customer and retailer rebates under risk aversion abstract in a supply chain setting we analyze a manufacturer s customer and retailer rebates which are sales incentives offered to the end buyers and retailers respectively the performance of both rebates is influenced by the retailer s objective and response to the promotion due to his intermediary position in the channel earlier studies investigating rebates in distribution channels have traditionally assumed that the retailer is risk neutral with the objective of maximizing expected profits in our paper we consider a risk averse retailer we formally model risk aversion by adopting the conditional value at risk cvar decision criterion using a stochastic and effective price dependent demand we analyze the manufacturer s rebate amount decisions and the retailer s joint inventory and pricing decisions in a game theoretical framework we provide several structural properties of the objective functions and show monotonicity of the retailer s decisions in the degree of risk aversion for the case of retailer rebates we characterize the unique equilibrium and for the case of customer rebates we prove the existence of an equilibrium using numerical examples we provide further insights on the impact of risk aversion for example given an exogenous wholesale price we observe a threshold value on the retailer s risk aversion parameter below above which the manufacturer is better off with retailer rebates customer rebates implying that the manufacturer s preferred rebate type can be different depending on whether the retailer is risk neutral or sufficiently risk averse

airline choice switching costs and frequent flyer programmes switching costs are costs that customers face when switching from one firm to another in markets such as the airline market where repeated purchases are common switching costs may be substantial in this paper the switching costs are estimated for domestic airline routes in sweden between 1992 and 2002 in addition the determinants of these switching costs are tested for in particular to what extent factors such as frequent flyer programmes and flag carriers have an effect on switching costs a substantial switching cost is found although a large part of this calculated switching cost can be attributed to perceived quality differences it is also found that frequent flyer programmes contribute a non negligible part of the switching cost the paper ends with a brief discussion on the welfare consequences of switching costs where the connection between habit formation and switching costs is discussed

closed loop advertising strategies in a duopoly using the lanchester model to describe the dynamics of the market where two firms compete for customers by advertising we solve the problem of determining an optimal advertising strategy for maximum discounted profits we develop both open and closed loop strategies and explain the relationship between them using a new mathematical approach we prove that our closed loop solution is a global nash equilibrium the closed loop strategy is time variant and depends linearly on the actual market share the time variant coefficient incorporates the discount factor its computation requires the solution of a backward differential equation and a set of two nonlinear differential equations for an initial value problem the closed loop advertising expenditures are proportional to the open loop advertising expenditures and to the square of the competitor s actual market share this provides a very practical adaptive control rule that allows the manager to adjust the actual advertising expenditure and to deviate f

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

controlling measurement errors in models of advertising competition abstract commercial market research firms provide information on advertising variables of interest such as brand awareness or gross rating points that are likely to contain measurement errors this unreliability of measured variables induces bias in the estimated parameters of dynamic models of advertising consequently advertisers either under or overspend on advertising to maintain a desired level of brand awareness monte carlo studies show that the magnitude of bias can be serious when conventional estimation methods such as ordinary least squares and errors in variables are employed to obtain parameter estimates therefore the authors have developed two new approaches that either reduce or eliminate parameter bias using these methods advertisers can determine an unbiased optimal advertising budget even if advertising variables are measured with error the application of these methods to estimate the extent of measurement noise in empirical advertising data is illustrated

dynamic promotional budgeting and media allocation this paper address the managerial problem of promotional budgeting and media allocation in a dynamic competitive framework we develop an extended lanchester model that is able to analyze multi instrument promotion in an oligopoly the competitors each with a different initial position as well as economic value of the market share and communication effectiveness adopt the strategy of maximizing their net present value of discounted profits taking the other players actions into account the resulting differential game is solved using a novel method providing both the open loop strategy and the closed loop strategy for each firm we prove that our solution is a global nash equilibrium we develop a simple formula that when applied to an open loop strategy readily generates a feedback strategy we also show that for both open and closed loop strategies the proportion of the budget allocated to each instrument is invariant with time and depends only on instrument effectiveness we illustrate the results and provide several managerial rules and discuss their application in practice finally we show that our model favorably compares with other model in the literature in explaining actual data

optimal acquisition and remanufacturing policies for multi product remanufacturing systems abstract this paper studies an acquisition and remanufacturing problem in a market driven multi product remanufacturing system where the remanufacturer acquires multiple used products cores of highly variable quality under independently uncertain demand and carbon emissions regulation in order to balance between the environmental and economic benefit the problem is formulated as a nonlinear programming model in presence of the quality variability of cores and carbon tax scheme subject to budget and risk constraints since the average cost of the remanufactured products is independent of the remanufacturing quantity the model is then decomposed into two separated sub problems namely the remanufacturing problem and the acquisition problem in the remanufacturing problem the optimal remanufacturing policies including the optimal remanufacturing cost thresholds and the optimal remanufacturing rate are derived in the acquisition problem the optimal policies of core portfolio acquisition quantities and remanufacturing quantities can be derived the acquisition problem viewed as an extended multi product newsvendor problem mpnp is a convex optimization problem furthermore a two tier bisection method with polynomial computational complexity can be developed to obtain the optimal policies based on the karush kuhn tucker kkt conditions finally numerical experiments are provided to show the application of the model and the effect of the quality variability

interaction of pricing advertising and experience quality a dynamic analysis for certain goods or services the quality of the product can be assessed by customers only after consumption we determine the optimal time paths for pricing advertising and quality for a profit maximizing firm facing demand that is influenced both by this experience quality as well as by advertising in particular there may exist two optimal trajectories separated by an indifference threshold in which the firm has the same utility of converging to either of the two long run steady states or to put it in a nutshell the optimal mix of marketing instruments may lead to history dependence one implication is that there may be a market failure such that a government subsidy could help reach the steady state that is best for the economy in the sense of having greater sales and a higher quality product

