COMPUTER 

OPTIMIZATION OF 

CUTTING YIELD 

FROM 

RESEARCH 

PAPER 

FPL 318 

FOREST PRODUCTS LABORATORY 

FOREST SERVICE 

U.S. DEPARTMENT OF AGRICULTURE 

MADISON, WISCONSIN 

1978 

MULTIPLE-RIPPED 

BOARDS 
The use of trade, firm, or corporation 

names in this publication is for the information and convenience of the reader. 

Such use does not constitute an official endorsement or approval by the U.S. Department of Agriculture of any product or service 

to the exclusion of others which may be 

suitable. 
COMPUTER OPTIMIZATION OF 

CUTTING YIELD FROM 

MULTIPLE-RIPPEDBOARDS 

By 

Abigail R. Stern 

and 

Kent A. McDonald 

Forest Products Laboratory,1/ Forest Service 

U.S. Department of Agriculture 

INTRODUCTION 

Multiple ripping of boards, followed by 

crosscutting to remove defects, is an operation used by both the hardwood flooring and 

the softwood cut-up industries. Because of 

the rising cost of lumber and the increasing 

demand on the timber supply, utilizing each 

board more efficiently is becoming more important. 

The two steps in making better 

processing decisions to improve utilization 

of each board are to: (1) automatically locate 

defects, and (2) optimize sawline placement 

based on defect locations. 

A system that automatically locates 

defects in lumber has been developed and is 

being tested at the Forest Products 

Laboratory 2/ . Boards are scanned with 

ultrasound under computer control and 

defect location data are automatically collected. The computer program used was 

designed to: (1) control the scanning 

process, (2) store collected data on tape, (3) 

optimize sawline placement based on defect 

locations, and (4) draw the board and cutting 

solution on a line plotter. 

The purpose of this paper is to describe 

RIPYLD (RIP YieLD)--that part of the computer program that optimizes sawline 

placement for maximum yield. RIPYLD obtains the multiple ripping and crosscutting 

solutions using defect location data, and is 

an expansion of earlier efforts to maximize 

cutting yields of boards using computer 

analyses 3/, 4/, 5/. In RIPYLD, any kerf width 

can be used and cuttings can be any length 

(either random or specified), and any width. 

RIPYLD has the option of manufacturing 

either specified length cuttings or random 

length cuttings. Up to five cutting lengths 

and three cutting widths can be used in the 

specified length option. If the random length 

option is chosen, three cutting widths and 

minimum acceptable cutting length must be 

specified. 

Sawing variables are the maximum number of rip saws to be used on any board, and 

the sawkerf, which will be used in both the 

rip cuts and crosscuts. 

1/ The Laboratory is maintained in Madison, 

Wisconsin, in cooperation with the University of Wisconsin. 

2/ McDonald, Kent A. 1978. Lumber defect detection 

by ultrasonics. USDA For. Serv. Res. Pap. FPL 311. 

For. Prod. Lab., Madison, Wis. 

3/ Wodzinski, Claudia, and Eldona Hahm. 1966. A 

computer program to determine yields of lumber. USDA 

For. Serv., For. Prod. Lab., Madison, Wis. 

4/ Erickson, Bernard J., and Donald C. Markstrom. 

1972. Predicting softwood cutting yields by computer. 

USDA For. Sew. Res. Pap. RM-98. Rocky Mountain For. 

Range. Exp. Sta., Fort Collins, Colo. 

5/ Cornwell. Larry W., and John K. Kalita. 1977. The 

development of a computer program to automate the 

cutting of gunstock blanks. Dept. of Mathematics. 

Western Illinois University, Macomb, Ill. 
PROGRAM RIPYLD 

Input 

Input parameters that must be specified 

for the RIPYLD program are: (a) board and 

defect information, (b) cutting bill 

requirements, and (c) sawing variables. 

An X-Y coordinate system grid is superimposed on the board, and each unit grid 

area is designated as either defective (1) or 

clear (0) (fig. 1). The number of X-grids in the 

length, the number of Y-grids in the width, 

and the sizes of X-grid and Y-grid (in inches) 

must be specified. 

