INTERNAL CONSISTENCY IN MODELS OF OPTIMAL RESOURCE USE UNDER UNCERTAINTY

For several decades, economists have been concerned with the problem of optimal resource use under uncertainty. In many studies, researchers assume that prices evolve according to an exogenous stochastic process and solve the corresponding dynamic optimization problem to yield an optimal decision rule for exploitation of the resource. This study is motivated by our attempt to understand the relationship between efficiency in resource markets and optimal harvest decisions in which price is an exogenous state variable. The literature on optimal commodity storage finds that in a rational expectations equilibrium commodity prices are stationary and serially correlated. Yet recent papers on optimal timber harvesting that assume exogenous stationary prices generate harvest rules inconsistent with the price processes on which they are based. In this study, we investigate the appropriate form of the stochastic process governing prices of renewable resources. We develop a model in which timber is supplied by profit-maximizing managers with rational expectations and aggregate timber demand is subject to independent exogenous shocks. In contrast to earlier studies, prices are endogenously determined. Managers know the structure of the timber market and form expectations of future market equilibria in making optimal harvesting decisions. We show under general conditions that efficient timber prices are stationary and serially correlated. Stationarity and serial correlation are shown to arise from two sources: the occurrence of stock-outs (i.e., depletion of the inventory) and stock-dependent growth of the resource. Further, we show that prices retain these properties even in the absence of stock-outs. Simulations are used to further illustrate the analytical results. Our findings have implications for a large number of economic analyses of optimal resource use. First, our results reveal why extraction rules for renewable resources based on exogenous price specifications are internally inconsistent, even when the specification conforms to the stochastic behavior of prices generated by an efficient market. These prices arise in a particular structural environment, and if large numbers of resource managers adopt the harvesting rule, the underlying structural environment would change, and the price process would deviate from that used to derive the harvesting rule. Second, we show that there can be no gains from exploiting the stochasticity of resource prices in a rational expectations world, a finding that challenges the prescriptive policies for resource use found in many studies, including those on option values. Third, our results show that time-series analyses designed to test for the efficiency of renewable resource markets cannot distinguish prices generated in an efficient market from those generated in an inefficient market. Finally, we extend the literature on optimal storage. Previous models of commodity storage models are shown to be a special case of our model involving age-independent depreciation of the inventory.Resource /Energy Economics and Policy,

The Dynamic Behavior of Efficient Timber Prices

The problem of when to optimally harvest trees when timber prices evolve according to an exogenous stochastic process has been studied extensively in recent decades. However, little attention has been given to the appropriate form of the stochastic process for timber prices, despite the fact that the choice of a process has important effects on optimal harvesting decisions. We develop a simple theoretical model of a timber market and show that there exists a rational expectations equilibrium in which prices evolve according to a stationary ARMA(1,1) process. Simulations are used to analyze a model with a more general representation of timber stock dynamics and to demonstrate that the unconditional distribution for rational timber prices is asymmetric. Implications for the optimal harvesting literature are: 1) market efficiency provides little justification for random walk prices, 2) unit root tests, used to analyze the informational efficiency of timber markets, do not distinguish between efficient and inefficient markets, and 3) failure to recognize asymmetric disturbances in time-series analyses of historical timber prices can lead to sub-optimal harvesting rules.

The Firm’s Perception of Demand Shocks and the Expected Profitability of Capital under Uncertainty

This paper revisits the results of the pioneering models of the firm under demand uncertainty and analyses the apparent disparity with respect to the signal of the investment-uncertainty relationship predicted by them. In the 1970’s-1980’s the modelling of demand uncertainty at the firm level taking into account the firm’s optimal choice of factor inputs constituted a cutting-edge research topic. But while setting the standards in the literature of the firm’s optimal behaviour under uncertainty, those models did not clarify the rationale behind the disparity of the results concerning the impact of increased uncertainty on the firm’s desired investment. In the context of an isoelastic stochastic demand function, where the shock variable may enter either linearly or non-linearly, we show it is the way the firm perceives the demand shocks that, by determining the shape of the profit function, establishes the signal of the investment-uncertainty relationship predicted by the model.Demand Uncertainty; Expected Profitability; Shock Perception; Jensen’s Inequality.

