United States 

Department of 

Agriculture 

Forest Service 

Northeastern Forest 

Experiment Station 

Research Paper NE-586 

Reduce Dimension Costs 

by Using WALNUT 

David G. Martens 

Lumber Grade Informat ion 

(Select only three) 

Input 

Factors 

FAS 

Yield Ad j . (percent 

Volume Constraints 

(M bf) -0- 0.0 -....I --I -0- -0- I--.. -0- 

PF1 = Help PF3 = Exit PF7 = Prev. screen PF8 = Next screen 

I 
The Author 

David G. Martens, research forest products technologist, received a B.S. degree in forest products from 

lowa State University in 1961 and an M.S. degree in 

wood technology from lowa State in 1963. After graduation, he joined the staff at the Northeastern Forest 

Experiment Station's Forestry Sciences Laboratory at 

Princeton, West Virginia, where he has been conducting or supervising research to improve the efficiency 

of wood use. 

Manuscript received for publication 10 January 1986 

Abstract 

A computer program called WALNUT is described that 

determines the least-cost combination of lumber 

grades required to produce a given cutting order of 

walnut furniture dimension parts. If the least-cost mix 

is not available, WALNUT can be used to determine 

the next best alternative. The steps involved in using 

the program are described. 
American black walnut has long been a favorite species for furniture in this country. However, increasing 

demand for fine furniture and decreasing supplies 

of high-quality ,walnut lumber have made prices skyrocket. As a result, furniture dimension manufacturers 

making walnut parts have been caught in the middle 

of a cost-price squeeze. 

To help alleviate this situation, a computer program 

called WALNUT has been developed that determines 

the least-cost mix of walnut lumber grades required to 

produce a given dimension cutting order. Through 

linear programing techniques, WALNUT correlates the 

cost associated with each grade of lumber with the 

predicted yields of each cutting size obtainable from 

that grade to arrive at the combination with the lowest 

total-mst. The program is easy to use and can be 

quickly adapted to fit most furniture rough mills and 

dimension manufacturing operations. 

Data Entry 

Input to the WALNUT program is accomplished using 

the Data Entry screen shown in Figure 1. For future 

reference, the date, name or model number of the 

cutting order, and the thickness of the lumber required 

are entered. The input factors used by the program 

include the cost per thousand board feet (M bf) associated with each grade of walnut to be considered in 

the possible least-cost mix, any adjustments desired in 

the predicted yields for each giade, and any volume 

constraints to be placed on the grades. 

The cost of each grade should represent the sum of 

all costs associated with that grade through the rough 

Input 

Factors 

Lumber Grade Information 

(Select only three) 

2C 1C SEL FAS 

PFI = Help PF3 = Exit PFI = Prev. screen PF8 = Uext screen 

/ 

mill. Cost items to be included are at the discretion 

of the user but could include those for lumber purchase, delivery, drying and handling, rough-mill cutup, 

inventory, and overhead. 

The yield adjustment factor can be used to adapt the 

basic yields for admissible defects, heavy thicknesses 

of lumber, or general rough-mill efficiency. The yield 

values used in WALNUT are derived from nomographs published in USDA Forest Service Research 

Paper FPL-162 entitled "Dimension Yields From Black 

Walnut Lumber." The actual numerical yield values 

and the width adjustments for Firsts and Seconds 

(FAS), Selects (SEL), No. 1 Common (IC), and No. 2 

Common (2C) are extrapolated from Tables 3-10 (Appendix). The yields for each length within a grade 

are based on the longest length obtained from that 

grade and are expressed as the net board feet of 

parts available per M bf of rough lumber input. Consequently, you can place a decimal after the second 

digit and consider them percentage yields. Yields are 

for random-width cuttings of 1 inch or wider. Yields for 

specific widths are obtained by subtracting the appropriate width adjustment from the random-width yields. 

Although the WALNUT program can accommodate 

lengths from 10 to 96 inches and specified widths up 

to 5% inches, the length limitations differ for individual 

grades of walnut lumber. As shown in the yield tables, 

the longest length available is 96 inches from FAS, 

90 inches from SEL, 80 inches from 1C, and 70 

inches from 2C. 

