approximately twenty percent different from forecast values

agricultural productivity revisited this paper describes production accounts for agriculture output is defined as gross production leaving the farm as opposed to real value added inputs are not limited to capital and labor but include intermediate inputs as well we derive index numbers of gross output capital labor and intermediate inputs these data are used to construct indexes of total factor productivity we then compare the contributions of input growth and productivity growth to economic growth the important role of productivity growth in agriculture becomes immediately apparent

revenue management with limited demand information in this paper we consider the classical multifare single resource leg problem in revenue management for the case where demand information is limited our approach employs a competitive analysis which guarantees a certain performance level under all possible demand scenarios the only information required about the demand for each fare class is lower and upper bounds we consider both competitive ratio and absolute regret performance criteria for both performance criteria we derive the best possible static policies which employ booking limits that remain constant throughout the booking horizon the optimal policies have the form of nested booking limits dynamic policies which employ booking limits that may be adjusted at any time based on the history of bookings are also obtained we provide extensive computational experiments and compare our methods to existing ones the results of the experiments demonstrate the effectiveness of these new robust methods

due date dd quotation and capacity planning in make to order companies results from an empirical analysis the current competitive context puts manufacturers under increasing pressure to provide products and services that meet the particular requirements of individual customers calling for high flexibility in business processes the complexity and the uncertainty of demand are particularly high in customized contexts such as the make to order mto and engineer to order eto sectors where the ability to deal with more and more differentiated requirements in terms of product features delivery lead time and cost is crucial in order to be competitive in such a context due date dd quotation and capacity evaluation at the customer enquiry stage are of strategic importance having a large impact on the company performance despite the large impact on company performance the importance of dd setting and order acceptance processes and related decisions is often underestimated in practice and the issue is underexposed in the literature as the applicability of most of the proposed models is limited and there are too few empirical studies describing the practices adopted for capacity and delivery lead time management in industrial contexts this study is aimed at developing an understanding of these practices based on a sample of 15 italian capital goods manufacturers an interpretative framework is proposed in order to identify the main contextual factors impacting company choices a model that formalizes the decision process for setting dds in the analyzed cases is then proposed suggesting different procedures depending on the type of enquiry submission dd set by companies or customers and customer order fast or slow

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

revenue management approach to stochastic capacity allocation problem abstract to formulate stochastic capacity allocation problems in a manufacturing system the concept and techniques of revenue management is applied in this research it is assumed the production capacity is stochastic and hence its exact size cannot be forecasted in advance at the time of planning there are two classes of frequent and occasional customers demanding this capacity the price rate as well as the penalty for order cancellation caused by overbooking is different for each class the model is developed mathematically and we propose an analytical solution method the properties of the optimal solution as well as the behavior of objective function are also analyzed the objective function is not concave in general however we prove it is a unimodal function and by taking advantage of this property the optimal solution is determined

pricing and revenue management the value of coordination the integration of systems for pricing and revenue management must trade off potential revenue gains against significant practical and technical challenges this dilemma motivates us to investigate the value of coordinating decisions on prices and capacity allocation in a stylized setting we propose two pairs of sequential policies for making static decisions on pricing and revenue management that differ in their degree of integration hierarchical versus coordinated and their pricing inputs deterministic versus stochastic for a large class of stochastic price dependent demand models we prove that these four heuristics admit tractable solutions satisfying intuitive sensitivity properties we further evaluate numerically the performance of these policies relative to a fully coordinated model which is generally intractable we find it interesting that near optimal performance is usually achieved by a simple hierarchical policy that sets prices first based on a nonnested stochastic model and then uses these prices to optimize nested capacity allocation this tractable policy largely outperforms its counterpart based on a deterministic pricing model jointly optimizing price and allocation decisions for the high end segment improves performance but the largest revenue benefits stem from adjusting prices to account for demand risk this paper was accepted by yossi aviv operations management

