Planning cost-effective operational forest inventories

We address a Bayesian two-stage decision problem in operational forestry where the inner stage considers scheduling the harvesting to fulfill demand targets and the outer stage considers selecting the accuracy of pre-harvest inventories that are used to estimate the timber volumes of the forest tracts. The higher accuracy of the inventory enables better scheduling decisions but also implies higher costs. We focus on the outer stage, which we formulate as a maximization of the posterior value of the inventory decision under a budget constraint. The posterior value depends on the solution to the inner stage problem and its computation is analytically intractable, featuring an NP-hard binary optimization problem within a high-dimensional integral. In particular, the binary optimization problem is a special case of a generalized quadratic assignment problem. We present a practical method that solves the outer stage problem with an approximation which combines Monte Carlo sampling with a greedy, randomized method for the binary optimization problem. We derive inventory decisions for a dataset of 100 Swedish forest tracts across a range of inventory budgets and estimate the value of the information to be obtained.