optimal capacity expansion over an infinite horizon the problem of choosing an optimal initial capacity expansion from a finite number of durable facility sizes is affected by potential future expansion decisions as we consider such expansions over longer and longer study horizons the optimal initial facility choice can fluctuate due to end of study effects we discuss an algorithm that will determine for arbitrary deterministic demand profiles how long a horizon is sufficient to reach stability in the first facility choice moreover it is shown that this first choice is the optimal first choice for the infinite horizon problem we also establish an explicit analytical formula for a study horizon guaranteed to provide a first facility size that followed by an infinite horizon expansion strategy will attain a discounted cost within a predetermined maximal error of the optimal infinite horizon cost

a path dependent contingent claims approach to capacity investments this note presents a contingent claims approach to strategic capacity planning we develop models for capacity choice and expansion decisions in a single firm environment where investment is irreversible and demand is uncertain these models illustrate specifically the relevance of path dependent options analysis to planning capacity investments when the firm adopts demand tracking or average capacity strategies it is argued that asian average type real options can explain hysteresis phenomena in addition to providing superior control of assets in place

multi resource investment strategies operational hedging under demand uncertainty abstract consider a firm that markets multiple products each manufactured using several resources representing various types of capital and labor and a linear production technology the firm faces uncertain product demand and has the option to dynamically readjust its resource investment levels thereby changing the capacities of its linear manufacturing process the cost to adjust a resource level either up or down is assumed to be linear the model developed here explicitly incorporates both capacity investment decisions and production decisions and is general enough to include reversible and irreversible investment the product demand vectors for successive periods are assumed to be independent and identically distributed the optimal investment strategy is determined with a multi dimensional newsvendor model using demand distributions a technology matrix prices product contribution margins and marginal investment costs our analysis highlights an important conceptual distinction between deterministic and stochastic environments the optimal investment strategy in our stochastic model typically involves some degree of capacity imbalance which can never be optimal when demand is known

technological expectations and adoption of improved technology abstract attention is focused upon the adoption demand rather than the creation supply of new technology which improves from time to time based on the expected flow of technological progress over which the firm demander has no control it must decide either to adopt the current best available technology or to postpone adoption the distinguishing features of the model are that more than one technological innovation is anticipated and expectations about the likelihood of such innovations are revised as time passes since the last innovation our analysis shows that the firm will adopt the current best practice if its technological lag exceeds a certain threshold moreover as time passes without new technological advances it may become profitable to purchase a technology that has been available even though it was not profitable to do so in the past

investment and capacity choice under uncertain demand this paper extends the real options literature by discussing an investment problem where a firm has to determine optimal investment timing and optimal capacity choice at the same time under conditions of irreversible investment expenditures and uncertainty in future demand after the project is installed with a certain maximum capacity this capacity is fixed as an upper boundary to the output and cannot be adjusted later on it turns out that in the framework of this once and for all decision uncertainty in future demand leads to an increase in optimal installed capacity but on the other hand it causes investment to be delayed to an extent that even small uncertainty makes waiting and accumulation of further information the optimal decision for large ranges of demand limiting the capacity which may be installed weakens this extreme effect of uncertainty

money credit and banking in monetary models where agents are subject to trading shocks there is typically an ex post inefficiency since some agents are holding idle balances while others are cash constrained this problem creates a role for financial intermediaries such as banks who accept nominal deposits and make nominal loans in general financial intermediation improves the allocation the gains in welfare come from the payment of interest on deposits and not from relaxing borrowers liquidity constraints we also demonstrate that when credit rationing occurs increasing the rate of inflation can be welfare improving

demand modeling of stochastic product diffusion over the life cycle abstract planning during the product life cycle plc poses a number of challenges for managers due to the pace of change and uncertainties in the marketplace the ability to better understand predict and make decisions based on manifestations of demand forms a set of important operational problems that ultimately affect the profitability of enterprises this paper models the stochastic diffusion of a product in the market as a geometric brownian motion gbm process that has a time varying drift rate the model is calibrated such that model parameters are able to feature different product types and diffusion conditions imperfect information on the expected peak demand is treated as model uncertainty and a bayesian approach is employed to update knowledge on it the demand model demonstrates robust performance over a wide range of conditions despite model uncertainty it provides both qualitative and quantitative information for manufacturers and service providers to design strategies for stochastic plc conditions as well as dynamic production planning

