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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.
Keywords: forest planning models, mixed-integer programming, area-based adjacency constraints, area-restriction models
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Linear programming (LP) formulations of forestwide management planning problems were first introduced in the 1960s (Curtis 1962, Loucks 1964, Kidd et al. 1966, Nautiyal and Pearse 1967, Ware and Clutter 1971). When these models were proposed, solving even small LP models was a challenge because of the limitations of computers at the time. Some addressed these computational challenges by developing alternative algorithms for solving the problems. For example, Walker (1976) developed the binary search method to schedule harvests over time to maximize the net present value of the harvest subject to a downward-sloping demand curve. Hoganson and Rose (1984) developed a Lagrangian decomposition approach that divides large problems with forestwide harvest targets into many smaller dual problems that optimize individual management unit (stand) decisions. The smaller problems are tied together by the global problem of finding a set of shadow prices that result in the approximate satisfaction of forestwide constraints when the individual management unit solutions are aggregated. A significant breakthrough in both model size and solution time came when Johnson and Scheurman (1977) proposed an alternative formulation of the LP harvest scheduling problem, which they called...