Abstract: A method for sequencing the cutting of elongated stock such as boards of lumber having random unusable lengths containing knots, discoloration or the like for reducing waste when cutting a mix or mixture of different grades of lumber into furniture parts by making optimum selection of parts to be cut concurrently, the method including the steps of establishing the required lengths, board footage and quantities of pieces of each length to be cut, determining a value factor for each desired length, determining waste factors for all possible combinations of lengths, establishing the probability of having a given length of usable stock in each of the grades of stock being processed, determining from said required lengths, required quantities, required board footage, value factors, probabilities, grade mix and waste factors, the combination of parts to be cut at one time which results in the lowest waste for the entire cutting.