Comparing linear programming and mixed integer programming formulations for forest planning on the Naval Surface Weapons Center, Dahlgren, Virginia

This research project examined the ability to combine spatial data analysis and mathematical programming techniques in developing a multiple-use land management plan for a public forest in northeastern Virginia. Linear programming-based timber management scheduling models were constructed utilizing the Model I formulation of Johnson and Scheurman (1977). The models were formulated as mixed strata-based, area-based models (Johnson and Stuart 1987) that maximized present net worth subject to a fixed timberland base, an ending inventory requirement, workload control restrictions, and harvest volume control restrictions. The linear programming-based models which incorporated spatial data analysis capabilities were solved using mixed-integer programming.

The model was used to assess the costs of implementing spatial restrictions designed to address forest resource management concerns, in particular, timber production and reserve status acreage for wildlife habitat purposes. The impact of imposing alternative spatial stand allocation requirements and different levels of reserve status acreage was evaluated by measuring the cost in terms of reductions in the present net value (PNV) of timber benefits and timber harvest volumes. The results indicate that the optimal solution value is more sensitive to the level of reserve status acreage imposed on the model than to the spatial restrictions for stand allocations placed on the model.