the risk averse newsvendor problem under spectral risk measures a classification with extensions abstract we study the risk averse newsvendor problem by defining the objective function as a spectral risk measure we analyze the problem under different types of return formulations focusing on the impact of risk aversion and cost parameters on the optimal ordering decision we show that the monotonicity of the return function with respect to random demand determines the structural properties of the problem when the return function is monotone in demand realization optimal order quantity does not depend on the return margin but only on the overage and underage costs and it has a monotone relation to risk aversion however if return is non monotone in demand impact of risk aversion depends on the specific setting and it can also be non monotone additionally it is non increasing in the margin which leads to varying impact of selling price under distinct settings

stochastic linear programming games with concave preferences abstract we study stochastic linear programming games a class of stochastic cooperative games whose payoffs under any realization of uncertainty are determined by a specially structured linear program these games can model a variety of settings including inventory centralization and cooperative network fortification we focus on the core of these games under an allocation scheme that determines how payoffs are distributed before the uncertainty is realized and allows for arbitrarily different distributions for each realization of the uncertainty assuming that each player s preferences over random payoffs are represented by a concave monetary utility functional we prove that these games have a nonempty core furthermore by establishing a connection between stochastic linear programming games linear programming games and linear semi infinite programming games we show that an allocation in the core can be computed efficiently under some circumstances

outsourcing and capacity planning in an uncertain global environment firms employing offshore outsourcing strategies may face both exchange rate and demand uncertainties in this paper we show that the firms may benefit from operational option to switch production by keeping capacities with both domestic and foreign suppliers the value of the operational option increases as the exchange rate uncertainty or demand uncertainty increases in addition when the firms become risk averse they may use domestic capacity to hedge against offshore capacity as a result the firms may choose to hold local capacity even if it exhibits negative marginal contribution to the profit furthermore risk averse firms may keep more total capacity than risk neutral firms

modeling asymmetric competition the effects of the marketing actions of one brand can be distributed among its competitors market shares in a complex manner this paper presents and illustrates methods for modeling brand competition and brand strategies in markets where competitive effects can be differentially and asymmetrically distributed we discuss the empirical specification parameter estimation and competitive strategy implications of the models proposed price and advertising competition among eleven brands of an australian household product is used to illustrate the application of these procedures

optimal inventory decisions for a risk averse retailer when offering layaway abstract layaway allows economically disadvantaged budget constrained consumers to purchase expensive items through amortized payments and nominal program fees as opposed to using high interest financing options such as credit cards and payday loans we consider a risk averse retailer s ordering decisions when offering a layaway program we use the net loss and total loss functions found in the literature to determine a risk averse retailer s optimal order quantity under conditional value at risk cvar we next analyze the effects of the model parameters retailer s risk aversion the market default rate enrollment fee cancellation fee and so on on the optimal order quantity decisions we show that the optimal order quantity depends on different loss functions and different demand distribution functions further we show that as market default rate increases or the retailer becomes more risk averse then a rational retailer will not offer a layaway program

on sales effort and pricing decisions under alternative risk criteria abstract in the literature different risk criteria are proposed for risk averse decision making but it is often unclear which risk criteria should be used and what their differences may be this study investigates this problem when a risk averse make to order firm decides its pricing and sales effort two factors affecting demand we consider alternative risk criteria commonly used in the literature namely expected utility theory eut mean variance mv mean semideviation ms value at risk var conditional value at risk cvar and loss aversion la we find that all of these criteria lead to similar qualitative behaviors regarding how risk loss averse decisions deviate from risk neutral ones a particularly interesting result is that the form of demand randomness i e additive or multiplicative can completely reverse the effect of risk loss aversion in certain cases we also find that the risk aversion models i e eut mv ms var and cvar are essentially equivalent in inducing the same set of optimal solutions under adverse market states however loss aversion is a mild version of risk aversion in that the la model can only lead to a subset of the solutions generated by other models these results may not be valid for other applications such as the newsvendor pricing problem so we can conclude that the relationship between alternative risk criteria is case sensitive and should be evaluated more carefully

financial management in inventory problems risk averse vs risk neutral policies abstract in this work we discuss the effect of risk measure selection in the determination of inventory policies we consider an inventory system characterized by the loss function of luciano et al 2003 var as a risk measure for multi period static inventory models international journal of production economics 81 82 375 384 we derive the optimization problems faced by risk neutral quadratic utility mean absolute and cvar decision makers results show that while the global nature of the optimal policy is assured for risk coherent and risk neutral decision makers the convexity of the quadratic utility problem depends on the stochastic properties of demand we investigate the economic and stochastic determinants of the different policies this allows us to establish the conditions under which each type of decision maker is indifferent to imprecision in the distribution families finally we discuss the numerical impact of the choice of the risk measure by means of a multi item inventory the introduction of an approach based on savage scores allows us to offer a quantitative measurement of the similarity discrepancy of policies reflecting different risk attitudes

newsvendor solutions via conditional value at risk minimization abstract in this paper we consider the minimization of the conditional value at risk cvar a most preferable risk measure in financial risk management in the context of the well known single period newsvendor problem which is originally formulated as the maximization of the expected profit or the minimization of the expected cost we show that downside risk measures including the cvar are tractable in the problem due to their convexity and consequently under mild assumptions on the probability distribution of products demand we provide analytical solutions or linear programming lp formulation of the minimization of the cvar measures defined with two different loss functions numerical examples are also exhibited clarifying the difference among the models analyzed in this paper and demonstrating the efficiency of the lp solutions

endogeneity and simultaneity in competitive pricing and advertising a logit demand analysis in this article we use four data sets to provide a benchmark study of the effects of accounting for endogeneity and simultaneity in estimating marketing mix effects in a logit demand framework we compare the results obtained from accounting for endogeneity only to those from accounting for both endogeneity and simultaneity and in the latter case we allow for more general models of firm behavior to examine the consequences of imposing assumptions about the behavior of firms we find that accounting for both endogeneity and simultaneity not only affects the parameter estimates but also results in efficiency gains that affect the statistical significance of the estimates

