Dynamic selection of harvests with adjacency restrictions: The SHARe model

A dynamic forest management model is developed that incorporates spatial and temporal harvesting adjacency restrictions. The spatial harvesting requirements are modeled through the use of 0–1 integer programming models. A variety of different specifications of harvest adjacency constraints is developed and their relative impact on computational efficiency examined. Many researchers have turned to heuristic methods to approach such spatially constrained integer programming problems in the past, especially problems which include harvest flow restrictions. However, the spatially constrained integer programming model developed here, SHARe (Selecting Harvests with Adjacency Restrictions), can be solved optimally. We solve problems up to 441 units on a square grid (21 × 21) using exact optimization methods. Multiple solutions are provided for hypothetical data. In most cases, depending on the structure of the adjacency constraints, the model solved without any or with only a few branch and bound nodes. This result is due, in large part, to the model being based on the classic shortest path network flow model, which is known to have special integer solution properties. In addition, we also determined that certain adjacency constraint structures are more favorable to achieving all-integer solutions than others, when used in conjunction with the network flow model developed here.