a deterministic inventory model for deteriorating items with stock dependent demand rate abstract a deterministic inventory model is developed by assuming that the demand rate is stock dependent and the items deteriorate at a constant rate the expression for the average net profit over one production run is derived and its optimization with respect to the decision variables q initial stock and t duration of a production cycle is carried out this leads to two highly nonlinear equations which are solved by using a subroutine neqnf in imsl math library in cyber 180 480a computer system the optimal solution so derived is compared with that for the no deterioration 0 case sensitivity of the optimal solution to changes in parameter values is examined several aspects of the functional form for the demand rate are considered in a separate section finally the salient features of the problem and its solution are discussed in brief

an inventory model for deteriorating items with stock dependent consumption rate and shortages under inflation and time discounting this paper derives an inventory model for deteriorating items with stock dependent consumption rate and shortages under inflation and time discounting over a finite planning horizon we show that the total cost function is convex with the convexity a simple solution algorithm is presented to determine the optimal order quantity and the optimal interval of the total cost function the results are discussed with a numerical example and particular cases of the model are discussed in brief a sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out

timing and real indeterminacy in monetary models an increasingly common approach to the theoretical analysis of monetary policy is to ensure that a proposed policy does not introduce real indeterminacy and thus sunspot fluctuations into the model economy policy is typically conducted in terms of directives for the nominal interest rate this paper uses a discrete time money in the utility function model to demonstrate how seemingly minor modifications in the trading environment result in dramatic differences in the policy restrictions needed to ensure real determinacy these differences arise because of the differing pricing equations for the nominal interest rate

inventory control under temporal demand heteroscedasticity abstract this paper studies an inventory control problem when the variance of demand is time varying and exhibits temporal heteroscedasticity we use a first order autoregressive process to characterize the dynamic changes in the level of demand over time and a garch 1 1 structure to describe the changes in the variance of demand under these demand settings we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order up to level policy we show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance the decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored the relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated computational results show that ignoring temporal heteroscedasticity can increase firm s inventory costs by as much as 30 when demand autocorrelation is highly positive

on the calculation of safety stocks when demand is forecasted the inventory control literature generally assumes that the demand distribution and all its parameters are known in practical applications it is often suggested to estimate the demand variance either directly or based on the one period ahead forecast errors the variance of the lead time demand essential for safety stock calculations is then obtained by multiplying the estimated per period demand variance by the length of the lead time however this is flawed since forecast errors for different periods of the lead time are positively correlated even if the demand process itself does not show process auto correlation as a result these traditional procedures lead to safety stocks that are too low this paper presents corrected lead time demand variance expressions and reorder levels for inventory systems with a constant lead time where demand fluctuates around a constant level firstly we derive the exact lead time forecast error of mean demand conditional on the true demand variance secondly we derive for normally distributed demand the correct reorder level under uncertainty of both the demand mean and variance we show how the results can be implemented in inventory models and particularly discuss batch ordering policies combined with moving average and exponential smoothing forecasts we find that traditional approaches can lead to safety stocks that are up to 30 percent too low and service levels that are up to 10 percent below the target

expectation shocks and learning as drivers of the business cycle psychological factors market sentiments and less than fully rational shifts in beliefs are widely believed to play a role in the economy yet they are rarely considered in macroeconomic models this paper evaluates the empirical role of expectational shocks on business cycle fluctuations the paper relaxes the rational expectations assumption to exploit survey data on expectations in the estimation of a new keynesian model which allows for learning by economic agents expectation shocks affect the formation of expectations and capture waves of optimism and pessimism that lead agents to form forecasts that deviate from those implied by their learning model the empirical results uncover a crucial role for these novel expectations shocks as a major driving force of the u s business cycle expectation shocks regarding future real activity are the main source of economic fluctuations accounting for roughly half of business cycle fluctuations

