bank spread with uncertain deposit level and risk aversion abstract this paper derives a model of the banking firm under uncertainty and risk aversion the selection of the bank s optimal spread between loan and deposit rates is emphasized the model s results provide some implications for bank asset quality capital regulation and deposit insurance for example it is shown that increases in the level of equity capital tend to increase the bank s spread under dara this implies an improvement in bank asset quality on the other hand as the deposit supply function becomes more volatile the bank s spread narrows which implies a decline in the quality of the bank s assets

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

on the determinants of bank interest margins under credit and interest rate risks abstract this paper explores the determinants of optimal bank interest margins based on a simple firm theoretical model under multiple sources of uncertainty and risk aversion the model demonstrates how cost regulation credit risk and interest rate risk conditions jointly determine the optimal bank interest margin decision we find that the bank interest margin is positively related to the bank s market power to the operating costs to the degree of credit risk and to the degree of interest rate risk an increase in the bank s equity capital has a negative effect on the spread when the bank faces little interest rate risk the effect of rising interbank market rate on the spread is ambiguous and depends on the net position of the bank in the interbank market our findings provide alternative explanations for the empirical evidence concerning bank spread behavior

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

dynamic pricing with real time demand learning in many service industries the firm adjusts the product price dynamically by taking into account the current product inventory and the future demand distribution because the firm can easily monitor the product inventory the success of dynamic pricing relies on an accurate demand forecast in this paper we consider a situation where the firm does not have an accurate demand forecast but can only roughly estimate the customer arrival rate before the sale begins as the sale moves forward the firm uses real time sales data to fine tune this arrival rate estimation we show how the firm can first use this modified arrival rate estimation to forecast the future demand distribution with better precision and then use the new information to dynamically adjust the product price in order to maximize the expected total revenue numerical study shows that this strategy not only is nearly optimal but also is robust when the true customer arrival rate is much different from the original forecast finally we extend the results to four situations commonly encountered in practice unobservable lost customers time dependent arrival rate batch demand and discrete set of allowable prices

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

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

game theoretic pricing models in hotel revenue management an equilibrium choice based conjoint analysis approach abstract this paper explores a game theoretically founded approach to conjoint analysis that determines equilibrium room rates under differentiated price competition in an oligopolistic hotel market competition between hotels is specified in terms of market share functions that can be estimated using multinomial logit models of consumer choice the approach is based on choice based conjoint analysis that permits the estimation of attributes weights part worths for an additive utility formulation of the utility function from this room rates that equilibrate the market conditioned on the differences in services and facilities offered by competing hotels can be determined the approach is illustrated by an example

service escape profiting from customer cancellations this paper explores the benefits of letting customers escape from prepurchased service contracts by offering refunds for cancellations we show that such a policy creates opportunities for multiple selling in a capacity constrained service i e collecting cancellation fees from advance buyers who cancel and then reselling the freed slots the better the alternative that motivates a cancellation the more profitable is a refund for cancellations policy compared with a no refund policy that locks in customers in contrast to previous research on money back guarantees for durable goods we show that offering refunds for service cancellations can be profitable 1 without charging a higher price compared with a no refund policy and 2 even when advance buyers would be willing to abandon the service for no refund also service providers should decrease rather than increase the customer hassle cost of cancellations our research also suggests a new profit advantage of advance selling i e capturing some of the consumer added surplus created when customers find new alternatives and are therefore willing to pay a fee to terminate the prepurchased contract finally yield management research typically assumes exogenous no shows by advance buyers we suggest that offering refunds for cancellation reduces the need to reserve capacity for high paying customers and improves capacity utilization

measuring rents and interest rate risk in imperfect financial markets the case of retail bank deposits traditional measures of interest rate risk assume that prices of financial assets and liabilities are set in perfectly competitive markets however evidence suggests that many retail financial markets do not follow the competitive paradigm in this paper we employ a general contingent claims framework to value rents earned by banks in demandable retail deposit markets our analysis provides a natural and economically meaningful measure of interest rate risk for these imperfectly competitive markets using monthly survey data on now accounts and mmdas we estimate the value of retail deposit rents and deposit durations for more than 200 commercial banks

the determinants of bank interest margins theory and empirical evidence this paper has developed a model of bank margins or spreads in which the bank is viewed as a risk averse dealer it was demonstrated that an interest spread or margin would always exist and that this was the result of transactions uncertainty faced by the bank moreover it was shown that this pure spread depended on four factors the degree of managerial risk aversion the size of transactions undertaken by the bank bank market structure and the variance of interest rates the model implied that liability and asset structures had to be analyzed together since they were directly interrelated through transactions uncertainty it was shown that because of this transactions uncertainty hedging behavior was perfectly rational within an expected utility maximizing framework extending the model from a structure with one kind of loan and deposit to loans and deposits with many maturities should lead to further interesting insights into margin determination especially as portfolio effects may become apparent

the impact of dynamic price variability on revenue maximization abstract the objective of this article is to analyze the effect of dynamic price variability on revenue maximization while dynamic pricing is a common practice in tourism this is the first comprehensive study on the relationship between price variability and revenue maximization within the framework provided by the literature on intertemporal price discrimination price fairness inventory controls and organizational culture this research proposes and applies a new hedonic revenue model on a sample of 21 687 observations the findings suggest that higher dynamic price variability leads to higher hotel revenues strategic room unavailability and review rating also exert a clear positive revenue impact overall the benefits from charging different prices for the same service intertemporal price discrimination and limiting the number of units available before the demand is known inventory control outweigh the potential negative effects of price unfairness and organizational culture the paper concludes by providing actionable levers for hospitality managers

