Abstract:
Although some of the most difficult problems in forest management occur as a result of timber harvest operations, present methodology in harvest planning emphasizes guidelines which rely heavily upon the experience of the individual forest manager for their correct application. This study was undertaken in an effort to develop a comprehensive methodology to assist forest managers in the design of timber harvest cutting units and the assignment of logging equipment: to those units. The objective of the methodology is to maximize the total value of the timber harvested from a planning area, net of variable and fixed harvesting and transportation costs. The methodology thus developed consists of a two-part procedure. The first part considers the specific topographic and timber conditions on the planning area, plus any harvesting restrictions which may have been imposed on portions of the area because of expected environmental problems, This information is combined with the known mechanics of the logging systems under consideration to determine the feasibility and cost of harvesting each parcel of timber from the area. The second part of the methodology consists of a heuristic optimization algorithm which seeks to assign timber parcels to harvesting facilities so that total timber value, net of fixed and variable harvesting and transportation costs, is maximized. The output from this algorithm is a detailed harvest plan which specifies yarding system assignments and the physical layout of cutting units for each yarding system thus assigned. The optimization problem confronted in this study is an application of facilities location theory, but with two unique characteristics which render the conventional mixed integer programming formulation unsuitable for this problem. First, the planning area is visualized as being dichotomized into timber parcels of equal size, each of which is to be assigned to some harvesting facility. Thus, the problem is a fully discrete one, and can be formulated as a 0-1 integer programming problem. Second, the problem exhibits a special "cascading fixed charge" structure. Stated simply, this implies that several levels of fixed charges must be incurred for any complete facility installation. Thus, if a specific logging cableway is to be emplaced at a certain landing, then the fixed charge associated with the construction of the landing must already have been incurred, and the fixed charge associated with the installation of some yarding system at the landing must also have been incurred. Unfortunately the 0-1 integer programming formulation appropriate for this problem requires many thousands of variables and constraints, even for relatively small planning areas. To overcome the computational difficulties associated with the solution of such large integer programming problems, a heuristic algorithm was developed to find satisfactory, rather than optimal solutions. Applied to a realistic forest planning problem with 5507 variables and 6555 constraints, the algorithm found an initial feasible solution after 93.3 minutes on a CDC 3300 computer. The run was terminated after a total of 120 minutes, with the value of the final solution being only 0.09 percent better than that of the initial solution. Although the exact solution could not be verified, computational experience with smaller problems suggests that the initial feasible solution obtained with this algorithm is usually very close to the optimal solution.