forecast frequency in rolling horizon hedging heuristics for capacity expansion this paper describes a simulation study of the effect of forecast revisions and hedges against demand uncertainty in a rolling horizon heuristic for capacity expansion the model is based on data collected in the utilities division of a large chemical manufacturing plant a seasonal integrated moving average model for the demand is used to generate forecasts while capacity additions are determined by applying a simple timing rule to various hedges around the forecast the simulation results indicate that hedging forecasts by their prediction limits rather than a fixed buffer significantly reduces undercapacity at the expense of a small increase in capacity cost the prediction limit hedge is more robust to delays in reforecasting

modelling the uk gilt edged market in this paper we examine the sectoral demand for uk gilt edged securities the tobin markowitz model of portfolio choice generates the prediction that asset holdings should be negatively correlated with the own price and positively correlated with the prices of major substitutes in contrast for all the five major groups of uk gilt holders we find evidence consistent with a reverse correlation between the own price and market holdings which we argue arises due to the passive revaluation of existing holdings we examine the empirical evidence using both cointegration analysis of stock holdings and a dynamic model of net transactions

strategic facility location a review abstract facility location decisions are a critical element in strategic planning for a wide range of private and public firms the ramifications of siting facilities are broadly based and long lasting impacting numerous operational and logistical decisions high costs associated with property acquisition and facility construction make facility location or relocation projects long term investments to make such undertakings profitable firms plan for new facilities to remain in place and in operation for an extended time period thus decision makers must select sites that will not simply perform well according to the current system state but that will continue to be profitable for the facility s lifetime even as environmental factors change populations shift and market trends evolve finding robust facility locations is thus a difficult task demanding that decision makers account for uncertain future events the complexity of this problem has limited much of the facility location literature to simplified static and deterministic models although a few researchers initiated the study of stochastic and dynamic aspects of facility location many years ago most of the research dedicated to these issues has been published in recent years in this review we report on literature which explicitly addresses the strategic nature of facility location problems by considering either stochastic or dynamic problem characteristics dynamic formulations focus on the difficult timing issues involved in locating a facility or facilities over an extended horizon stochastic formulations attempt to capture the uncertainty in problem input parameters such as forecast demand or distance values the stochastic literature is divided into two classes that which explicitly considers the probability distribution of uncertain parameters and that which captures uncertainty through scenario planning a wide range of model formulations and solution approaches are discussed with applications ranging across numerous industries

simultaneous capacity and production management of short life cycle produce to stock goods under stochastic demand this paper derives the optimal simultaneous capacity and production plan for a shortlife cycle produce to stock good under stochastic demand capacity can be reduced as well as added at exogenously set unit prices in both cases studied with and without carryover of unsold units a target interval policy is optimal there is a usually different target interval for each period such that capacity should be changed as little as possible to bring the level available into that interval our contribution in the case of no carry over is a detailed characterization of the target intervals assuming demands increase stochastically at the beginning of the life cycle and decrease thereafter in the case of carry over we establish the general result and show that capacity and inventory are economic substitutes the target intervals decrease in the initial stock level and the optimal unconstrained base stock level decreases in the capacity level in both cases optimal service rates are not necessarily constant over time a numerical example illustrates the results

intertemporal optimization of the coal production capacity in china in terms of uncertain demand economy environment and energy security abstract as coal is the main energy source in china coal overcapacity and undercapacity have negative impacts on the economy environment and energy security to reveal the optimal production capacity opc an intertemporal optimization model under uncertainty is established by a combined dynamic programming influence factor scenario analysis monte carlo method dp if sa mc the opcs in 1990 2025 are solved to minimize the expected cost to the economy and environment driven by the production capacity pc under energy security in addition we define and calculate the pc deviation pcd or the deviation of the actual pc apc from the opc the results show that compared with the apc the opc has advantages of more stable development more timely adjustment and lower cost and it provides cost savings of 302 857 billion yuan in 1990 2017 according to pcd china s coal industry existed under the risk of overcapacity in 1990 1999 and 2009 2017 and undercapacity in 2000 2008 and it can experience overcapacity for most of the time without capacity reduction policies in future the optimal management of the pc should be based on the opc and pcd over the next 5 10 years rather than the current capacity utilization rate and focus on overcapacity management in the long run

