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 value of tax shields is equal to the present value of tax shields abstract fernandez 2004b the value of tax shields is not equal to the present value of tax shields journal of financial economics 73 145 165 argues that the present value effect of the tax saving on debt cannot be calculated as simply the present value of the tax shields associated with interest this contradicts standard results in the literature it implies that even though the capital market is complete value additivity is violated as a consequence adjusted present value formulae of a standard sort cannot be used also fernandez s argument implies that the value of the tax saving differs from conventional estimates by a considerable amount we reconcile fernandez s results with standard valuation formulae for the tax saving from debt we show that as one would expect the value of the debt tax saving is the present value of the tax savings from interest the apparent violation of value additivity in the fernandez paper comes from mixing the miles and ezzell and miller and modigliani leverage policies

the value of tax shields is not equal to the present value of tax shields abstract the value of tax shields is the difference between the present values of two different cash flows each with their own risk the present value of taxes for the unlevered company and the present value of taxes for the levered company for constant growth companies the value of tax shields in a world with no leverage cost is the present value of the debt times the tax rate times the unlevered cost of equity discounted at the unlevered cost of equity this result arises as the difference of two present values and does not mean that the appropriate discount for tax shields is the unlevered cost of equity

weather and intraday patterns in stock returns and trading activity abstract we examine the relation between weather in new york city and intraday returns and trading patterns of nyse stocks while stock returns are found to be generally lower on cloudier days cloud cover has a significant influence on stock returns only at the market open there are significantly more seller initiated trades when there is more cloud cover at the market open which is consistent with the return results cloudy skies are associated with higher volatility and less market depth over the entire trading day finally cloud cover is not significantly correlated with spread measures and turnover ratios the findings overall suggest that weather has a significant influence on investors intraday trading behavior

a simple approach for assessing the cost of system nervousness abstract a well known problem in coordinating supply chain inventories is that replenishment decisions are revised due to stochastic demands this issue is often referred to as system nervousness the literature distinguishes between two types of nervousness setup oriented and quantity oriented it is widely accepted that cost of nervousness is difficult to measure we argue that this cost can be evaluated by means of three well established inventory control strategies static uncertainty dynamic uncertainty and static dynamic uncertainty these strategies reflect extreme cases with regard to the setup and the quantity oriented nervousness and provide a simple yet an objective measure to assess the cost of system nervousness our results are of practical importance we highlight that the setup oriented nervousness which is considered to be the most critical in practice can be eliminated with a minor cost penalty this is however not the case for the quantity oriented nervousness

optimal dynamic pricing for expanding networks this paper analyzes the dynamic pricing decision of a monopolist marketing a new product or service whose consumption value increases with the expansion of the network of adopters we characterize an optimal pricing strategy which maximizes the present value of the monopolist s profits subject to the dynamics of the demand for network access these dynamics depend among other factors on the current price and consumer anticipations about future network growth we examine the effects of changes in the growth anticipations and the discount rate on the optimal equilibrium access price and network size it is shown that higher growth anticipations and a lower discount rate result in a lower equilibrium price and a larger network

managing online auctions current business and research issues the internet s computational power and flexibility have made auctions a widespread and integral part of both consumer and business markets though online auctions are a multi billion dollar annual activity with a growing variety of sophisticated trading mechanisms scientific research on them is at an early stage this paper analyzes the current state of management science research on online auctions it develops a broad research agenda for issues such as the behavior of online auction participants the optimal design of online auctions the integration of auctions into the ongoing operation of firms and the use of the data generated by online auctions to inform future trading mechanisms these research areas will draw from applied and theoretical work spanning management science economics and information systems

is it the weather response abstract kamstra kramer and levi kkl in their comment seem to miss the main point of our paper many things are correlated with the seasons so it is difficult to distinguish between them when we try to explain the well known summer winter pattern in stock returns finding an isolated seasonal affective disorder sad effect without proper control variables does not disprove our point but strengthens it to sidestep all of the issues they raise and take our point to the extreme we show using plain vanilla regressions that the seasonal stock market pattern they attribute to sad can also be explained by variables like ice cream consumption or airline travel the new variations of sad variables onset and incidence kkl propose in their recent work for north america are even more problematic than the original sad variables we find that these new sad proxies are not significant in countries where according to kkl they should be canada and the united states