Description 

First, all possible combinations of rip 

widths that will fit within the width of the 

board are determined and stored. For example, if the possible rip widths are 2, 2.5, and 3 

inches and there are four rip saws available, 

there are 34= 81 possible permutations of rip 

widths to try. However, if the board is 9 inches wide and the kerf is 0.125 inches, only 

27 permutations, including kerfs, will fit 

within the width of the board (table 1). 

Then, for each stored combination of rip 

widths, the board is “sawn” by the computer. 

The board is always ripped first, with the first 

rip width always positioned at the edge of the 

board with the lowest Y coordinate. 

Solutions with the first rip positioned at the 

other edge of the board are not considered. 

After ripping, the clear areas within each rip 

are located. 

If random lengths are desired, only 

defects and lengths shorter than the 

Table 1. -- Rip combinations of 2.0”, 2.5”, and 3.0” that fit in 9” wide board 

Rip widths (in.) 

Total width (in.) 

(including 0.125” kerf 

1st Rip 2ndRip 3rdRip 4th Rip between rips) 

2 
Figure 1.--ln the X-Y coordinate system 

grid superimposed on the board, each unit 

grid area is designated as either defective (1) 

or clear (0). 

specified minimum cutting length are 

removed by crosscutting. Otherwise, 

specified lengths are made by crosscutting 

the clear areas and removing the defects. 

Longest cuttings are always salvaged first 

even if a higher yield would result from a 

combination of shorter cuttings. 

For each clear cutting found and cut out, 

surface area of the cutting is calculated. Surface areas of cuttings are summed to obtain 

the total yield of the board. 

After total yield of clear cuttings from 

the board for a rip combination is calculated, 

the yield is compared to the previous 

maximum yield. If the new yield is greater, it 

is stored as the new maximum. The new yield 

is also compared to the previous minimum 

yield and, if less, becomes the new 

minimum. 

output 

Output from RIPYLD contains complete 

information about both the maximum and 

minimum yield solutions. Included are the 

percent yield of clear cuttings from the 

board, the rip width combination, the crosscut locations, and a piece tally if the specified length option is used. 

3 

At the Forest Products Laboratory, the 

same computer (Harris 6024) that is used to 

collect defect information from the Defectoscope 2/ is used to control a line plotter. 

The minimum or maximum solution is plotted, including the outline of the board, defect 

locations, rip cuts, and crosscuts. Alternatively, theoutput could bedirected to computer controlled saws, stored an tape, or 

displayed on a TV screen or printer. 

Examples of the plots with RIPYLD 

solutions are shown in figures 2 through 6. A 

90-inch long, 9-inch wide board with the defects found by the Defectoscope, was outlined on a data grid 0.5 inch by 05 inch (fig.2). 

The board was “sawn” with a 0.125-inch 

kerf, into random-length cuttings with a 

minimum length of 10 inches. RIPYLD chose 

between rip widths of 2”, 2.5”, and 3”. The 

optimum yield of 80.84 percent was achieved 

with a rip combination of 2”, 2.5”, 2”, 2” (fig. 

3). The minimum solution with a 65.73 percent yield was from a rip combination of 2”, 

2”, 3” (fig. 4). There was not enough room for 

another rip at the top of the board, so 1.625” 

was not utilized. 

The same board was again “sawn” with 

a 0.125-inch kerf and combinations of 2”, 

2.5”, and 3” rip widths (figs. 5, 6). However, 

here the specified length option was used 

with a choice of 50”, 40”, 30”, 20”, and 10” 

cuttings. Piece tallies are included on the 

plots. The optimum solution (fig. 5) was a 

2.5”, 2”, 2”, 2” rip combination with 54.80 

percent yield. The minimum solution of 44.94 

percent yield (fig. 6) was found with a rip 

width combination of 2”, 2”, 3”. Again, the 

top 1.625” of the board was not utilized. 

SUMMARY 

RIPYLD is a computer program that optimizes the cutting yield from multiple-ripped 

boards. Decisions are based on 

automatically collected defect information, 

cutting bill requirements, and sawing 

variables. The yield of clear cuttings from a 

board is calculated for every possible permutation of specified rip widths and both the 

maximum and minimum percent yield 

solutions are saved. Solutions include rip cut 

and crosscut locations as well as the percent 

yield of clear cuttings. 
Figure 2.--Defectswere outlined by the Defectoscope on a grid of 

0.5 inch by 0.5 inch. 

