Optimum Sequence of Cutting Bills

A procedure is offered for selecting an optimum sequence for the assignment of lengths to crosscut saws in the rough end of a furniture plant or dimension mill. The procedure assumes that only five lengths at a time will be assigned to a sawyer. The specific question approached can be stated, “For a given cutting bill, what should be the original combination of five lengths and in what sequence should the remaining lengths be assigned to the crosscut sawyer to minimize the lumber input requirements of a given grade?” The data on which the sequencing rules were developed was for No. 1 common lumber. Essentially the rules are used to identify the most difficult lengths to satisfy. Then rather than taking the most difficult lengths in sequence, the rules determine a balance such that the difficult lengths are spread over the duration of the cutting operation. There are eight rules which are used in various combinations depending on the characteristics of the cutting bill. When the rules were applied to a set of 86 cutting bills for which a total enumeration of cutting sequences had been performed to identify the optimum sequence, 84 percent of the selected sequences were within 10 board feet of the lumber requirement for the optimum sequence. In 50 percent of the cases the selected sequence was the optimum sequence, and in only five cases was the deviation of lumber requirement from the optimum greater than 50 board feet.

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