capacity rationing decision procedures with order profit as a continuous random variable abstract when expected demand is more than available capacity a make to order manufacturer should take the more profitable orders and reject the less profitable orders in order to better allocate its limited capacity and maximize its profit however various orders will arrive at different times in the future so the manufacturer cannot look at all the order inquiries at the same time and choose the most profitable ones when an order inquiry arrives the manufacturer must promptly determine without knowing exactly what the future orders might be whether to accept the order or to reject the order thus reserving the capacity for future more profitable orders this study focuses on such an order selection decision problem under the following assumptions 1 the arrival of future customer orders is a poisson process 2 the capacity requirement of a future customer order is a continuous random variable and 3 the profit per unit capacity used by an order is also a continuous random variable under the stochastic problem assumptions this study investigates two decision procedures that determine whether to accept or to reject an order inquiry based on the available information including 1 current available manufacturing capacity 2 capacity requirement by the order and 3 the profit per unit capacity of the order one procedure is called static probability capacity rationing decision procedure spcr the other one is called dynamic stochastic capacity rationing decision procedure dscr simulation experiments are conducted to validate the proposed procedures an optimal solution method that uses 0 1 knapsack problem formulation to obtain the decisions with perfect information is used to measure the effectiveness of the proposed procedures the results show that the approach utilizing dscr outperforms other approaches by providing the highest profit and is also very robust under various problem conditions

quality differentiation and conditional spatial price competition among hotels abstract it is generally accepted that location is the dominant product attribute for hotels accordingly studies on price competition have often utilized fixed geographic boundaries when defining competitive sets when travelers are willing to substitute location and quality however the spatial extent of competition can depend on the hotels quality therefore it can be hypothesized that geographic boundary of price competition among hotels is conditional on quality differentiation through an empirical analysis based on two stage least squares modified to test for spatial price competition the present study finds that hotels compete with more distant neighbors of similar quality than those who are quality differentiated in addition the results also suggest possibility of cooperation among neighboring hotels similar in quality implications and suggestions are presented along with the findings of the study which is expected to contribute to the literature by suggesting a new perspective on the relationship between quality differentiation and price competition among hotels

the failure of models that predict failure distance incentives and defaults statistical default models widely used to assess default risk fail to account for a change in the relations between different variables resulting from an underlying change in agent behavior we demonstrate this phenomenon using data on securitized subprime mortgages issued in the period 1997 2006 as the level of securitization increases lenders have an incentive to originate loans that rate high based on characteristics that are reported to investors even if other unreported variables imply a lower borrower quality consistent with this behavior we find that over time lenders set interest rates only on the basis of variables that are reported to investors ignoring other credit relevant information as a result among borrowers with similar reported characteristics over time the set that receives loans becomes worse along the unreported information dimension this change in lender behavior alters the data generating process by transforming the mapping from observables to loan defaults to illustrate this effect we show that the interest rate on a loan becomes a worse predictor of default as securitization increases moreover a statistical default model estimated in a low securitization period breaks down in a high securitization period in a systematic manner it underpredicts defaults among borrowers for whom soft information is more valuable regulations that rely on such models to assess default risk could therefore be undermined by the actions of market participants

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

service cancellation and competitive refund policy although previous research demonstrates the profitability of partial refund policies in a monopoly setting there is a certain lack of ubiquity in practice about these refunds in competitive service markets this raises the question of how a partial refund policy may work and whether it is even sustainable in a competitive environment this study investigates how competition may influence the profitability and the equilibrium choice of refund policies it is shown that partial refunds may endogenously change the nature of strategic interaction between service providers from local monopolies into a competition regime which moderates the gains from exploiting the efficiency enhancing effect of partial refunds a whole range of pure strategy equilibria can be obtained as a result of the interplay between the efficiency improving and the competition intensifying effects when the capacity is small large such that the efficiency improving the competition intensifying effect is dominant both firms in equilibrium follow identical partial zero refund policies moreover interestingly the symmetric firms may end up in an asymmetric equilibrium in which one firm follows a partial refund policy and the other adopts a zero refund policy