Stock Management in Hospital Pharmacy using Chance-Constrained Model Predictive Control

One of the most important problems in the pharmacy department of a hospital is stock management. The clinical need for drugs must be satisfied with limited work labor while minimizing the use of economic resources. The complexity of the problem resides in the random nature of the drug demand and the multiple constraints that must be taken into account in every decision. In this article, chance-constrained model predictive control is proposed to deal with this problem. The flexibility of model predictive control allows taking into account explicitly the different objectives and constraints involved in the problem while the use of chance constraints provides a trade-off between conservativeness and efficiency. The solution proposed is assessed to study its implementation in two Spanish hospitals.Junta de Andalucía P12-TIC-240

Inventory Model with Seasonal Demand: A Specific Application to Haute Couture

In the stochastic multiperiod inventory problem, a vast majority of the literature deals with demand volume uncertainty. Other dimensions of uncertainty have generally been overlooked. In this paper, we develop a newsboy formulation for the aggregate multiperiod inventory problem intended for products of short sales season and without replenishments. A distinguishing characteristic of our formulation is that it takes a time dimension of demand uncertainty into account. The proposed model is particularly suitable for applications in haute couture, i.e., high fashion industry. The model determines the time of switching primary sales effort from one season to the next as well as optimal order quantity for each season with the objective of maximizing expected profit over the planning horizon. We also derive the optimality conditions for the time of switching primary sales effort and order quantity. Furthermore, we show that if time uncertainty and volume uncertainty are independent, order quantity becomes the main decision over the interval of the primary selling season. Finally, we demonstrate that the results from the two-season case can be directly extended to the multi-season case and the limited resource multiple-item case

Downward wage rigidity and optimal steady-state inflation

This paper examines the impact of downward wage rigidity (nominal and real) on optimal steady-state inflation. For this purpose, we extend the workhorse model of Erceg, Henderson and Levin (2000) by introducing asymmetric menu costs for wage setting. We estimate the key parameters by simulated method of moments, matching key features of the cross-sectional distribution of individual wage changes observed in the data. We look at five countries (the US, Germany, Portugal, Belgium and Finland). The calibrated heterogeneous agent models are then solved for different steady state rates of inflation to derive welfare implications. We find that, across the European countries considered, the optimal steady-state rate of inflation varies between zero and 2%. For the US, the results depend on the dataset used, with estimates of optimal inflation varying between 2% and 5%. JEL Classification: E31, E52, J4downward wage rigidity, DSGE Models, optimal inflation

Demand forecasting for companies with many branches, low sales numbers per product, and non-recurring orderings

We propose the new Top-Dog-Index to quantify the historic deviation of the supply data of many small branches for a commodity group from sales data. On the one hand, the common parametric assumptions on the customer demand distribution in the literature could not at all be supported in our real-world data set. On the other hand, a reasonably-looking non-parametric approach to estimate the demand distribution for the different branches directly from the sales distribution could only provide us with statistically weak and unreliable estimates for the future demand. Based on real-world sales data from our industry partner we provide evidence that our Top-Dog-Index is statistically robust. Using the Top-Dog-Index, we propose a heuristics to improve the branch-dependent proportion between supply and demand. Our approach cannot estimate the branch-dependent demand directly. It can, however, classify the branches into a given number of clusters according to an historic oversupply or undersupply. This classification of branches can iteratively be used to adapt the branch distribution of supply and demand in the future.Comment: 6 pages, 7 figure

Evaluation of Procurement Scenarios in One-Dimensional Cutting Stock Problem with a Random Demand Mix

The one-dimensional cutting stock problem describes the problem of cutting standard length stock material into various specified sizes while minimizing the material wasted (the remnant or drop as manufacturing terms). This computationally complex optimization problem has many manufacturing applications. One-dimensional cutting stock problems arise in many domains such as metal, paper, textile, and wood. To solve it, the problem is formulated as an integer linear model first, and then solved using a common optimizer software. This paper revisits the stochastic version of the problem and proposes a priority-based goal programming approach. Monte Carlo simulation is used to simulate several likely inventory order policies to minimize the total number of shortages, overages, and the number of stocks carried in inventory