technological learning and renewable energy costs implications for us renewable energy policy abstract this paper analyzes the relationship between current renewable energy technology costs and cumulative production research development and demonstration expenditures and other institutional influences combining the theoretical framework of learning by doing and developments in learning by searching with the fields of organizational learning and institutional economics offers a complete methodological framework to examine the underlying capital cost trajectory when developing electricity cost estimates used in energy policy planning models sensitivities of the learning rates for global wind and solar photovoltaic technologies to changes in the model parameters are tested the implications of the results indicate that institutional policy instruments play an important role for these technologies to achieve cost reductions and further market adoption

on modeling the advertising operations interface under asymmetric competition abstract using a market share attraction structure of advertising competition and following a supermodular game approach this article demonstrates for an asymmetric oligopoly the directional impact of changes in model parameters on the marketing controlled variables of all rivals advertising budgets and the operations controlled variables of all rivals ordered quantities importantly the various changes are examined analytically empirically and numerically in both non dominated and dominated asymmetric oligopolies in this regard the results indicate that firms in a dominated oligopoly one firm of market share larger than or equal to 50 behave differently compared to firms in a non dominated oligopoly each firm of market share less than 50 in response to changes in model parameters furthermore changes in model parameters are investigated in terms of their relative influential impact on a variety of equilibrium measures in this regard the findings indicate that for the analyzed model the marketing parameters exert much more influence on the equilibrium measures than the operations parameters additionally a change in the mode of competition from non cooperation oligopoly to cooperation joint ownership dictates that strong asymmetric firms of favorable marketing and operations parameters continue advertising but at lower levels and weak asymmetric firms of less favorable parameters cease advertising altogether

integrated operational and financial hedging with capacity reshoring abstract we consider a multinational corporation that employs capacity reshoring production switching and financial hedging to manage supply demand mismatches and currency risk we optimize mean conditional value at risk cvar by decomposing operations and finance operational flexibility maximizes expected profit subject to a cvar constraint whereas financial hedging minimizes cvar subject to a minimum expected profit we report three main findings first operational flexibility and financial hedging can be complements operational flexibility enhances profitability and reduces downside risk while financial hedging minimizes downside risk and can affect the feasible set of capacity portfolios albeit indirectly by relaxing a cvar constraint second operational flexibility and financial hedging are substitutes in risk reduction though the latter has greater risk reduction effects in cvar when used alone third coordinating operations and finance is crucial for minimizing substitution effects efficient financial hedging depends on rigorous estimation of cash flow distribution as shaped by operational flexibility and a capacity portfolio s feasibility relies on financial hedging because of the cvar constraint

the risk averse and prudent newsboy the effects of risk and risk aversion in the single period inventory newsboy problem are examined comparative static effects of changes in the various price and cost parameters are determined and related to the newsboy s risk aversion the addition of a random background wealth and of an increase in the riskiness of newspaper demand are also examined although many of the comparative effects generally are ambiguous some fairly simple restrictions on preferences and or risk increases are shown to lead to qualitatively deterministic results

a duopolistic model of dynamic competitive advertising abstract this paper proposes a differential game model of competitive advertising decisions for non durable products by extending the lanchester model and the deal model of competitive advertising in the literature the proposed model is compared empirically with the lanchester model for model fitting and forecast accuracy it is shown that the model is suitable for an actual market and out performs the lanchester model in forecast accuracy the model provides a sensible modeling alternative to the lanchester model for the study of dynamic competitive advertising decisions necessary and sufficient conditions for open loop and closed loop nash equilibrium solutions to the model are discussed a numerical algorithm for open loop and closed loop nash strategies to the model is developed

supply quality management with wholesale price and revenue sharing contracts under horizontal competition abstract in a number of industries e g the airplane industry aerospace industry auto industry or computer industry certain suppliers essentially have a monopoly on the production technology for key components and inevitably manufacturers in these industries have common suppliers a key part of manufacturers work with suppliers concerns improving the quality of their respective products which gives rise to a collaborative activity usually termed as supply quality management when the manufacturers are competitors they do not wish to see a common supplier dividing his involvement in quality improvement unequally between themselves and their rivals however as the suppliers collaborate with several manufacturers it is highly questionable whether their efforts will be strictly equivalent for each manufacturer in this paper a non cooperative dynamic game is formulated in which a single supplier collaborates with two manufacturers on design quality improvements for their respective products the manufacturers compete for market demand both on price and design quality the paper analyzes how each party should allocate resources for quality improvement over time in order to take into account the potential coordinating power of the compensation scheme adopted in this type of decentralized setting we compare the possible outcomes under a wholesale price contract and a revenue sharing contract

the risk averse newsvendor problem with random capacity abstract we study the effect of capacity uncertainty on the inventory decisions of a risk averse newsvendor we consider two well known risk criteria namely value at risk var included as a constraint and conditional value at risk cvar for the risk neutral newsvendor we find that the optimal order quantity is not affected by the capacity uncertainty however this result does not hold for the risk averse newsvendor problem specifically we find that capacity uncertainty decreases the order quantity under the cvar criterion under the var constraint capacity uncertainty leads to an order decrease for low confidence levels but to an order increase for high confidence levels this implies that the risk criterion should be carefully selected as it has an important effect on inventory decisions this is shown for the newsvendor problem but is also likely to hold for other inventory control problems that future research can address