competitive capacity expansion under demand uncertainty abstract we analyze the capacity expansion behavior of firms in a duopoly faced with an uncertain new market the market demand may be high or low with a given probability mass function firms obtain private information about the market size and build their capacity before the market demand is known once the demand is revealed firms enter a capacity constrained price competition phase which determines their revenues two scenarios are considered first when firms choose their capacities simultaneously in the investment phase and second when they do so sequentially for each case we determine the unique symmetric nash equilibrium excess capacity can occur in equilibrium in the industry it is seen that preempting the competitor in the capacity expansion phase offers first mover benefits we argue that the sequential moves game is more prone to equilibrium excess capacity compared to the simultaneous case we show that preemption is a good strategy if the investing environment is either highly optimistic or highly pessimistic if the industry outlook is only moderately optimistic a capacity planner is still better off preempting his competitor however the industry may encounter overcapacity as a consequence

landfill construction and capacity expansion we study the optimal capacity and lifetime of landfills taking into account their sequential nature such an optimal capacity is characterized by the so called optimal capacity condition particular versions of this condition are obtained for two alternative settings first if all the landfills are to have the same capacity and second if each of them is allowed to have a different capacity in the second case we obtain an optimal control problem with mixed elements of both continuous and discrete time the resulting optimization problems involve dividing a time horizon of planning into several subintervals of endogenously decided length the results obtained may be useful to address other economic problems such as private and public investments consumption decisions on durable goods etc

economic investment times for capacity expansion problems abstract a simple rule for the determination of the optimal investment time for a capacity expansion problem is provided based on a general class of stochastic demand processes of practical interest the timing rule is shown to be independent of the descriptive characteristics of the demand process and thus can be considered to be robust in nature

capacity expansion for random exponential demand growth with lead times the combination of demand uncertainty and a lead time for adding capacity creates the risk of capacity shortage during the lead time we formulate a model of capacity expansion for uncertain exponential demand growth and deterministic expansion lead times when there is an obligation to provide a specified level of service the service level defined in terms of the ratio of expected lead time shortage to installed capacity is guaranteed by timing each expansion to begin when demand reaches a fixed proportion of the capacity position under this timing rule the optimal facilities to install can be determined by solving an equivalent deterministic problem without lead times numerical results show the effects of the demand parameters and lead time length on the expansion timing the interaction of timing with expansion size is explored for the case when continuous facility sizes are available with economies of scale

planning for surprise water resources development under demand and supply uncertainty i the general model a study of water resources development in south sweden revealed that water consumption unexpectedly stopped growing after construction had begun on a large project to expand water supplies the project had a long lead time for completion and planning had been based on traditional deterministic forecasts of future water use to explore the implications of such an uncertain structural shift in future consumption patterns we develop a model for determining the timing for initiating such a project in this model the original consumption forecast may be disrupted at some random future time by an event called a surprise as in the swedish situation we have modeled the surprise as an unexpected stagnation in future demand growth and benefit levels we show that this form of uncertainty makes desirable delaying the initiation of the project beyond the time optimal under the original forecast we then extend the model to include the lead time for the project as a variable and demonstrate that the lead time should be reduced from that optimal under a deterministic future finally we incorporate the option of abandoning the project when the surprise occurs and show that higher salvage values for the project lead to earlier optimal commitment times

capacity expansion under stochastic demands we consider the problem of optimally meeting a stochastically growing demand for capacity over an infinite horizon under the assumption that demand for product follows either a nonlinear brownian motion or a non markovian birth and death process we show that this stochastic problem can be transformed into an equivalent deterministic problem consistent with earlier work by a manne the equivalent problem is formed by replacing the stochastic demand by its deterministic trend and discounting all costs by a new interest rate that is smaller than the original in approximate proportion to the uncertainty in the demand

