@article{oai:soar-ir.repo.nii.ac.jp:00011256, author = {伊藤, 精晤}, journal = {信州大学農学部演習林報告}, month = {Oct}, note = {A systematic enumeration procedure is repeated successively according to the nodes shown on the solution tree. When any evidence is found on any node that no feasible or optimal solution exists, that node is abandoned, and the computation is abbreviated. This procedure is called implicit enumeration. The characteristics of FOA which differ from Balas' additive algorithm are: (1) the solution tree itself is smaller in size and each node has different possibilities for optimality and feasiblity of the solution according to the location on the tree, therefore, (2) the enumeration sequence of nodes can be determined automatically, (3) the three standards that may become the evidence for abbreviation of enumeration are established so that the number of exhaustive enumerations (enumeration that is procedured in practice) is eliminated. Before applying this program, meaningless variables must be rejected to reduce the size of zero-one problems, and subcompartments must be arranged in the decreasing order of their area in order to accelerate the computation. This algorithm was translated into a computer program and the computation time is examined by using numerical examples. It becomes clear that the computation time lengthens in proportion to the problem's size, however, (1) only a short time is needed when the constraints are lax, that is, there is a wide range of allowable cutting volume or cutting area in each period, and (2) on the contrary, when the constraints are limited, the computation time becomes notably longer. Further, it is clear that the computation time is strictly proportioned to the number of exhaustive enumerations. Define the ratio r: r=(the number of exhaustive enumerations)/(the number of all nodes on the solution tree), the ratio r can be seen as the efficiency of FOA program. Although the ratio r changes mainly depend on the constraints as mentioned above, r is between 0.099～0.00007% by the numerical examples as shown in the table. That is, from 99.9% to 99.99993% of whole nodes are abandoned and the computation is abbreviated.〓 As a result, FOA can become practical and efficient for forestry oriented zero-one problems. It can be concluded that the timber harvest scheduling problem by individual compartments, although the number of compartments are limited, can be solved by a zero-one integer linear program. This FOA program was applied to Kiso national district forest to predict a sustained yield plan, and a plan was formed. The forest is divided into three working sections, and in each section, the cutting period of each compartment is scheduled so that logging and cilviculture can be sustained continually for 20 years. The optimal solution indicates not only the total cutting volume and area, but also clarifies the cutting period of the individual compartments. Therefore, each compartment is evaluated as to whether it can be logged or not in each of the planning periods. The cutting sequence or neighbouring relationship of each cutting compartment can be discussed. As an element of harvest scheduling, forest road planning is formulated to the constraints in a zero-one problem and some examples are tested. A forest road plan is drawn on a map and the roads are difinded as to which compartments they intersect. When schedule of road construction is recieved, then the compartments which are not ready to transport are rejected from the immediate cutting schedule. This harvesting schedule was applied to a forest of 20 compartments and the results follow: By comparing the problem with road planning and the problem without road planning, it becomes clear that (1) if the limits of the cutting volume or cutting area in each period are wide, feasible and optimal solutions can be found in both problems. (2) On the contrary, when the limits are narrow, a feasible solution does not exist in the problem with road planning. Forest allocation in the future are visualized and discussed. A disirable cutting period of each compartment indicated by the optimal solution is drawn on the map, and the spacial order is evaluated from managerial and/or environmental view points. Requirements of any compartment that need its cutting schedule changed, are added to the constraints of the zero-one problem. Then the revised problem is recalculated and the new optimal solution is shown on the map. By this repetition, a final optimal solution that can satisfy the spacial order intended by planners is found. In the examples the results show that the total cutting volume decreases when the constraints are limited, that is, the demands of the individual compartments and the demands of optimization of the whole are opposed to each other. It can be concluded that to attain an ideal spacial order in a management forest, a strict scheduling of cutting compartments is required. The zero-one problem discussed in this paper can contribute to this requirement. The auther believes an optimal solution of a mathematical problem is always information that may assist in the better decision making of planners, and the in-place harvest scheduling method surely gives useful information that was not previously available to the forest management planner., Article, 信州大学農学部演習林報告 19: 67-100(1982)}, pages = {67--100}, title = {風景概念の論理的構造に関する考察(II)}, volume = {19}, year = {1982} }