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UBC Theses and Dissertations

A method of evaluating bucking and sawing strategies for sawlogs McPhalen, James Charles


the last few years the sawmilling industry has faced the economic pressure of increasing raw material costs, increasing conversion costs and limited product value due to competition from other products, one result of this pressure has been the development of process control systems which automate many of the cutting decisions required to convert tree-length logs into marketable products. Regardless of whether saws are positioned automatically or manually, a set of cutting instructions is essential. These instructions should, for the available log supply, provide the most economical yield consistent with market demands and mill constraints. Two critical decisions are made in converting logs into lumber. The bucking decision constrains the lumber length and hence may limit the value of the lumber. The sawing decision determines the lumber products which can be sawn from the resulting short logs. The two decisions cannot be analyzed in isolation. In order to determine the bucking strategy which yields the mix of short logs which will produce the maximum lumber value it is necessary to know the sawing pattern which will be used to convert the logs into lumber. Similarly, given a limited log supply of fixed characteristics, limited sawmill capacity and restrictions on market demand for lumber products, the optimum sawing strategy cannot be determined without information on the population of short logs which will develop from the bucking decision. Formulating the problem of determing optimum bucking-saving decisions for a limited log supply and limited sawmill capacity as a linear programming model is attractive but the large number of alternative cutting decisions make such a formulation intractable. The problem of deterring optimal bucking and saving strategies for a single log can be modelled as a dynamic programming recursion. However, the dynamic programming approach cannot efficiently handle the large number of constraints inherent in formulating an optimum bucking-sawing strateqy for a given population of tree-length logs. It was shown that the linear and dynamic programming models could be combined using Dantzig-wolfe decomposition. The linear model determines the combination of cutting strategies which optimize an objective function subject to constraints. The dynamic programming model supplies the linear model with new activities as required. The decomposition approach is attractive because it avoids the necessity of working with all possible activities in the linear programme. The L.P. calculates with the basis inverse and the dynamic programming sub-problem generates new bucking-sawing activities as required by the L. P. The efficiency of the technique was demonstrated by determing optimal bucking and sawing strategies for a population of 967 long logs.

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