good luck or good policy an expectational theory of macro volatility switches abstract in an otherwise unique equilibrium model agents are segmented into a few informational islands according to the signal they receive about others expectations even if agents perfectly observe fundamentals rational exuberance equilibria rex can arise as they put weight on expectational signals to refine their forecasts constant gain adaptive learning can trigger jumps between the equilibrium where only fundamentals are weighted and a rex this determines regime switching in macro volatility despite unchanged monetary policy and time invariant distribution of exogenous shocks in this context a tight inflation targeting policy can lower expectational complementarity preventing rational exuberance although its effect is non monotone

expectations and the stability problem for optimal monetary policies eine auf den fundamentaldaten beruhende regelbindung der geldpolitik ohne selbstverpflichtung die bei vollkommen rationalen erwartungen der privaten akteure optimal ware ist instabil wenn diese akteure de facto den ublichen regeln des adaptiven lernens folgen dieses problem lasst sich dadurch beheben dass die erwartungen privater akteure berucksichtigt und in geeigneter weise in die optimale geldpolitik einbezogen werden diese eindeutige schlusfolgerung gilt auch dann wenn sich der geldpolitische entscheidungstrager und die privaten akteure in einem simultanen lernprozess befinden unsere ergebnisse zeigen wie wichtig es ist die geldpolitik angemessen zu gestalten und dabei nicht nur die fundamentaldaten sondern auch direkt die beobachteten erwartungen privater haushalte und unternehmen zu berucksichtigen

behavioral learning equilibria we propose behavioral learning equilibria where boundedly rational agents learn to use a simple univariate linear forecasting rule with correctly specified unconditional mean and first order autocorrelation in the long run agents learn the best univariate linear forecasting rule without fully recognizing the more complex structure of the economy an important feature of behavioral learning equilibria is simplicity and parsimony which makes coordination of individual expectations on such an aggregate outcome more likely in a first application an asset pricing model driven by ar 1 ar 1 dividends a unique behavioral learning equilibrium exists characterized by high persistence and excess volatility and it is stable under learning in a second application the new keynesian phillips curve multiple equilibria coexist learning exhibits path dependence and inflation may switch between low and high persistence regimes

on an inventory model with deteriorating items and decreasing time varying demand and shortages in this paper we present an optimal procedure for finding the replenishment schedule for an inventory system with shortages in which items deteriorate at a constant rate and demand rates are decreasing over a known and finite planning horizon a numerical example is presented to illustrate the procedure

determining safety stock in the presence of stochastic lead time and demand we consider the problem of setting safety stock when both the demand in a period and the lead time are random variables there are two cases to consider in the first case the parameters of the demand and lead time distributions are known in the second case they are unknown and must be estimated for the case of known parameters a standard procedure is presented in the literature in this paper examples are used to show that this procedure can yield results that are far from the desired result a correct procedure is presented when the parameters are unknown it is assumed that a simple exponential smoothing model is used to generate estimates of demand in each period and that a discrete distribution of the lead time can be developed from historical data a correct procedure for setting safety stocks that is based on these two inputs is given for two popular demand models the approach is easily generalized to other models of demand safety stock calculation is simplified when certain normality assumptions are valid simulation results in the appendix indicate when these assumptions about normality are reasonable

the eoq models modified by introducing discount of purchase price or increase of setup cost abstract the eoq model of inventory problem can determine ordering cycle and quantity when the purchase unit price is constant ordering cycle and ordering quantity which minimize the one day s average inventory cost is not dependent on the purchase price but if purchase price may change the eoq model must be modified the purchase unit price is discounted as the ordering becomes larger the discount of purchase price is described with a decreasing function of ordering quantity this function is not always continuous with respect to the ordering quantity under this condition one day s average profit can be defined and we can determine ordering cycle and ordering quantity which maximize one day s average profit moreover we consider the situations under which the setup cost depends on the ordering quantity in this case the setup can be described with the increasing function of ordering quantity we show that the eoq model can be applied if it is modified by introducing the continuous setup cost function this function is not differentiable at some levels of ordering quantity

bayes solution to dynamic inventory models under unknown demand distribution this paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate

revisiting the value of information sharing in two stage supply chains abstract there is a substantive amount of literature showing that demand information sharing can lead to considerable reduction of the bullwhip effect inventory costs the core argument analysis underlying these results is that the downstream supply chain member the retailer quickly adapts its inventory position to an updated end customer demand forecast however in many real life situations retailers adapt slowly rather than quickly to changes in customer demand as they cannot be sure that any change is structural in this paper we show that the adaption speed and underlying unknown demand process crucially affect the value of information sharing for the situation with a single upstream supply chain member manufacturer and a single retailer we consider two demand processes stationary or random walk these represent two extremes where a change in customer demand is never or always structural respectively the retailer and manufacturer both forecast demand using a moving average where the manufacturer bases its forecast on retailer demand without information sharing but on end customer demand with information sharing in line with existing results the value of information turns out to be positive under stationary demand one contribution though is showing that some of the existing papers have overestimated this value by making an unfair comparison our most striking and insightful finding is that the value of information is negative when demand follows a random walk and the retailer is slow to react slow adaptation is the norm in real life situations and deserves more attention in future research exploring when information sharing indeed pays off

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

on non uniqueness in rational expectations models an attempt at perspective abstract many macroeconomic models involving rational expectations give rise to an infinity of solution paths even when the models are linear in all variables some writers have suggested that this non uniqueness constitutes a serious weakness for the rational expectations hypothesis one purpose of the present paper is to argue that the non uniqueness in question is not properly attributable to the rationality hypothesis but instead is a general feature of dynamic models involving expectations it is also argued that there typically exists in a very wide class of linear rational expectations models a single solution that excludes bubble or bootstrap effects one that occur only because they are arbitrarily expected to occur a systematic procedure for obtaining solutions free from such effects is introduced and discussed in addition this procedure is used to interpret and reconsider several prominent examples with solution multiplicities including ones developed by fischer black and john b taylor

near rationality heterogeneity and aggregate consumption the simple permanent income model provides a good description of the medium long run behavior of aggregate non durables consumption but fails to describe its short run behavior in this paper i present a non representative agent model with near rational macroeconomic units a la akerlof yellen that simultaneously explains the observed excess smoothness of consumption to wealth innovations and the excess sensitivity of consumption to lagged income changes this models also explains conditional asymmetries found in the data in good times consumers respond more promptly to positive than negative wealth shocks while the opposite is true in bad times in spite of the presence of large non diversifiable idiosyncratic uncertainty the estimated dollar equivalent utility cost of the macroeconomic near rational strategy required to explain the aggregate facts is only about 0 037 percent of consumption per year where gamma is the coefficient of relative risk aversion copyright 1995 by ohio state university press

assessing the effects of using demand parameters estimates in inventory control and improving the performance using a correction function inventory models need some specification of the distribution of demand in order to find the optimal order up to level or reorder point this distribution is unknown in real life and there are several solutions to overcome this problem one approach is to assume a distribution estimate its parameters and replace the unknown demand parameters by these estimates in the theoretically correct model earlier research suggests that this approach will lead to underperformance even if the true demand distribution is indeed the assumed one this paper directs the cause of the underperformance and quantifies it in case of normally distributed demand furthermore the formulae for the order up to levels are corrected analytically where possible and otherwise by use of simulation and linear regression simulation shows that these corrections improve the attained performance

inflation forecasts and monetary policy proposals for inflation targeting as a strategy for monetary policy leave open the important operational question of how to determine whether current policies are consistent with the long run inflation target an interesting possibility is that the central bank might target current private sector forecasts of inflation either those made explicitly by professional forecasters or those implicit in asset prices we address the issue of existence and uniqueness of rational expectations equilibria when the central bank uses private sector forecasts as a guide to policy actions in a dynamic model which incorporates both sluggish price adjustment and shocks to aggregate demand and aggregate supply we show that strict targeting of inflation forecasts is typically inconsistent with the existence of rational expectations equilibrium and that policies approximating strict inflation forecast targeting are likely to have undesirable properties we also show that economies with more general forecast based policy rules are particularly susceptible to indeterminacy of rational expectations equilibria we conclude that although private sector forecasts may contain information useful to the central bank ultimately the monetary authorities must rely on an explicit structural model of the economy to guide their policy decisions this abstract was borrowed from another version of this item this abstract was borrowed from another version of this item