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

multi dimensional price elasticity for leisure and business destinations in the low cost air transport market evidence from easyjet this study investigates the price elasticity of demand in the european low cost carrier lcc industry by analysing internet fares for all easyjet flights departing from the amsterdam schiphol airport towards 21 european destinations between march and september 2015 results suggest that the price elasticity of demand greatly varies across different dimensions ranging from 0 535 for the business oriented route of hamburg to 1 915 for the leisure oriented route of split price elasticity is also found to be higher for reservations made more days in advance for reservations and departures occurring on weekends and for flights taking off during lunchtime and in the summer period all results are consistent with the different behaviours of leisure and business passengers and the ongoing increase in the business component of the lcc passenger mix

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

joint production and pricing decisions with setup costs and capacity constraints we consider the problem of setting prices and choosing production quantities for a single product over a finite horizon for a capacity constrained manufacturer facing price sensitive demands there is a fixed cost per production run and a variable cost per unit produced both of which may vary by period we characterize properties of the optimal solution considering cases with constant and time varying capacity and with and without speculative motive for holding inventory we show that counter to intuition optimal prices may increase as the capacity increases even when capacity is constant over the horizon we also show that increases in capacity do not always exhibit diminishing marginal returns our procedure produces solutions with much higher profits than can be obtained from a sophisticated sequential procedure in which a well informed and optimum seeking marketing department makes pricing decisions and the manufacturing department seeks to satisfy the resulting demands at minimum cost our results also suggest that firms with seasonal demand and tight capacity constraints should be more aggressive in setting prices to manage their demands than what is typically done in practice finally we discuss how a decision maker can use our procedure as an aid in solving multiproduct versions of the problem

issuer credit quality and the price of asset backed securities following the financial market crisis of the past few years critics and scholars have identified numerous problems related to all parties associated with securitization including investors rating agencies issuers underwriters and borrowers some of this research focuses on the rating process itself adam ashcraft paul goldsmith pinkham and james vickery 2009 show that observable credit fundamentals deteriorated relative to ratings between 2005 and 2007 efraim benmelech and jennifer dlugosz 2009 find that collateralized debt obligations cdos rated by only one rating agency are more likely both to be downgraded and to suffer more severe downgrades than cdos rated by more than one agency joshua coval jakub jurek and erik stafford 2009a point out that ratings of cdos were highly unreliable due to models that were highly sensitive to even small errors in economic projections or losses and that underestimated the correlation of risks across various debt securities other research focuses on the conflicts of interest between parties who participate in the underlying processes of originating and bundling loans and collecting payments from delinquent borrowers chris downing dwight jaffee and nancy wallace 2009 find that some residential mortgage backed securities trade in a market for lemons where originators can use private information to determine which mortgage issuer credit quality and the price of asset backed securities

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

quantity discounts managerial issues and research opportunities marketing managers frequently administer pricing policies involving substantial quantity discounts however our understanding of the precise role of these discounts and their design is quite limited this paper reviews and integrates the economics and marketing literature and presents a detailed analysis of the policies of four firms in order to i specify the variety of motivations for quantity discounts ii provide guidelines to managers in designing quantity discount schedules and iii set out the most fruitful directions for future research

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

capital services in u s agriculture concepts comparisons and the treatment of interest rates this paper begins with a review of the methods and assumptions used to measure capital service flows two data series on capital inputs in u s agriculture are briefly described and compared we show that measures of capital services are sensitive to the treatment of interest rates notably the use of fixed versus variable market rates significantly affects measures of the quantity and productivity of agricultural capital in the united states we conclude that when calculating capital usage in u s agriculture the use of a fixed interest rate generates more plausible estimates than the use of an annual market rate