beyond expected utility subjective risk aversion and optimal portfolio choice under convex shortfall risk measures abstract we conduct a decision theoretic analysis of convex shortfall risk measures regarding their flexibility to represent subjective risk aversion and discuss the implications for the choice of optimal portfolios as convex shortfall risk measures are closely related to the expected utility functional we draw upon the expected utility framework as our benchmark first we show that unlike expected utility convex shortfall risk measures do always represent constant absolute risk aversion this constitutes a significant limitation when changing initial wealth of e g investors is relevant interestingly though it is exactly this limitation that provides additional degrees of freedom in representing subjective risk aversion beyond expected utility when initial wealth is fixed as e g in returned based portfolio selection models in the tradition of markowitz 1952 second we apply convex shortfall risk measures to the standard portfolio problem between a riskless and a risky asset we provide a procedure that allows inferring the optimal portfolios under convex shortfall risk measures from certain optimal expected utility portfolios the procedure incorporates the additional degrees of freedom in modeling subjective risk aversion and thus allows more flexible and realistic portfolios compared to expected utility third we address the optimal portfolio choice between a riskless and a risky asset in the presence of an additional background risk again we prove a correspondence result between optimal portfolios under convex shortfall risk measures and expected utility and obtain more flexible and realistic portfolios compared to expected utility we also compare the optimal risky investments without and with background risk and provide a necessary and sufficient condition for a reduction of the risky investment

quality improvement and goodwill accumulation in a dynamic duopoly abstract this paper analyzes optimal advertising and quality improvement decisions by duopolist firms competing in a dynamic setting an extended version of the lanchester model is formulated where conformance quality and goodwill are both involved in competition for market share each competitor s new customer attraction rate depends on its own goodwill while the disloyalty rate for current customers is influenced by the proportion of defective items the search for a non cooperative solution by qualitative as well as numerical means leads to definition of the optimal path for advertising and improvement efforts for each competitor examined under a wide range of configurations

on the generalizability of advertising pulsation monopoly results to an oligopoly this paper introduces for the first time an analytical framework for modeling and analyzing sales response to advertising pulsation for competitive markets of mature products in continuous time for discrete piecewise policies that allow unequal cycle lengths employing a nash equilibrium solution concept this study supported with numerical analysis demonstrates that there is an oligopolistic as opposed to a monopolistic justification for advertising at a constant rate in the presence of concave response functions or advertising according to a pulsing policy in the presence of s shaped response functions the article employs a modeling framework whereby each of a set of competitors responses to advertising spending is governed mainly by lanchester type response is used to analyze the game resulting from cyclical advertising policies that are strictly adhered to by all players a non discounted averaged performance is used to assess the purported optimality of different variants of piecewise constant policies

manufacturer s return policy in a two stage supply chain with two risk averse retailers and random demand abstract this paper studies the manufacturer s return policy and the retailers decisions in a supply chain consisting of one manufacturer and two risk averse retailers under a single period setting with price sensitive random demand we characterize each retailer s risk embedded objective via conditional value at risk and construct manufacturer stackelberg games with and without horizontal price competition between the retailers we explore through numerical studies the effects of the retailers aversion to risk and other parameters on the manufacturer s return policy and profit and the retailers decisions we further investigate the effect of distribution asymmetry by comparing the results with normal and lognormal demand

a learning curve model with knowledge depreciation abstract empirical studies in several industries have verified that unit costs decline as organizations gain experience or knowledge in production which is referred to as the learning curve effect in the past two decades there has also been analytical work on the relationship between a firm s learning curve effects and its pricing and output decisions learning rates differ significantly across firms in the same industry and recent empirical evidence has shown that knowledge depreciation may be an important reason for these differences we propose and analyze a learning curve model with knowledge depreciation and provide several new insights first we show that there exists a steady state where knowledge level and unit cost remain constant over time and there exists an optimal path to this steady state many empirical researchers have observed this plateau phenomenon whereby unit costs decline but reach saturation after some time while this has been traditionally modeled exogenously in the learning curve literature by assuming that cost reduction stops at some level of knowledge through a convex decreasing unit cost function we provide an alternative endogenous explanation we are also able to show that unlike in the model without knowledge depreciation the production rate along the optimal path to the steady state may decrease over time also the knowledge level along the optimal path may actually decline over time finally we show that the optimal production rate decreases at higher interest rates and increases at higher knowledge depreciation rates in turn this implies that a high interest rate environment discourages firms from achieving high knowledge levels and results in higher prices on the other hand higher knowledge depreciation rates result in higher production rates and lower prices

effects of higher order moments on the newsvendor problem abstract in this paper we propose a stochastic programming model for the well known single period newsvendor problem by adopting the conditional value at risk cvar as the risk metric in the objective function the demand uncertainty is modeled in terms of discrete scenarios that reflect the empirical distributions implied by market demand data our numerical results demonstrate that the higher order moments skewness and kurtosis of demand have obvious effects on the newsvendor problem and the stochastic programming framework provides a flexible and effective decision support tool for the newsvendor problem

the loss averse newsvendor model with backordering abstract in this paper we study the optimal order quantity in the loss averse newsvendor model with backordering we first obtain the optimal order quantity to maximize the expected utility to hedge against the risk arising from the uncertainty of market demand we introduce the conditional value at risk cvar measure and derive the optimal order quantity to maximize the cvar objective about utility it is found that the optimal order quantity with the cvar objective is decreasing in the confidence level and thus is smaller than the optimal order quantity to maximize the expected utility it is proved that under the optimal order quantity with the cvar objective the loss averse newsvendor s expected utility is decreasing in the confidence level it further confirms that high risk implies high return and low risk comes with low return

artificial compatibility barriers to entry and frequent flyer programs if supplier firms can discriminate between buyers agents acting on behalf of employers principals and those making purchases for themselves then these firms may be able to create demand side entry barriers by creating what may be called artificial compatibility between otherwise unrelated goods or services even if there are no differences in costs between incumbent and potential entrant there will be an incentive to offer in kind inducements to agents these inducements may lead to entry barriers and their use may be a nash equilibrium we argue that frequent flyer programs are instances of the creation of such artificial compatibility

risk shaping in production planning problem with pricing under random yield abstract in this paper we address a basic production planning problem with price dependent demand and stochastic yield of production we use price and target quantity as decision variables to control the risk of low production yield the value of risk control becomes more important especially for products with short life cycle where high losses are unbearable in the short run in this cases optimization of a solely scalar function of profit is not sufficient to control the risk we apply conditional value at risk cvar measure to model the risk preferences of the producer the producer is interested in shaping the risk by bounding from below the means of tail distributions of profit for different values of the resulting model is nonconvex we propose an efficient solution algorithm and present a sufficient optimality condition