monopolist pricing with dynamic demand and production cost this paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream the interdependency of cost and demand on cumulative production makes the problem inherently dynamic cost is assumed to be declining with cumulative production learning curve effect while demand is a function of price and cumulative sales representing word of mouth and saturation effects the paper addresses this problem in a general framework that includes several previous results as special cases and provides new insights in other situations while the learning curve and word of mouth effect cause prices to be lower than the price that maximizes immediate revenues the saturation factor has the opposite effect the price path over time is affected by these factors and the interest rate we characterize the price path under several different situations and interpret the results for policy guidelines

on the benefits of pooling in production inventory systems we study inventory pooling in systems with symmetric costs where supply lead times are endogenously generated by a finite capacity production system we investigate the sensitivity of the cost advantage of inventory pooling to various system parameters including loading service levels demand and production time variability and structure of the production system the analysis reveals differences in how various parameters affect the cost reduction from pooling and suggests that these differences stem from the manner in which the parameters influence the induced correlation between lead time demands of the demand streams we compare these results with those obtained for pure inventory systems where lead times are exogenous we also compare inventory pooling with several forms of capacity pooling

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

comparison of s s and s nq inventory control rules with respect to planning stability abstract the application of a rolling horizon planning framework in inventory control causes different order release decisions in successive planning cycles these lead to the so called planning system nervousness in this paper for a single stage inventory system with arbitrary stochastic demand it is shown analytically how the setup oriented planning stability concerning deviations of planned orders in all periods of a given stability horizon is influenced by the use of s s and s nq control rules it turns out that the reorder point s does not affect stability whereas the lot size determining parameters s s and q as well as the level of uncertainty have a considerable impact the paper is concluded with directions for further research

the slicing approach to valuing tax shields abstract the literature develops the theoretical rationale for the value of tax shields vts on the following misguided basis it uses required rate of return on assets or wacc as the discount rate for capitalization it uses expected rate of return on assets roa or roi as a proxy for wacc and it is not aware of 1 the influence of the difference between expected rate of return on equity and required rate of return on equity rroe on vts 2 the fact that rroe is equity normal profit which is not measurable 3 the economic content of the weight attached to the vts capacity and 4 the co definition of tax shield and leverage return this paper takes tax shields and leverage return as a system and provides a knife interest rate roi cost price to slice the vts capacity into earned vts and unearned vts earned vts is vts unearned vts is the value of leverage return because leverage return is tax payable

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

is it the weather comment this comment discusses some errors in a recent paper by jacobsen and marquering jacobsen b marquering w 2008 is it the weather journal of banking and finance 32 4 526 540 in which the authors challenge our previous finding that stock market returns exhibit seasonal patterns consistent with the influence of seasonal affective disorder on investor risk aversion we find that we cannot replicate the authors findings even after corresponding with them furthermore we document several problems with their methodology including misspecification of their economic model misspecification of their econometric model and use of inappropriate data while we agree that seasonal affective disorder is not an explanation for all variation in equity markets we do maintain that careful analysis leads to economically and statistically significant evidence of the effect we originally documented

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

does the law of one price hold in international financial markets evidence from tick data abstract this paper investigates the validity of the law of one price lop in international financial markets by examining the frequency size and duration of inter market price differentials for borrowing and lending services one way arbitrage using a unique data set for three major capital and foreign exchange markets that covers a period of more than seven months at tick frequency we find that the lop holds on average but numerous economically significant violations of the lop arise the duration of these violations is high enough to make it worthwhile searching for one way arbitrage opportunities in order to minimize borrowing costs and or maximize earnings on given funds we also document that such opportunities decline with the pace of the market and increase with market volatility

periodic pricing of seasonal products in retailing this paper studies intertemporal pricing policies when selling seasonal products in retail stores we first present a continuous time model where a seller faces a stochastic arrival of customers with different valuations of the product for this model we characterize the optimal pricing policies as functions of time and inventory we use this model as a benchmark against which we compare more realistic models that consider periodic pricing reviews we show that the structure of the optimal pricing policies in this case is consistent with the procedures observed in practice retail stores successively discount the product during the season and promote a liquidation sale at the end of the planning horizon we also show that the loss experienced when implementing periodic pricing reviews instead of continuous policies is small when the appropriate number of reviews is chosen several interesting economic insights emerge from our analysis for example uncertainty in the demand for new products leads to higher prices larger discounts and more unsold inventory finally we study the effect of announced discount policies on prices and profits we show that stores that have adopted this type of strategy usually set prices such that with high probability the merchandise is sold during the first periods and the largest discounts rarely take place