price discrimination on booking time abstract even if consumers are forward looking and free to choose when to purchase a firm can price discriminate on booking time if consumers learn their valuations at different times and consumers who learn later have higher valuations the model is related to our work on optimal screening with returns contracts akan ata and dana 1 but here we consider a simpler binary valuation distribution and consider more realistic consumer learning assumptions the main contribution is to show that the profitability of screening on time is robust to relaxing the assumption that consumers learn instantaneously in addition to analyzing a bad news model in which information arrives gradually we characterize a general bound on consumer optimism that guarantees that the instantaneous learning results are robust

operations research in inventory management a review and critique the objectives of inventory management including the relevant related costs are examined in this paper a brief review of standard problems that have been effectively solved is presented however we point out that a serious gap exists between theory and practice in many organizations suggestions are made for bridging this gap finally a list is provided of a number of research problems whose implementable solution would have a major beneficial impact on the practice of inventory management

is the market for mortgage backed securities a market for lemons this paper models and provides empirical evidence for the quality of assets that are securitized through bankruptcy remote special purpose vehicles spvs the model predicts that assets sold to spvs will be of lower quality lemons compared to assets that are not sold to spvs we find strong empirical support for this prediction using a comprehensive data set of sales of mortgage backed securities freddie mac participation certificates or pcs to spvs over the period 1991 through 2002 valuation estimates based on a structural two factor model indicate that pcs sold to spvs are on average valued 0 39 lower per 100 of face value relative to pcs not so sold for the four largest coupon groups in our full sample of freddie mac pcs we find a lemons spread of 4 6 basis points in terms of yield to maturity and this spread accounts for 13 45 of the overall prepayment spread of these securities jel d82 g13 g14 g21

the structure of u s agricultural technology 1910 78 this paper utilizes 1910 78 time series data and a single product aggregate translog profit function to measure the structure of u s agricultural technology duality relations are used to devise a multifactor measure of biased technical change a measure of nonhomotheticity is introduced which indicates the effects scale change has had on aggregate cost shares the empirical analysis finds that different nonhomothetic technologies characterized the prewar and postwar periods differing technical change biases are consistent with relative price trends during the two periods showing that the long run structure of u s agricultural technology has been consistent with the hayami ruttan induced innovation theory

managing capacity in tightly constrained systems abstract many make to order firms face total expected demand in excess of available capacity this is particularly true in the short range for capital intensive firms such as those in the flow process industry firms making short life cycle products such as those in high fashion apparel industry and printing shops in such situations the manager is left with the difficult task of allocating the available capacity between competing classes of products and or customers at the same time the manager is faced with the challenge of achieving delivery dependability and speed in order to stay competitive in this paper i describe the problem contrast it with a class of problems known as perishable asset revenue management problems review recent literature that presents alternative approaches for managing capacity such as capacity rationing improved coordination mechanisms and subcontracting and discuss fruitful avenues for future research

testing the induced innovation hypothesis an error correction model of south african agriculture abstract this paper applies cointegration techniques to a model of induced innovation based on the two stage constant elasticity of substitution ces production function this approach results in direct tests of the inducement hypothesis which are applied to data for south african commercial agriculture for the period 1947 1991 south african data is used because the policy changes have been substantial enough that the factor and price ratios have turning points rather than being monotonic the time series properties of the variables are checked cointegration is established and an error correction model ecm constructed allowing factor substitution to be separated from technological change finally the ecm formulation is subjected to causality tests which show that both the factor price ratios and r d and extension expenditures are granger prior to the factor saving biases of technological change thus each stage of the analysis corroborates the inducement hypothesis however straightforward price inducement is only part of the explanation of changes in factor ratios policy induced innovation in response to tax concessions and subsidised credit is also present

equilibrium price dispersion under demand uncertainty the roles of costly capacity and market structure when capacity is costly and prices are set in advance firms facing uncertain demand will sell output at multiple prices and limit the quantity available at each price i show that the optimal price strategy of a monopolist and the unique pure strategy nash equilibria of oligopolists both exhibit intrafirm price dispersion moreover as the market becomes more competitive prices become more dispersed a pattern documented in the airline industry while generating similar predictions the model differs from the revenue management literature because it disregards market segmentation and fare restrictions that screen customers