robust inventory decision under distribution uncertainty a cvar based optimization approach abstract we study the robust inventory decision making problem faced by risk averse managers with incomplete demand information in a newsvendor setting three basic models are developed expected profit maximization cvar based profit maximization and a combination of the two each model is robustly formulated under the assumption of ellipsoid discrete distribution and again under the box discrete distribution each robust model can be mathematically transformed into a second order cone program for ellipsoid uncertainty or into a general convex optimization problem for box uncertainty both transformed problems can be optimally solved directly we offer propositions with proof to show the equivalence of the transformed problems with the original ones numerical examples are given to validate the proposed approach we find that the performances under both ellipsoid and box uncertain distributions are robust finally sensitivity analysis with respect to risk averse levels and trade off coefficients is conducted to validate the proposed models and solution approaches

dynamic optimal control models in advertising recent developments this paper presents a review of recent developments that have taken place in the area of dynamic optimal control models in advertising subsequent to the comprehensive survey of the literature by sethi in 1977 the basic problem underlying these models is that of determining optimal advertising expenditures and possibly other variables of interest over time for a firm or a group of competing firms under consideration this optimization is done subject to some dynamics that define how these variables translate into sales and in turn into profits the purpose of this update is twofold on the one hand new contributions in the areas already treated in the earlier survey are reviewed on the other hand new trends in the advertising literature since 1977 such as quality as an additional marketing instrument cumulative sales models pulsing advertising and advertising as a part of corporate models of the firm are discussed the models covered in this update are organized under six headings models with ca

marketing production decisions in an industrial channel of distribution this paper presents a model that considers the interface between marketing and production decisions in a channel of distribution of industrial goods comprised of a manufacturer and a distributor the key issue investigated is the nature of the coordination within the channel in light of an unstable pattern of seasonal demand the investigation which focuses on dynamic issues considers production activities such as product delivery and inventory policy and their link to marketing strategies such as pricing policies the focus here is on the dynamic nature of the coordinational aspects of the various policies for example the following questions are addressed what is the distributor s pricing strategy throughout the season what is the nature of the contractual price in the channel under what conditions should the distributor carry no inventory throughout the seasonal period under what conditions should the manufacturer carry no inventory what is the impact of the seasonal parameters and differing h

a model of advertising competition using a dynamic model of advertising rivalry between competitors in a duopoly the author obtains analytical results for the case of pure market share rivalry in a mature market a more general mod

accurate response by postponement abstract accurate response and postponement are two strategies for a firm to deal with demand uncertainty and better match supply with demand under accurate response reactive capacity could be used for customized make to order mto production according to customer demands on the other hand using postponement a firm could perform the non postponed activities speculatively and use reactive capacity only to customize the final product thereby enhancing the profitability of accurate response surprisingly existing research in the areas of accurate response and postponement does not address this potential in this paper we aim to fill this gap by proposing a stylized model for accurate response by postponement specifically we analyze a situation where a manufacturer is faced with uncertain demand for a product during a short selling season the manufacturer has three supply options first it can manufacture and offer a standardized version of the product second it can use postponement by manufacturing a standard component speculatively and customizing it once demands are revealed at the beginning of the selling season third it can produce customized products in a pure make to order fashion during the selling season this situation is modeled as an extension of a newsvendor problem our main research question is then to analyze specifically under which conditions postponement is part of the optimal supply strategy and more generally what kinds of supply strategies will arise in different model settings

consumption and habits evidence from panel data the purpose of this paper is to test for the presence of habit formation in consumption decisions using household panel data we use the test proposed by meghir and weber 1996 and estimate the within period marginal rate of substitution between commodities which is robust to the presence of liquidity constraints to that end we use a spanish panel data set in which households are observed up to eight consecutive quarters this temporal dimension is crucial since it allows us to take into account time invariant unobserved heterogeneity across households fixed effects and therefore to investigate if the relationship between current and past consumption reflects habits or heterogeneity our results confirm the importance of accounting for fixed effects when analyzing intertemporal consumption decisions allowing for time non separabilities once fixed effects are controlled for and a proper set of instruments is used the results yield supporting evidence of habit formation in the demand system of food at home transport and services

finite change comparative statics for risk coherent inventories abstract this work introduces a comprehensive approach to the sensitivity analysis sa of risk coherent inventory models we address the issues posed by i the piecewise defined nature of risk coherent objective functions and ii by the need of multiple model evaluations the solutions of these issues are found by introducing the extended finite change sensitivity indices fcsi s we obtain properties and invariance conditions for the sensitivity of risk coherent optimization problems an inventory management case study involving risk neutral and conditional value at risk cvar objective function illustrates our methodology three sa settings are formulated to obtain managerial insights numerical findings show that risk neutral decision makers are more exposed to variations in exogenous variables than cvar decision makers

the learning curve and optimal production under uncertainty this article examines the implications of the learning curve in a world of uncertainty we consider a competitive firm whose costs decline with cumulative output because the price of the firm s output evolves stochastically future production and cumulative output are unknown and are contingent on future prices and costs we derive an optimal decision rule that maximizes the firm s market value produce when the price exceeds a critical level which is a declining function of cumulative output we show how the shadow value of cumulative production the total value of the firm and the decision to produce depend on the volatility of the price and other parameters uncertainty increases the critical price required for the firm to produce but also increases the value of thefirm thus during periods of high volatility firms facing a learning curve ought to be producing less but are worth more

differential game models of advertising competition abstract differential game methodology combines two attractive features that are critical to the study of advertising competition dynamics and multi competitor decision making a focused review of two decades of differential game modeling of advertising competition indicates that insights gained to date while valuable are of a limited nature and research in the area needs to extend beyond present limits four recent studies are offered as examples of possible directions to follow in continued research

