A problem of forest harvesting and road building solved through model strengthening and Lagrangean relaxation

we consider a problem of forest planning on pine plantations over a two to five year horizon. Basic decisions concern the areas to harvest in each period, the amount of timber to produce to satisfy aggregate demands for log exports, sawmills and pulp plants, and the roads to build for access and storage of timber. A linear programming model with 0-1 variables describes the decision process. Solution strategies involve strengthening of the model, lifting some of the constraints, and applying Lagrangean relaxation. Results on real planning problems show that even as these problems become more complex, the proposed solution strategies lead to very good solutions, reducing the residual gap for the most difficult data set from 162% to 1.6%, and for all data sets to 2.6% or less.