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

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

revenue management without forecasting or optimization an adaptive algorithm for determining airline seat protection levels we investigate a simple adaptive approach to optimizing seat protection levels in airline revenue management systems the approach uses only historical observations of the relative frequencies of certain seat filling events to guide direct adjustments of the seat protection levels in accordance with the optimality conditions of brumelle and mcgill 1993 stochastic approximation theory is used to prove the convergence of this adaptive algorithm to the optimal protection levels in a simulation study we compare the revenue performance of this adaptive approach to a more traditional method that combines a censored forecasting method with a common seat allocation heuristic emsr b

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

induced bias of technical change in agriculture the united states and japan 1880 1980 because of extreme differences in factor endowments and price ratios among factors between the united states and japan both countries have experienced sharply different patterns of factor use and productivity growth in agriculture for the past 100 years of modern economic growth in this study the method of testing the hicksian hypothesis of induced innovation was developed using the two level ces production function the model was applied to the historical data of u s and japanese agricultural development for 1880 1980 the results were consistent with the hypothesis that different patterns of technical change in the two countries were induced by differences in the levels and the movements in relative factor prices

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

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 nonparametric approach to multiproduct pricing developed by general motors gm the auto choice advisor website http www autochoiceadvisor com recommends vehicles to consumers based on their requirements and budget constraints through the website gm has access to large quantities of data that reflect consumer preferences motivated by the availability of such data we formulate a nonparametric approach to multiproduct pricing we consider a class of models of consumer purchasing behavior each of which relates observed data on a consumers requirements and budget constraint to subsequent purchasing tendencies to price products we aim at optimizing prices with respect to a sample of consumer data we offer a bound on the sample size required for the resulting prices to be near optimal with respect to the true distribution of consumers the bound exhibits a dependence of o n log n on the number n of products being priced showing thatin terms of sample complexitythe approach is scalable to large numbers of products with regards to computational complexity we establish that computing optimal prices with respect to a sample of consumer data is np complete in the strong sense however when prices are constrained by a price ladderan ordering of prices defined prior to price determinationthe problem becomes one of maximizing a supermodular function with real valued variables it is not yet known whether this problem is np hard we provide a heuristic for our price ladder constrained problem together with encouraging computational results finally we apply our approach to a data set from the auto choice advisor website our analysis provides insights into the current pricing policy at gm and suggests enhancements that may lead to a more effective pricing strategy

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

induced innovation in u s agriculture time series direct econometric and nonparametric tests the hypothesis of induced innovation is tested for u s agriculture using a high quality state level panel data set and three disparate testing techniques time series direct econometric and nonparametric we find little support for the hypothesis that conclusion is robust across testing techniques however as with all empirical tests of this hypothesis conducted to date ours focus only on the demand side of the hypothesis the hypothesis could have been rejected simply because the marginal cost of developing and implementing input saving technologies for the relatively expensive inputs is greater than for the relatively cheap inputs copyright 2009 oxford university press

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

structural properties of markov modulated revenue management problems abstract the admission decision is one of the fundamental categories of demand management decisions in the dynamic model of the single resource capacity control problem the distribution of demand does not explicitly depend on external conditions however in reality demand may depend on the current external environment which represents the prevailing economic financial social or other factors that affect customer behavior we formulate a markov decision process mdp to maximize expected revenues over a finite horizon that explicitly models the current environment we derive some structural results of the optimal admission policy including the existence of an environment dependent thresholds and a comparison of threshold levels in different environments we also present some computational results which illustrate these structural properties finally we extend some of the results to a related dynamic pricing formulation

price guarantees in dynamic pricing and revenue management we present a new model for revenue management of product sales that incorporates both dynamic pricing and a price guarantee the guarantee provides customers with compensation if prior to a fixed future date the price of the product drops below a level specified at the time of purchase we consider the problem of simultaneously determining optimal dynamic price and guarantee policies for items from a fixed stock when demand depends both on the price and on the parameters of the price guarantee the model can be used for pricing any items with limited availability over a fixed time horizon we formulate this model as a discrete time optimal control problem prove the existence of its optimal solution explore some of the structural properties of the solution present lower bounding heuristics for solving the problem and report numerical results

