Modelling and decomposition for planning long-term forest harvesting in an integrated industry structure

Abstract

Economists' models for optimal forest rotation have typically focused on the unit area landholder since the early work of Faustmann. This focus on the growth process has ignored the existence of an industry with an ongoing need to keep mills working at some significant fraction of capacity. In this paper we discuss a model framework that will enable the calculation of regeneration harvest policies in a long term context of wood supply to an integrated industry. The paper briefly reviews the literature on economic approaches to forest rotation and then goes on to examine the mathematical programming approaches, particularly the Model I and Model II forms discussed by Johnson and Scheurmann. Only the work of Barros and Weintraub attempts to model both growth and harvest together with an integrated industry structure. Their work, however, uses the Model I formulation, which severely restricts the alternative regeneration harvest policies. We examine a new model based on a Model II type of modelling of the forest growth and harvesting. Like Barros and Weintraub, we use a simple integrated industry structure. The resulting mathematical programming model is large but possesses considerable special structure. We outline a simple approach to decomposition to permit the rapid solution of this model and report on some preliminary computational experience.