an industry equilibrium analysis of downstream vertical integration this paper investigates the effect of product substitutability on nash equilibrium distribution structures in a duopoly where each manufacturer distributes its goods through a single exclusive retailer which may be either a franchised outlet or a factory store static linear demand and cost functions are assumed and a number of rules about players expectations of competitors behavior are examined it is found that for most specifications product substitutability does influence the equilibrium distribution structure for low degrees of substitutability each manufacturer will distribute its product through a company store for more highly competitive goods manufacturers will be more likely to use a decentralized distribution system this article was originally published in marketing science volume 2 issue 2 pages 161 191 in 1983

coping with risk management and fill rate in the loss averse newsvendor model abstract in this paper we introduce the cvar conditional value at risk measure to hedge against the risks for the loss averse newsvendor we derive the optimal order quantities for the loss averse newsvendor to maximize the cvar objective of utility with and without the shortage cost respectively it is shown that when shortage cost is not considered an increase in the degree of loss aversion leads to a decrease in the fill rate therefore the newsvendor should strike a balance between the two conflicting targets in selecting the optimal order quantity when the shortage cost is taken into account and sufficiently large it is proved that an increase in the degree of loss aversion leads to an increase in the fill rate to manage both of the two targets the newsvendor should order more items in this case our sensitivity analysis further verifies that high risk implies high return and low risk comes with low return based on the analysis some management insights for the risk management of the loss averse newsvendor are presented

optimal decisions for the loss averse newsvendor problem under cvar abstract most of the existing literature about the newsvendor problem mainly focused on choosing an optimal order quantity to maximize the expected profit of a risk neutral newsvendor however some studies pointed out that in practice managers decisions as to order quantities always deviate from the profit maximization order quantity which is referred to as decision bias in the newsvendor problem then many studies introduced other preferences rather than risk neutrality of the newsvendor to explain such a decision bias this paper thus introduces loss aversion to the research of the newsvendor decision bias we propose a new definition to the loss averse newsvendor problem legacy loss which is defined either as the loss for excess order or the shortage penalty for lost sales when sales time is due the optimal decisions of a loss averse newsvendor are obtained through the following three ways i minimizing the expected legacy loss ii minimizing cvar of legacy loss by combining the cvar measure in risk management iii minimizing the combination of expected legacy loss and cvar of legacy loss and are compared with other existing results besides we present some properties of the optimal decisions as well as relations among them some numerical examples are given to illustrate the obtained results

impact of risk aversion on optimal decisions in supply contracts abstract we introduce the concept of conditional value at risk as the evaluation criterion in a supply contract model we first derive the manufacturer s optimal decisions and then analyze the impact of risk aversion on the manufacturer s decisions we follow by conducting numerical experiments to observe how the manufacturer s risk attitude affects his decisions we obtain results that characterize the explicit relationship between the manufacturer s risk attitude and his optimal decisions we also show the dependence of the decision variables on the price and cost parameters which is seldom given in the literature

an empirical analysis of dynamic nonprice competition in an oligopolistic industry this article develops a dynamic model of nonprice competition in an oligopolistic industry and uses it to analyze advertising competition in the u s cigarette industry the model generalizes existing studies by allowing advertising to affect both firm market shares and the total size of the market the model also allows dynamic conjectural variations to arise from the intertemporal links created by the durability of advertising we use these dynamic conjectural variations to distinguish alternative models of competitive interaction we estimate the complete model of firm production demand and advertising choice by using data for u s cigarette producers the results indicate that firm advertising primarily affects the level of market demand with a firm s effect on rival firms market shares arising through variations in the number of brands sold empirical results on firm behavior suggest that firms act as if their advertising choices will alter the future advertising choices of rival firms in both the high tar and low tar cigarette markets

a risk averse competitive newsvendor problem under the cvar criterion abstract we study a risk averse newsvendor problem with quantity competition and price competition under the conditional value at risk cvar criterion we characterize the optimal quantity and pricing decisions under both quantity and price competition for quantity competition we consider two demand splitting rules namely proportional demand allocation and demand reallocation although competition always leads to overstocking interestingly it does not necessarily lead to a profit loss in certain competitive environments such as demand reallocation by avoiding reducing overstocking that results from competition under the risk neutral criterion for price competition we consider both additive and multiplicative demand we find that the order quantity sale price and the expected profit decrease in the degree of risk aversion further both high price sensitivity and competition intensity force decision makers to lower their prices however high price sensitivity always reduces the order quantity while competition can have the opposite effect

an oligopoly model of dynamic advertising competition abstract an oligopoly model is presented that allows the determination of feedback nash equilibrium advertising strategies for an oligopoly analyses of symmetric and asymmetric oligopolies with the model show that unit contribution and advertising effectiveness have positive effects on a competitor s own advertising and steady state sales while discount rate and decay rate have negative effects an asymmetric analysis further shows that unit contribution and advertising effectiveness affect positively and discount rate and decay rate negatively a competitor s rivals advertising but have effects in opposite directions regarding rivals steady state sales the symmetric and asymmetric analyses also show that steady state sales per competitor decline with the number of competitors in the oligopoly while total oligopoly steady state sales increase the model is applied empirically to the triopolistic competition involving anheuser busch sabmiller and molson coors in the beer industry

asymmetry and ambiguity in newsvendor models a basic assumption of the classical newsvendor model is that the probability distribution of the random demand is known but in most realistic settings only partial distribution information is available or reliably estimated the distributionally robust newsvendor model is often used in this case where the worst case expected profit is maximized over the set of distributions satisfying the known information which is usually the mean and covariance of demands however covariance does not capture information on asymmetry of the demand distribution in this paper we introduce a measure of distribution asymmetry using second order partitioned statistics semivariance is a special case with a single partition of the univariate demand with mean variance and semivariance information we show that a three point distribution achieves the worst case expected profit and derive a closed form expression for the distributionally robust order quantity for multivariate demand the distributionally robust problem