Figure 3.--The board in figure 2 was “sawn” by the computer, into 

random-length cuttings, 10-inch minimum. This optimum yield of 

81% was achieved with a rip combination of 2”, 2.5”, 2”, and 2”. 

Figure 4.--Minimum solution for the same board yielded 65%, with 

a rip combination of 2”, 2”, 3”. 
WIDTH LENGTH 

50” 40” 30” 20” 10” 

Figure 5.--The same board “sawn” again, this time with specifiedlength cuttings ranging from 50” to 10”, yielded an optimum of 

55% from rips of 2.5”, 2”, 2”, 2”. 

WIDTH LENGTH 

50” 40” 30” 20” 10” 

Figure 6.--The minimum solution for the same conditions was 45% 

from rips of 2”, 2”, 3”. 
APPENDIX I 

RIPYLD Variables 

Input 

Dimensions of data grid 

NP - number of grid units in the board length 

NSCANS - number of grid units in the board width 

XGRlD - length of unit grid on axis (inches) 

YGRID - width of unit grid on Y axis (inches) 

Defect information 

BOARD(NSCANS,NP) = 0 if the grid unit is clear = 1 if the grid unit is a defect 

Cutting bill 

NWIDTH - number of rip widths to choose from (maximum of 3) 

WIDTH(3) - up to 3 widths can be specified (inches) 

RANDOM=TRUE - random length cuttings 

SAWMIN - minimum length acceptable cutting 

RANDOM=FALSE - specified length cuttings 

NLEN - number of specified cutting lengths (maximum of 5) 

CUTLEN(5) - up to 5 lengths (inches) 

(Must be in order: CUTLEN(1)=maximum) 

Sawing variables 

NSAW - number of rip saws available 

KERF - sawkerf for both ripping and crosscutting 

output 

Rip combinations 

RIPCOM(81,4) - combinations of rip widths that fit in the board width. 

(Maximum 81 combinations, 4 rip saws) 

NRIP(81) - number of rips that will fit in the board width for 

each combination stored in RIPCOM 

Solutions 

MINCOM - index to RIPCOM and NRlP of the lowest yield combination 

MAXCOM -index to RIPCOM and NRlP of the highest yield combination. 

REJECT =TRUE -no clear cuttings can be found for any rip combination. 

= FALSE .at least 1 clear cutting is found 

ACT -index to solution of current rip combination 

MAX - index to maximum yield solution 

MIN - index to minimum yield solution 

YIELD(3) - percent of clear area of the board for ACT, MAX, MIN 

solutions 

PIECE(5,3,3) - piece tally (5 lengths, 3 widths,) for ACT, MAX, MIN 

solutions 

CROSS(150,3) - X-coordinates of crosscuts for ACT, MAX, MIN solutions 

NXCUT(4,3) number of crosscuts in each rip for ACT, MAX, MIN 

solutions 

6 
Variables used in flowcharts 

I 

BEG 

END 

CLRKNT 

MINLEN 

XCUT 

NP 

RANDOM = 

- present grid position on X axis 

- beginning of defect (grid number) 

- last defect grid encountered 

- number of clear grids encountered since last defectgrid 

- number of grid units in the minimum cutting length 

- subroutine to store crosscut locations and to calculate 

yield 

- number of X-grids in the board 

TRUE - random length option 

FALSE - specified length option 

7 
SUBROUTINE RIPYLD 

SYMBOL REFERENCED AT LINES (MINUS MEANS SYMBOL DEFINED, 

NAME EXCLUDING SUBPROGRAM CALLS AND EQUIVALENCE) 

STATEMENT DEFINED 

NUMBER AT LINE REFERENCED AT LINES 
SUBROUTINE XCUT 

Places crosscuts, calculates cutting yields 

11 
SUBROUTINE XCUT 
SYMBOL REFERENCED AT LINES (MINUS DEFINED 

NAME EXCLUDING CALLS AND AT LINE LINES