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

on optimal service capacity allocation policy in an advance selling environment in continuous time abstract based on some general reasonable assumptions this paper employs the techniques of calculus of variations and optimal control theory to derive 10 main propositions associated with a service provider who aims at maximizing the present value of revenues profits over a planning horizon in continuous time employing an aggregate pricing response function that is dependent on excess capacity and a convex service cost formulation the results show that i for a zero discount rate and unanticipated competitive entry units of service capacity are allocated evenly over time ii for a zero discount rate and anticipated competitive entry units of allocated service capacity are increasing over time iii for a positive discount rate and unanticipated competitive entry units of allocated service capacity are decreasing over time and iv for a positive discount rate and anticipated competitive entry units of allocated service capacity are increasing over time or are decreasing at first then increasing later in addition the questions of how deep a service firm should advance sell whether advance selling is optimal in continuous time and whether excess capacity could be an optimal strategy have been addressed furthermore related sensitivity analyses are performed and endpoint constraints together with alternative shapes of the service cost function are discussed the managerial implications of the study s results have been demonstrated

an analysis of the source and nature of technical change the case of u s agriculture this paper proposes a methodology to investigate the process of technical change with a focus on the dynamic effects of r d investments on productivity and on the induced innovation hypothesis for both inputs and outputs the approach builds on a nonparametric representation of the underlying technology an application to u s agriculture is presented by distinguishing between private and public r d investments the analysis provides useful insights into the source and the dynamic nature of technical progress

an integrated product planning model for pricing and bundle selection using markov decision processes and data envelope analysis abstract when bundling products during the product planning stage there are a number of possible combinations that can be offered to customers consider a firm that offers n distinctive products then there are 2 n n 1 possible bundling combinations now if we wish to make pricing and bundle selection decisions keeping in my mind limited inventory and a finite time horizon then the size of the state space could be very large and finding an optimal solution could be impossible to tackle this issue we formulate an integrated model that utilizes a markov decision process and data envelope analysis bundle selections are made using data envelope analysis in each decision epoch once the efficient bundles are selected they are priced by solving a markov decision process using dynamic programming numerical examples are solved to exhibit the model s potential in solving real world problems

research note overselling with opportunistic cancellations in many business sectors such as airlines hotels trucking and media advertising customers arrivals and willingness to pay are uncertain managers must decide whether to quote a price low enough to guarantee early sales or to quote a higher price and risk that some units remain unsold in allocating capacity they face a trade off between two types of potential losses 1 yield loss selling at a low price and losing a better price later and 2 spoilage loss waiting in vain to sell at a high price and losing the opportunity of an earlier low price offer yield loss means that consumers who value the product most do not get to use it and spoilage loss means that valuable products are wasted because no consumers get to use them sellers typically hedge against the risk of spoilage loss by selling some units early at low prices and against the risk of yield loss by blocking some units in hope of selling them later at a high price in this paper we show that the use of overselling with opportunistic cancellations can increase expected profits and improve allocation efficiency under this strategy the seller deliberately oversells capacity if high paying consumers show up even when capacity is already fully booked the seller then cancels the sale to some low paying customers while providing them with appropriate compensation we derive a new rule to optimally allocate capacity to consumers when overselling is used and show that overselling helps limit the potential yield and spoilage losses yield loss is reduced because the seller can capture more high paying customers by compensating low paying customers who give up their right to the product spoilage loss is reduced because the compensation decreases the price spread perceived by the seller and as a result the seller is less anxious to speculate and block units overselling with opportunistic cancellations assures that the product will be sold to consumers who value it most this means that everybody wins and resources are allocated more efficiently than in conventional selling