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

combined effects of capacity and time on fares insights from the yield management of a low cost airline abstract based on two strands of theoretical research this paper provides new evidence on how fares are jointly affected by in flight seat availability and purchasing date as capacity based theories predict it emerges that fares monotonically and substantially increase with flight occupancy after controlling for capacity utilization our analysis also supports time based theories indicating a u shaped temporal profile over a two month booking period as well as a sharp increase in fares in the two weeks prior to departure

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

bank commercial loan markets and the role of market structure evidence from surveys of commercial lending abstract this paper seeks to test two tenets that underlie the current practice of antitrust analysis in banking the first is the view that bank commercial loan markets are local in nature and the second is the view that banks in more concentrated markets are more likely to engage in some form of noncompetitive behavior tests of both of these tenets are conducted using an extensive set of loan specific survey information not previously employed to address these issues results consistent with the existence of local banking markets and the dominance of competitive differences as an explanation for observed differences in loan rates are found

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

the impact of loan prepayment risk and deposit withdrawal risk on the optimal intermediation margin abstract numerous studies have analyzed how a bank s intermediation margin varies with respect to such factors as credit quality funding risk bank capital deposit insurance and other factors however these studies ignore the potential that loans tend to prepay if interest rates decline and deposits tend to be withdrawn if interest rates rise taking this very fundamental fact into account we derive optimal loan rates and deposit rates when the bank is subject to loan prepayments and deposit withdrawals among other things we find that greater volatility of interest rates tends to increase the margin the strength of the correlation between the level of interest rates and the propensity to prepay loans withdraw deposits also plays an interesting role

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

contingent pricing to reduce price risks the price for a product may be set too low causing the seller to leave money on the table or too high driving away potential buyers contingent pricing can be useful in mitigating these problems in contingent pricing arrangements price is contingent on whether the seller succeeds in obtaining a higher price within a specified period we show that if the probability of obtaining the high price is not too high sellers profit from using contingent pricing while economic efficiency increases the optimal contingent pricing structure depends on the buyer s risk attitude a deep discount is most profitable if buyers are risk prone a consolation reward is most profitable if buyers are risk averse to motivate buyers to participate in a contingent pricing arrangement the seller must provide sufficient incentives consequently buyers also benefit from contingent pricing in addition because the buyers with the highest willingness to pay get the product contingent pricing increases the efficiency of resource allocation

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

learning about monetary policy rules abstract we study macroeconomic systems with forward looking private sector agents and a monetary authority that is trying to control the economy through the use of a linear policy feedback rule we use stability under recursive learning a la evans and honkapohja learning and expectations in macroeconomics princeton university press princeton new jersey 2001 as a criterion for evaluating monetary policy rules in this context we find that considering learning can alter the evaluation of alternative policy rules

are central banks projections meaningful central banks projections i e forecasts conditional on a given interest rate path are often criticized on the grounds that their underlying policy assumptions are inconsistent with the existence of a unique equilibrium in many forward looking models the present paper describes three alternative approaches to constructing projections that are not subject to that criticism using a standard new keynesian model as a reference framework yet and even though they imply an identical path for the interest rate the three approaches are shown

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

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

a time series cross section analysis of the determinants of australian trading bank loan deposit interest margins 1962 1981 abstract a theoretical model of the determination of trading bank interest margins based on the hedging theory of interest margin determination is tested on time series cross section data of australian trading banks generally the results are consistent with that theory that is there exists a stable non linear relationship between australian trading bank net loan deposit interest margins and measures of market power degree of absolute risk aversion and to interest rate uncertainty furthermore the shift from business sector to personal sector loan and deposit business is associated with increased bank interest margins

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

airline pricing under different market conditions evidence from european low cost carriers abstract traditional theories of airline pricing maintain that fares monotonically increase as fewer seats remain available on a flight this implies a monotonically increasing temporal profile of fares in this paper we exploit the presence of drops in offered fares over time as an indicator of an active yield management intervention by two main european low cost carriers and measure its effectiveness we find that reduction of the offered airfare by one standard deviation raises a flight s load factor on average by 2 7 percent a measure unaffected by the intensity of competition in a route furthermore yield management interventions are less effective the higher the share of leisure holiday and visiting friends and relatives traffic on the route this result runs counter to the common perception of leisure passengers being more responsive to price changes

