Measure twice, cut once: Optimal inventory and harvest under volume uncertainty and stochastic price dynamics

Abstract

Natural resources are often subject to state uncertainty: resource abundance is not known with certainty, but can be measured. Measurements are typically imperfect and costly to obtain. The decision of whether to invest in resource measurement may be influenced by other state variables, for example a resource commodity price. We introduce a mixed-observability model of optimal forest management featuring a partially-observable forest resource and perfectly-observable stochastic price. The decision maker optimizes the expected net present value of forest returns by choosing when to measure current forest volume (conduct an inventory), harvest and replant, or delay action. Parameter values are obtained from numerous forestry data sources. Optimal investment in inventory reduces the cost of uncertainty about timber volume and increases the predictability of returns. Moreover, price stochasticity interacts with inventory decisions to produce asymmetric effects of high and low prices on inventory timing. We also produce the first graphical Faustmann rule analogues for jointly-optimal inventory and harvest.