Optimal clear-area sawing patterns for furniture and millwork blanks

Product yield is a very important factor in determining the profitability of the furniture and moulding industries. The greatest potential for increased product yield occurs on the rough-mill cut-up line, where lumber is sawn to remove defects and to produce standard-sized pieces for further processing. Knowing the optimal sawing patterns for board clear areas is an important part of determining a suitable sawing pattern for an entire board. This paper briefly discusses various methods for finding these patterns, and presents a modified version of the Gilmore and Gomory algorithm, which is well suited to this task. These modifications permit the algorithm to execute within the speed and memory limits of a microcomputer. Also described is a method that decreases execution times by not calculating solutions for clear-area sizes that are seldom, if ever, required for complete-board solutions. Empirical results are presented to compare the performance of the modified version of the algorithm with the original implementation. Results illustrating the sensitivity of the algorithm to changes in the number of cutting bill elements, their sizes and values, and kerf width are also presented.

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