a near rational model of the business cycle with wage and price inertia this paper presents a model in which insignificantly suboptimal behavior causes aggregate demand shocks to have significant real effects the individual loss to agents with inertial price wage behavior is second order in terms of the parameter describing the shock while the effect on real economic variables is first order thus significant changes in business activity can be generated by anticipated money supply changes provided that some agents are willing to engage in nonmaximizing behavior which results in small losses

monetary policy judgment and near rational exuberance we study how the use of judgement or add factors in macroeconomic forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods we examine the possibility of a new phenomenon which we call exuberance equilibria i n the new keynesian monetary policy framework inclusion of judgement in forecasts can lead to self fulfilling fluctuations in a subset of the determinacy region we study how policymakers can minimize the risk of exuberance

an inventory model for deteriorating items with time proportional demand and shortages under inflation and time discounting this paper proposes a generalized dynamic programming model for inventory items with weibull distributed deterioration in this model the demand rate is assumed to be time proportional shortages are allowed and completely backordered and the effects of inflation and time value of money are taken into consideration the solutions of the model determine the optimal replenishment schedule over a finite planning horizon so that the present worth of total cost associated with the inventory system is minimized the proposed model permits variation in both the replenishment intervals and the service levels between order cycles as a result it generates a better solution than other optimization models having fixed order intervals and or fixed service levels the solution procedure is illustrated by two numerical examples and comparison with an existing model is carried out

economic ordering policy for deteriorating items over an infinite time horizon abstract in this paper a total cost model is presented for the inventory problem of deteriorating items a constant fraction of on hand inventory at the beginning of a period deteriorates during the period the demand for the items during a period is supplied at the end of the period however shortages accumulated during a scheduling period are supplied at the start of the next scheduling period an approach is suggested for determining economic ordering policy for the case of time varying demand and a search procedure is developed when demand is constant in each period

the taylor rule and optimal monetary policy where it denotes the fed s operating target for the federal funds rate pt is the inflation rate measured by the gdp deflator yt is the log of real gdp and y t is the log of potential output identified empirically with a linear trend the rule has since been subject to considerable attention both as an account of actual policy in the united states and elsewhere and as a prescription for desirable policy taylor argues for the rule s normative significance both on the basis of simulations and on the ground that it describes u s policy in a period in which monetary policy is widely judged to have been unusually successful taylor 1999 suggesting that the rule is worth adopting as a principle of behavior here i wish to consider to what extent this prescription resembles the sort of policy that economic theory would recommend i consider the question in the context of a simple but widely used optimizing model of the monetary transmission mechanism which allows one to reach clear conclusions about economic welfare the model is highly stylized but incorporates important features of more realistic models and allows me to make several points that are of more general validity out of concern for the robustness of the conclusions reached the analysis here addresses only broad qualitative features of the taylor rule and attempts to identify features of a desirable policy rule that are likely to hold under a variety of model specifications

sentiment and the u s business cycle abstract psychological factors are commonly believed to play a role on cyclical economic fluctuations but they are typically omitted from state of the art macroeconomic models this paper introduces sentiment in a medium scale dsge model of the u s economy and tests the empirical contribution of sentiment shocks to business cycle fluctuations the assumption of rational expectations is relaxed the paper exploits instead observed data on expectations in the estimation the observed expectations are assumed to be formed from a near rational learning model agents are endowed with a perceived law of motion that resembles the model solution under rational expectations but they lack knowledge about the solution s reduced form coefficients they attempt to learn those coefficients over time using available time series at each point in the sample and updating their beliefs through constant gain learning in each period however they may form expectations that fall above or below those implied by the learning model these deviations capture excesses of optimism and pessimism which can be quite persistent and which are defined as sentiment in the model different sentiment shocks are identified in the empirical analysis waves of undue optimism and pessimism may refer to expected future consumption future investment or future inflationary pressures the results show that exogenous variations in sentiment are responsible for a sizable above forty percent portion of historical u s business cycle fluctuations sentiment shocks related to investment decisions which evoke keynes animal spirits play the largest role when the model is estimated imposing the rational expectations hypothesis instead the role of structural investment specific and neutral technology shocks significantly expands to capture the omitted contribution of sentiment