an empirical investigation of advertising strategies in a dynamic duopoly the equilibrium profit maximizing advertising policies of firms operating in a dynamic duopoly are derived by linking in a single framework the econometric estimation of the market response function and the technique of differential games that characterizes dynamic competitive behavior we use the lanchester model of combat to represent the system dynamics that capture the competitive shifts due to investments in advertising by the two market rivals we determine the equilibrium advertising levels using both closed and open loop policies we also compare these equilibrium advertising policies for each firm to those obtained using an optimal control theory formulation wherein the advertising spending levels of the rival are assumed to be known the empirical results obtained by analyzing the advertising rivalry between coke and pepsi for the period 1968 1981 under the above three alternative spending policies provide some interesting insights into the nature of competition between these two market rivals a significant contribution of this paper is to extend the existing literature on advertising competition by integrating theoretical and empirical analyses

prisoner s dilemma on behavioral choices in the presence of sticky prices farsightedness vs myopia abstract when making decisions in a dynamic environment myopic supply chain members tend to ignore the future effects of their decisions on the evolution of state dynamics by contrast far sighted decision makers consider about the impacts of current decisions on both current profits and future profits in order to study how behavioral choices affect the operation decisions and profits of supply chain members we develop a differential game with sticky prices where one manufacturer purchases components from one supplier and makes final products for end customers the supplier decides on its wholesale price while the manufacturer sets its production quantity either of supply chain members has two behavioral choices myopia and farsightedness we derive and compare equilibrium solutions under four different behavioral combinations our analysis shows that there always exists a prisoner s dilemma caused by behavioral choices farsightedness is a dominant strategy for either the supplier or the manufacturer but both to act myopically makes both of them better off furthermore comparing with other scenarios the whole supply chain obtains the highest profit when both players are myopic in addition we introduce a revenue sharing contract with static wholesale price to mitigate the adverse impacts of the prisoner s dilemma

competitive dynamic advertising a modification of the case game abstract in this paper we consider a modified version of the advertising differential game of case 1979 we derive non cooperative nash equilibria for open loop controls as well as for feedback strategies we consider finite and infinite planning horizons the feedback equilibrium is shown to be robust against stochastic disturbances of the state equation

a risk tolerance analysis for a joint price differentiation and inventory decisions problem with demand leakage effect abstract price differentiation is a commonly used practice in revenue management rm to improve a firm s profitability however most studies in the literature have considered a risk neutral firm to demonstrate the benefits of price differentiation the main contribution of this paper is in considering several important objectives while determining the optimal product prices and order production quantities for a risk adjusted firm with demand leakage effects in the presence of a price dependent stochastic demand the objectives considered include the maximization of a firm s expected profit and maximizing the probability of exceeding the risk adjusted expected revenue closed form expressions for optimal product prices and production quantities are derived for several of these objectives a numerical study is also presented to calibrate the impact of a firm s risk tolerance and other factors such as demand leakage market demand variability on the firm s profitability and its optimal decision

the newsvendor problem review and directions for future research in this paper we review the contributions to date for analyzing the newsvendor problem our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand supplier costs and the buyer risk profile more specifically we analyze the impact of market price marketing effort and stocking quantity on customer demand how supplier prices can serve as a coordination mechanism in a supply chain setting integrating alternative supplier pricing policies within the newsvendor framework and how the buyer s risk profile moderates the newsvendor order quantity decision for each of these areas we summarize the current literature and develop extensions finally we also propose directions for future research

the impact of capital structure on advertising competition an empirical study this article examines the interaction between capital structure and advertising competition using a sample of firms that raise significant amounts of capital we find that firms whose financial leverage has decreased as a result of their new funding increase their advertising significantly more than firms whose leverage has increased we also find that these firms industry rivals respond less aggressively with their own advertising when they have more debt in their capital structure overall our results support the view that financial leverage has a dampening effect on the intensity with which a firm chooses to compete in the product market

a quick and easy method for estimating switching costs abstract i develop and test a method for a quick and easy calculation of consumer switching costs among brands in a given industry the theory developed and tested here maps observed brands prices and market shares onto the switching costs which deter a consumer of a specific brand from switching to any other competing brand then i demonstrate how users switching costs can be directly calculated in two different industries a the israeli cellular phone market and b the finnish market for bank deposits this calculation method can be used to calculate switching costs in a wide variety of other industries such as airlines health services computers software telecommunications and more

costly switching from a status quo abstract we axiomatically characterize a theory of status quo dependent choice where an agent faces switching costs that depend upon both the status quo and the alternative he switches to in a choice problem with a status quo the agent chooses the alternatives that yield the highest utility net of switching cost this generates status quo bias and also allows for a wide range of reference effects we examine the behavior of such agents in prisoner s dilemma pd games in a single pd game switching costs can lead to cooperation however across different pd games it is not anything goes and instead we derive necessary and sufficient conditions for cooperation rates to be consistent with our model we then verify that these conditions are satisfied by charness et al s 2016 experimental data we also perform a similar analysis for other theories such as models of status quo bias magical thinking inequity aversion and fairness and find that these theories make either invalidated or looser predictions

a risk averse newsvendor model under marketing dependency and price dependency abstract in this paper we analyze a single period inventory model where a risk averse newsvendor makes a joint decision on ordering pricing and marketing under the cvar risk measure criterion the newsvendor can exert marketing effort to enhance market demand we assume that the newsvendor s marketing effort affects the scale of the demand distribution and hence to model the marketing dependent demand as a multiplicative form we characterize sufficient conditions that guarantee existence and uniqueness of the optimal solutions under some mild assumptions on demand distribution expected demand function and marketing effort cost which are widely used in the related literature we show that the optimal order quantity increases in the newsvendor s marketing effort but the optimal price remains unchanged whether the demand is marketing dependent or not additionally we explore impact of exogenous parameters such as unit order cost salvage value and the newsvendor s risk aversion coefficient on the optimal decision variables and find that the optimal marketing effort always keeps the same changing direction with the optimal marketing independent order quantity as the exogenous parameters change this suggests that impact of the parameters on the optimal order quantity gets strengthened in the case of marketing dependent demand

