Comparing Model I and Model II formulations of spatially explicit harvest scheduling models with maximum area restrictions

This article investigates whether Johnson and Scheurman’s (For. Sci. Monogr. 18, Society of American Foresters, Bethesda, MD 1977) Model II formulation, which can dramatically reduce the size and difficulty of linear programming harvest scheduling models, offers similar potential for efficiency gains in solving spatially explicit harvest scheduling models with area-based adjacency constraints. A total of 150 hypothetical problems and 10 real problems were formulated using Models I and II. The hypothetical problems were distributed (30 each) in five categories: regulated forest problems with four, six, and eight planning periods and overmature forest problems with four and six periods. The length of the planning horizon was a key factor determining the relative performance of Model I and Model II formulations in spatially explicit forest management planning problems. Results from the hypothetical problems suggest that Model I formulations outperform Model II formulations for four period problems. However, Model II formulations perform significantly better than Model I formulations for problems with planning horizons of six and eight planning periods. Real forest results exhibit similar trends.