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

optimal pricing and quantity of products with two offerings this paper analyzes the decision of a firm offering two versions of a product a deluxe and a regular while both products satisfy the same market the deluxe version is sold at a high price relative to its cost and is aimed at the high end of the demand curve the regular version is sold at a low price relative to its cost and is targeted to customers at the low end of the demand curve this two offering strategy is especially popular with book publishers where a paperback book is introduced some time after the hardbound version is introduced the time between the introduction of the two versions of the product is accompanied by a downward shift in the demand curve due to customers losing interest in the product or satisfying their demand from a secondary used market we solve a profit maximization model for a firm using a two offering strategy the model is solved for linear and exponential deterioration in demand which is assumed to be deterministic also a model with linear deterioration in demand which is assumed to be stochastic is solved the results indicate that substantial improvements in profit can be obtained by using the two offering strategy numerical sensitivity analysis and examples are used to illustrate the results

optimal pricing and advertising policies for a one time entertainment event abstract we consider the problem of pricing and advertising a one time entertainment event three pricing policies are characterized and contrasted namely dynamic price dp constant price cp and two market price tmp in this last scenario the selling season is composed of a regular price period and a last minute price period with the switching date between the two markets being determined endogenously we show that the price is monotonically increasing over time in the dp scenario and that the last minute price is larger than the regular price in the tmp scenario in all three cases advertising is non increasing over time which is a feature often encountered in finite horizon dynamic optimization advertising models finally we compute the cost of simplification which is the difference in profits under dynamic pricing and constant pricing among other results we obtain that this loss is independent of the market size and increasing in the number of available tickets

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

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

managing capacity through reward programs rewarding customers with own products or services has become an increasingly popular practice across a spectrum of industries such as airlines hotels and telecommunication in these service industries firms face demand uncertainty and strict short term capacity constraint when the market demand is low firms hold excess capacities that would lead to intense price competition in this paper we study the adoption and design of reward programs in the context of capacity management we demonstrate that it is optimal for firms to offer capacity rewards when the market demand varies from one period to the other by offering the reward programs firms can effectively reduce available capacities when the market demand is low and hence credibly show their unwillingness to undersell such a commitment can encourage their competitors to set their prices high when firms provide reward programs if a firm sets a higher price than the other and sells less today in the future the firm can benefit from the other firm s larger reduction in available capacity through rewards thus reward programs also provide additional incentives for firms to set higher current prices finally since reward programs can add flexibility in adjusting the available capacities to the market demand firms increase the size of regular capacities with reward programs

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

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

modeling the banking firm a survey this paper reports on the status of the literature on micro bank modeling and assesses our understanding of the banking firm s optimal behavior this is no mean task for much has been written on banking broadly defined over the past couple of decades the review is developed in pieces each major subproblem is outlined and the analysis used to deal with the issue explicated this is not the best way to summarize the development of a field it should be immediately recognized one would prefer to have a smooth continuum of development moving the frontier of knowledge evenly through time and across subareas yet this is rarely the way a field develops more likely individual questions attract attention and are the subjects of a substantial number of contributions after a time the field moves on to the new area of interest the banking field is no exception before embarking upon the review however a couple of lines should be devoted to previous attempts there have been essentially three first pyle 1972 analyzes the uncertainty portfolio models at a time when little existed in the literature and hence one finds the review a bit vague and sketchy baltensperger s contributions 1978 1980 are the next serious and rather extensive reviews the quality of these

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

overselling in a competitive environment boon or bane in this paper we study the practice of overselling in a competitive environment where late arriving consumers value the good higher than early arriving ones but the former s arrival is uncertain we show that overselling is a dominant strategy for the firms however it can lead to a prisoners dilemma situation in which all firms are worse off overselling we further show that only when demand from the late consumers far exceeds the supply and there is a sufficiently high profit margin from reselling does overselling result in a pareto dominant outcome for the firms

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

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

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

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

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

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

the role of collateral in a model of debt renegotiation this paper studies the effect of debt renegotiation on the design of optimal loan arrangements in a model of borrowing and lending with asymmetric information renegotiation may occur because bankruptcy involves costly asset liquidation which is ex post inefficient the author shows that the extent of the entrepreneur s liabilities in the optimal loan contract depends upon the creditor s commitment to impose bankruptcy should default ever occur a limited liability arrangement is optimal whenever the creditor is precommited not to forgive any portion of the outstanding debt otherwise debt may efficiently be secured by outside collateral copyright 1994 by ohio state university press

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

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

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

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

optimal bank interest margin under capital regulation and deposit insurance this paper examines the relationships among capital regulation deposit insurance and the optimal bank interest margin in a model where loan losses are the source of uncertainty changes in capital regulation or deposit insurance premiums have direct effects on the bank s interest margin an increase in bank capital requirement or in deposit insurance premiums results in a reduced interest margin under nonincreasing risk aversion comparative static analysis also explores the relation between asset quality and interest margin it is shown that a mean preserving spread of the distribution of loan losses results in a reduced margin

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

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

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