Strengthening Cover Inequalities for Area-Based Adjacency Formulations of Harvest Scheduling Models

Spatially-explicit harvest scheduling models optimize the spatial and temporal layout of forest management actions in order to best meet management objectives such as profit maximization, even flow of products, or wildlife habitat preservation while satisfying a variety of constraints, including maximum harvest opening size constraints. A procedure is proposed that strengthens these arearestriction adjacency constraints. The approach is similar to extending and lifting procedures for cover inequalities in 0-1 knapsack problems. An algorithm is described that generates as many different strengthened constraints as possible from a given set of adjacency constraints. The polyhedral characteristics of the resulting inequalities are discussed and the computational performance of the strengthened formulation is compared with other models on sixty hypothetical and four real forest planning applications. The proposed inequalities were found to perform the best when used in a combined branch-and-bound and cutting planes framework.