the effects of professional forecast dissemination on macroeconomic volatility abstract this paper explores the role that professional forecast announcements can have on macroeconomic volatility bounded rational agents are used inside a medium scale dynamic stochastic general equilibrium dsge model with financial frictions modeled agents must form expectations about endogenous variables by selecting between three simple linear forecasting specifications some of which contain the inclusion of a professionally announced forecast of the economic variable historically calibrated simulations of the model show that the usage of the announced professional forecast by the agents in their adaptive learning forecast specifications can reduce the volatility in consumption inflation and wages by as much as 26 23 and 22 respectively however if the professional forecast is not disseminated well to the agents or biased in its dissemination agents will learn to ignore the announcement and macroeconomic volatility will increase further the inclusion of very noisy professional forecast signals can result in coordinated volatility cascades where agents could reduce macroeconomic volatility by ignoring the professional forecast but choose not to because of its previous forecast performance

production inventory models for a damageable item with variable demands and inventory costs in an imperfect production process in this paper economic production quantity epq models for breakable or deteriorating item are developed with variable demands being dependent on time or on hand stock here rate of production and holding cost are time dependent unit production cost is a function of both production reliability indicator and production rate set up cost is also partially production rate dependent the production process produces some imperfect quantities which are instantly reworked at a cost to bring back those units to the perfect ones the production process ultimately depends on both time and reliability indicator the models are formulated as optimal control problems and the total profit functions with effect of inflation and time value of money are expressed as finite integrals over the finite planning horizon the problems are solved using euler lagrange function based on variational calculus and newton raphson method to determine the optimal production reliability indicator r and then corresponding production rates and total profits in some cases results of the models for deteriorating item are obtained as particular cases from those of breakable item models similarly results of simple epq models without damageability are deduced as particular cases numerical experiments are performed to illustrate the models both numerically and graphically

the lucas critique policy invariance and multiple equilibria the lucas critique of econometric policy evaluation argues that the parameters of econometric models are subject to theoretical cross equation restrictions which follow from the fact that the endogenous variables of the models are chosen optimally by forward looking agents in this paper i argue that these facts alone are insufficient to generate such restrictions i present an example of a model in which there exist multiple stationary rational expectations equilibria one of which is supported by a process invariant forecast rule immunity to the lucas critique is proposed as a selection criterion in models with multiple equilibria

the strategy of professional forecasting we develop and compare two theories of professional forecasters strategic behavior the first theory reputational cheap talk posits that forecasters endeavor to convince the market that they are well informed the market evaluates their forecasting talent on the basis of the forecasts and the realized state if the market expects forecasters to report their posterior expectations honestly then forecasts are shaded toward the prior mean with correct market expectations equilibrium forecasts are imprecise but not shaded the second theory posits that forecasters compete in a forecasting contest with pre specified rules in a winner take all contest equilibrium forecasts are excessively differentiated

variations of order level inventory models for deteriorating items abstract order level inventory models for deteriorating items have been developed and solved with and without shortages the finite production rate is proportional to the demand rate which is time dependent the rate of deterioration also is taken to be time variable illustrative numerical examples are given and significant features of the results are discussed

gresham s law of model averaging an agent operating in a self referential environment thinks the parameters of his model might be time varying in response he estimates two models one with time varying parameters and another with constant parameters forecasts are then based on a bayesian model averaging strategy which mixes forecasts from the two models in reality structural parameters are constant but the unknown true model features expectational feedback which the agent s reduced form models neglect this feedback allows the agent s fears of parameter instability to be self confirming within the context of a standard linear present value asset pricing model we use the tools of large deviations theory to show that the agent s self confirming beliefs about parameter instability exhibit markov switching dynamics between periods of tranquility and periods of instability however as feedback increases the duration of the unstable state increases and instability becomes the norm even though the constant parameter model would converge to the constant parameter rational expectations equilibrium if considered in isolation the mere presence of an unstable alternative drives it out of consideration