markov perfect equilibrium advertising strategies of lanchester duopoly model a technical note we propose a numerical approach to compute stationary markov perfect nash equilibrium advertising strategies of the lanchester model the algorithm can be implemented using a standard mathematical package and importantly it does not require that the players discount their future earnings at a zero rate an assumption that has been made in the literature

recent developments in dynamic advertising research a variety of continuous time differential functions have been developed to investigate dynamic advertising problems in business and economics fields since major dynamic models appearing before 1995 have been reviewed by a few survey papers we provide a comprehensive review of the dynamic advertising models published after 1995 which are classified into six categories i nerlove arrow model and its extensions ii vidale wolfe model and its extensions iii lanchester model and its extensions iv the diffusion models v dynamic advertising competition models with other attributes and vi empirical studies for dynamic advertising problems for each category we first briefly summarize major relevant before 1995 models and then discuss major after 1995 models in details we find that the dynamic models reviewed in this paper have been extensively used to analyze various advertising problems in the monopoly duopoly oligopoly and supply chain systems our review reveals that the diffusion models have not been used to analyze advertising problems in supply chain operations which may be a research direction in the future moreover we learn from our review that very few publications regarding dynamic advertising problems have considered the supply chain competition we also find that very few researchers have used the diffusion model to investigate the dynamic advertising problems with product quality as a decision variable and the pricing decision has not been incorporated into any extant lanchester model the paper ends with a summary of our review and suggestions on possible research directions in the future

competition in a duopoly with sticky price and advertising abstract this paper develops a differential duopolistic game where price is sticky and firms can invest in market enlarging promotional activities which have a public good nature one finding indicates that advertising and not output as in fershtman and kamien econometrica 55 1987 1151 1164 is responsible for the higher stationary price found in the open loop equilibrium relative to the linear feedback one that is free riding is more intense when firms play linear markov feedback strategies however the collusive outcome can be approximated and opportunism eliminated if firms can engage in preplay negotiations where they select a nonlinear markov perfect strategy for output and advertising achieving the collusive outcome requires as in the folk theorem for infinitely repeated games the discount rate to be sufficiently small

multi product newsvendor problem with value at risk considerations abstract we consider the single period stochastic inventory newsvendor problem with downside risk constraints the aim in the classical newsvendor problem is maximizing the expected profit this formulation does not take into account the risk of earning less than a desired target profit or losing more than an acceptable level due to the randomness of demand we utilize value at risk var as the risk measure in a newsvendor framework and investigate the multi product newsvendor problem under a var constraint to this end we first derive the exact distribution function for the two product newsvendor problem and develop an approximation method for the profit distribution of the n product case n 2 a mathematical programming approach is used to determine the solution of the newsvendor problem with a var constraint this approach allows us to handle a wide range of cases including the correlated demand case that yields new results and insights the accuracy of the approximation method and the effects of the system parameters on the solution are investigated numerically

empirical analysis of closed loop duopoly advertising strategies closed loop perfect equilibria in a lanchester duopoly differential game of advertising competition are used as the basis for empirical investigation two systems of simultaneous nonlinear equations are formed one from a general lanchester model and one from a constrained model two empirical applications are conducted in one involving coca cola and pepsi cola a formal statistical testing procedure is used to detect whether closed loop equilibrium advertising strategies are used by the competitors rather than open loop strategies in the second application involving anheuser busch and miller the general model is estimated results indicate that closed loop equilibria better explain dynamic advertising competition than do open loop equilibria also closed loop equilibrium advertising strategies implied by model estimates show that competitive advertising levels may or may not be monotonic in market share

risk analysis with contractual default does covenant breach matter abstract mergers and acquisitions m a private equity and leveraged buyouts securitization and project finance are characterized by the presence of contractual clauses covenants these covenants trigger the technical default of the borrower even in the absence of insolvency therefore borrowers may default on loans even when they have sufficient available cash to repay outstanding debt this condition is not captured by the net present value npv distribution obtained through a standard monte carlo simulation in this paper we present a methodology for including the consequences of covenant breach in a monte carlo simulation extending traditional risk analysis in investment planning we introduce a conceptual framework for modeling technical and material breaches from the standpoint of both lenders and shareholders we apply this framework to a real case study concerning the project financing of a 64 million euro biomass power plant the simulation is carried out on the actual model developed by the financial advisor of the project and made available to the authors results show that both technical and material breaches have a statistically significant impact on the net present value distribution and this impact is more relevant when leverage and cost of debt increase

quality effects in different advertising models an impulse control approach abstract in this paper we integrate quality as a control variable in three classical dynamic optimal control models of advertising namely nerlove arrow vidale wolfe and ozga models quality refers to design quality which may deteriorate over time we assume that decisions in quality improvement can only be made at some exogenously given instants of time and consequently we use the formalism of impulse optimal control to determine optimal advertising and quality investments we report numerical results for the three models and discuss the impact of adding quality on the results

capacity allocation for dynamic process improvement with quality and demand considerations management of process improvement activities is an essential part of the manufacturing strategy of a firm to remain globally competitive in the long run this paper considers a manufacturing environment where process improvement activities require use of the productive capacity of the firm in addition to other investments thus the firm must allocate its productive capacity between production activities and improvement activities the output of production activities is used to meet customer demand process improvement activities improve the quality of the output which in turn leads to lower quality related costs both internal and external and possibly lower per unit production cost it is assumed that the demand function is downward sloping and that revenue is a concave function of output a continuous time finite horizon profit maximization resource allocation model is developed to find an optimal time path for process improvement activities and production activities computational results are provided to study the effect of various problem parameters on the optimal decisions