the timing of sales this paper presents a model of intertemporal price discrimination a fixed number of sellers produce a homogeneous good consumers with different preferences enter the market in each period and leave when they make a purchase the sellers typically vary their prices over time charging a high price in most periods but occasionally cutting the price to sell to a large group of customers with a low reservation price in some equilibria all stores lower their price at the same time and to the same level

intertemporal price discrimination and sales strategy under incomplete information this article examines intertemporal price variations to provide a theoretical explanation for them when firms have only incomplete information about consumers reservation prices for the commodity we contend that some intertemporal price variations can result from attempts by firms to discriminate among consumers we demonstrate that such price discrimination is the optimal policy for a seller if consumers have a higher time discount rate than producers

optimal price skimming by a monopolist facing rational consumers this paper considers the intertemporal pricing problem for a monopolist marketing a new product the key feature differentiating this paper from the extant management science literature on intertemporal pricing is the assumption that consumers are intertemporal utility maximizers a subgame perfect nash equilibrium pricing policy is characterized and shown to involve intertemporal price discrimination we compare this policy to the optimal policy for a monopolist facing myopic consumers and find that for any given state prices are always lower with rational consumers than with myopic consumers for plausible parameter values the assumption of consumer rationality can be shown to lead to large differences in optimal prices moreover if a monopolist facing rational consumers implements the optimal myopic consumer pricing policy profits can be significantly less than if the monopolist follows the equilibrium pricing policy for rational consumers

chapter 11 pricing models in marketing publisher summary this chapter brings together a set of diverse efforts in the recent literature on the modeling of price decisions and related questions in marketing there has been an impressive growth in the array of topics investigated in the literature various trends in the development of pricing models are evident from the foregoing review first one trend has been to develop theoretical models to describe observed pricing strategies in the marketplace and to derive conditions under which certain strategies are optimal this trend is clearly evident when one considers the area of dynamic pricing models another trend is an attempt to develop pricing models in which certain aspects of consumer behavior e g asymmetric response to price increases versus price decreases are incorporated this development is quite recent and does offer a large potential a third dominant direction is the use of game theoretic models for developing equilibrium pricing strategies

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

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

combinatorial auction design combinatorial auctions have two features that greatly affect their design computational complexity of winner determination and opportunities for cooperation among competitors dealing with these forces trade offs between desirable auction properties such as allocative efficiency revenue maximization low transaction costs fairness failure freeness and scalability computational complexity can be dealt with algorithmically by relegating the computational burden to bidders by maintaining fairness in the face of computational limitations by limiting biddable combinations and by limiting the use of combinatorial bids combinatorial auction designs include single round first price sealed bidding vickrey clarke groves vcg mechanisms uniform and market clearing price auctions and iterative combinatorial auctions combinatorial auction designs must deal with exposure problems threshold problems ways to keep the bidding moving at a reasonable pace avoiding and resolving ties and controlling complexity

theoretical models of sales promotions contributions limitations and a future research agenda our objective in this paper is to review theoretical models of sales promotions we highlight the key contributions of these models discuss their limitations and outline an agenda for future research managerial questions examined in these models include some very fundamental issues such as why firms resort to the use of sales promotions in mature markets and why the use of sales promotions has increased dramatically during the last two decades also included in this review are models that address firm level strategic issues such as the allocation of dollars between advertising and sales promotions and the relative emphasis on trade promotions vis a vis consumer promotions we also review theoretical models that explain how consumers respond to price promotions and what type of sales promotion tools may be superior to others in a particular market the review concludes with a possible agenda for future research

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

value and capacity of tax shields an analysis of the slicing approach abstract correctly valuing tax shields has been a challenge in corporate valuation a recent study by liu 2009 introduces the slicing approach to separating the tax shield into the earned and unearned parts liu also shows that the mm results are wrong and claims that the slicing approach has finally resolved the issue of pricing tax shields thereby bringing closure to the topic however through careful analysis we refute liu s main claims and restore the mm results there are still open questions and the topic is not completely resolved as claimed in liu 2009

an investigation of setup instability in non stationary stochastic inventory systems in stochastic inventory systems unfolding uncertainties in demand lead to the revision of earlier replenishment plans which in turn results in an instability or so called system nervousness in this paper we provide the grounds for measuring system nervousness in non stationary demand environments and gauge the stability and the cost performances of r s and s s inventory policies our results reveal that both the stability and the cost performance of inventory policies are affected by the demand pattern as well as the cost parameters and the r s policy has the potential to replace the cost optimal s s policy for systems with limited flexibility

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