economic order quantity models for ameliorating deteriorating items under inflation and time discounting the items that incur a gradual loss in quality or quantity over time while in inventory are usually called deteriorating items in reality there are some items whose value or utility or quantity increase with time and those items can be termed as ameliorating items in this paper an effort has been made to incorporate these two opposite physical characteristics of stored items into inventory model we develop models for ameliorating deteriorating items with time varying demand pattern over a finite planning horizon taking into account the effects of inflation and time value of money optimal solutions of the proposed models are derived and the effects of amelioration deterioration on the inventory replenishment policies are studied with the help of numerical examples

economic analysis of dynamic inventory models with non stationary costs and demand abstract with today s high rate of inflation observed in most world economies the accuracy of standard lot sizing models and their applicability to real inventory situations under inflationary conditions become questionable in this paper we have studied the effects of inflation and time value of money on the replenishment policies of items with time continuous non stationary demand over a finite planning horizon we have developed dynamic programming models for three commonly used replenishment policies in the inventory lot sizing literature with time varying demand and shortages in the case of linear time dependent demand we have performed a sensitivity analysis to investigate the impact of changing the system parameters on the present worth of the total cost of each of the three replenishment policies the results showed that the initial cycle length is virtually insensitive to the type of replenishment policy we have also extended the developed models to more practical inventory situations with exponentially deteriorating items and perishable products having fixed life time

stalking information bayesian inventory management with unobserved lost sales retailers are frequently uncertain about the underlying demand distribution of a new product when taking the empirical bayesian approach of scarf 1959 they simultaneously stock the product over time and learn about the distribution assuming that unmet demand is lost and unobserved this learning must be based on observing sales rather than demand which differs from sales in the event of a stockout using the framework and results of braden and freimer 1991 the cumulative learning about the underlying demand distribution is captured by two parameters a scale parameter that reflects the predicted size of the underlying market and a shape parameter that indicates both the size of the market and the precision with which the underlying distribution is known an important simplification result of scarf 1960 and azoury 1985 which allows the scale parameter to be removed from the optimization is shown to extend to this setting we present examples that reveal two interesting phenomena 1 a retailer may hope that compared to stocking out realized demand will be strictly less than the stock level even though stocking out would signal a stochastically larger demand distribution and 2 it can be optimal to drop a product after a period of successful sales we also present specific conditions under which the following results hold 1 investment in excess stocks to enhance learning will occur in every dynamic problem and 2 a product is never dropped after a period of poor sales the model is extended to multiple independent markets whose distributions depend proportionately on a single unknown parameter we argue that smaller markets should be given better service as an effective means of acquiring information

optimal and heuristic inventory replenishment models for deteriorating items with exponential time varying demand abstract in this paper we present optimal and heuristic procedures for the inventory replenishment problem in which items are deteriorating at a constant rate the demand rates are changing exponentially with time over a known and finite planning horizon we have developed an iterative numerical procedure to find the optimal replenishment schedule the first two heuristics are based on the economic order interval approximation the third heuristic restricts all the replenishment cycles over the planning horizon to be equal over the planning horizon the last three heuristics are extended versions of the silver meal heuristic the least cost approach and the least unit cost heuristic which were used in the inventory literature for the case of discrete time varying demand without deterioration we further assess the cost and computation time effectiveness of the six heuristics the results of a sample of 1440 problems show that the extended least cost approach is the most cost effective

what is wrong with taylor rules using judgment in monetary policy through targeting rules it is argued that inflation targeting is best understood as a commitment to a targeting rule rather than an instrument rule e ither ageneral targeting rule explicit objectives for monetary policy or a specific targeting rule a criterion for the forecasts of the target variables to be fulfilled essentially the equality of the marginal rates of transformation and substitution between the target variables targeting rules allow the use of judgment and extramodel information are more robust and easier to verify than optimal instrument rules and they can nevertheless bring the economy close to the socially optimal equilibrium