dynamic capacity expansion for a service firm with capacity deterioration and supply uncertainty motivated by the challenges faced by the telecom industry during the past decade in this paper we study a dynamic capacity expansion problem for service firms there is a random demand for the firm s capacity in each period the demand in excess of the capacity is lost and revenue is generated for the fulfilled demand at the beginning of each period the firm might increase its capacity through purchasing equipment for immediate delivery which is constrained by a random supply limit or it might sign a future contract for equipment delivery in the following period we assume that the firm s capacity might partially become obsolete due to natural deterioration or technology innovation we aim at characterizing optimal capacity expansion strategies and comparing the profit functions as well as the optimal control policies of different options specifically we show that the optimal capacity expansion policy for the current period is determined by a base stock policy compared with the case where no future contracts are available the optimal control parameters of capacity expansion are always smaller we further show that when the obsolescence rate is deterministic the optimal policy for capacity expansion through future contracts is also a base stock type the results are extended to the cases with stochastically dependent capacity supply limits and stochastically dependent demand processes which establish the robustness of the optimal policy in various market conditions

capacity expansion with interrupted demand growth abstract in most long range planning problems accurate forecasting of demand growth is often difficult sometimes unexpected shocks in the economy occur and disrupt the predicted growth rate of demand for example growth can unexpectedly cease for and indeterminate length of time due to crucial occurrnces such as wars economic recessions or oil price shocks in this paper we examine the effects of unforeseen demand plateaus on the capacity expansion problem of sizing and timing production facilities we assume that demand for capacity follows a stochastic process that is we allow for plateaus to happen at random future times and to continue for an uncertain duration when the demand process is generated by an alternating renewal process we show that demand plateaus result in a modified discounting rate and a modified import cost

small menu costs and large business cycles a macroeconomic model of monopoly i introduction the conflict between modern neoclassical and traditional keynesian theories of the business cycle centers upon the pricing mechanism in neoclassical models prices are fully flexible they represent the continuous optimization of economic agents and the continuous intersection of supply and demand in keynesian models prices are often assumed to be sticky they do not necessarily equilibrate all markets at all times one of the reasons for the resurgence of the equilibrium approach to macroeconomics has been the absence of a theoretical underpinning for this keynesian price stickiness this note shows that sticky prices can be both privately efficient and socially inefficient the business cycle results from the suboptimal adjustment of prices in response to a demand shock to the extent that policy can stabilize aggregate demand it can mitigate the social loss due to this suboptimal adjustment in some keynesian models prices are simply exogenously fixed 2 in others agents must set their prices in advance of the transaction date the act of altering a posted price is certainly costly these costs include such items as printing new catalogs and informing salesmen of the new price yet these menu costs are small and therefore generally perceived as providing only a weak foundation for these fixed price models however this inference is flawed small menu costs can cause large welfare losses the claim that price adjustment costs are small does not rebut the claim that they are central to understanding economic fluctuations

strategic capacity investment under uncertainty this article considers investment decisions within an uncertain dynamic and duopolistic framework each investment decision involves to determine the timing and the capacity level the simultaneous analysis of timing and capacity decisions extends work on entry deterrence accommodation to consider a timing delay element we find that when applying an entry deterrence policy the first investor or incumbent overinvests in capacity for two reasons first it delays the investment of the second investor or entrant second the entrant will invest in less capacity we also find that greater uncertainty makes entry deterrence more likely

estimating the discount rate policy reaction function of the monetary authority this paper estimates a policy rule that explains the sign and the magnitude of the federal reserve s fed s discount rate changes it sets out a two sided type ii tobit model and develops a procedure for its estimation considering the discrete and censored nature of the changes the results suggest that the fed has conducted discount rate policy counter cyclically to influence output and to curb inflation and that the fed s response to policy indicators varies over monetary regimes furthermore consistency is found between the model prediction of the discount rate change and a classification based on whether the change is technical or non technical copyright 1999 john wiley sons ltd