Reframing Forest Harvest Scheduling Models for Ecosystem Services Management

Linear programming models have been used in forest management planning since the 1960s. These models have been formulated in three basic ways: Models I, II, and III, which are defined by the sequences of management unit states represented by the variables. In Model I, variables represent sequences of states from the beginning of the planning horizon to the end. In Model II, variables represent sequences of states from one intervention to the next. Finally, in Model III, variables represent a single arc in a management unit’s decision tree, i.e., two states. The objectives of this paper are to clarify the definitions of these model variations and evaluate the advantages and disadvantages of each model. This second objective is to test the hypothesis that the relative performance of these models varies with the increasing number of ecosystem services (ES) incorporated into the models. This objective was achieved by formulating a case study problem using each model type. The case study includes three increasingly complex scenarios, each incorporating additional ecosystem services. Results show that despite having more variables and constraints, Model III requires the least time to formulate due to its less dense parameter matrix. Model II has the shortest solution times, followed closely by Model III, while Model I requires the longest times for both formulation and solution. These results are increasingly apparent in more complex scenarios.