The volume constraints factor is used to limit the 

amount of a grade being considered. The resulting 

evaluation may or may not use all of the grade in limited supply, but in no case will the least-cost grade 

mix contain more of that grade than the volume allowed. This feature of the program is generally used in 

determining next best alternatives. 

Cutting Order 

Once the grades and costs have been established, 

the individual sizes of pieces to be obtained are entered using the Cutting Order screen (Figs. 2-3). Each 

size of cutting is entered by length, width, type, and 

number required. WALNUT can accommodate 50 

sizes of cuttings or panels. An R is entered for panels 

that will be glued up from random-width pieces. An S 

is entered when each part is to have a specified width. 

Figure 1 .-Data Entry screen. 
CUTTING ORDER 

Width 

(in.) 

Yo. or 

pieces 

Length 

(in.) 

NO. or piece8 

P1 = Help PF3 = Exit PFT r Prev. Screen PF8 i Next Screw 

Figure 2.--Cutting order (screen 1). 

[tea Langth Width RIS* No. or Itea Length Width RIS* No. 01 

tie. (in.) (in.) pieoes Uo. (in.) (in.) pieces 

(32) 

PP1 = Nelp PF3 * Brit PP7 = Prev. Screen PP8 = b to Pile 

Options Screen 

Figure 3.--Cutting order (screen 2). 

WALNUT Printout 

The WALNUT printout consists of four sections: (1) 

the input information that was evaluated, (2) the leastcost grade mix, (3) the range and sensitivity analysis, 

and (4) the cutting instructions to obtain the desired 

cuttings. 

Input Information 

The first section is to be retained for future reference. 

It provides a record of the information that was on 

the Data Entry and the Cutting Order screens. 

Least-Cost Grade Mix 

The second section provides the least-cost grade mix 

solution (Table 1). For each grade of lumber, the printout shows the predicted lumber volume required, the 

grade's contribution to the total production cost, the 

net board feet of cuttings to be obtained from it, the 

percent yield, and the totals of these items for the 

entire cutting order. 

For the costs and conditions we have specified, this 

solution represents the best that we can do. There is 

no other combination of grades and volumes that will 

result in a lower total cost. 

Range and Sensitivity Analysis 

The range and sensitivity analysis (Table 1) is the key 

to using WALNUT as a decisionmaking tool. It indicates how good our current least-cost grade mix is relative to the next best alternatives. As such, it also 

indicates how we might allocate our lumber when conditions are less than optimal. 

The range and sensitivity analysis shows the range 

over which the input cost of each grade can move 

without changing the least-cost grade mix, assuming 

that the input cost of the other grades remains constant. By varying the input cost of one grade while 

holding the others constant, the program determines 

at what level of input cost there would be a change in 

how the grades are used to obtain the cuttings required. The "associated gross volumes" column lists 

the volume of the grade that would be used at that 

input cost. 

In Table 1, it can be seen that if the input cost of 1C 

dropped by $1.66 per M bf to $1,108.34, the volume 

of 1C used in the alternative least-cost mix would increase by 45 percent to 5.500 M bf. Since the alternative mix must have the same total cost as o1.r current 

least-cost mix, it stands to reason that if more 1C lumber is used in the solution, it must use less of at least 

one of the other grades. By examining the associated 

gross volumes shown for the other grades, you can 

determine that at the lower input cost for IC, no FAS 

would be used and the amount of 2C would be reduced to 13.974 M bf. Proof can be obtained by comparing the total cost of our current grade mix with that 

of the alternative mix for the input cost conditions in 

this example. Total costs would be: 
FAS 1 C 2C Total 

Current ($1,792 x 0.656) + ($1,108.34 x 3.798) + ($575 x 15.210) =$14,131 

Alternative ($1,792 x 0) + ($1,108.34 x 5.500) + ($575 x 13.974) =$14,131 

With this knowledge, the manager could choose the 

alternative grade mix under current cost conditions, 

eliminating the need for FAS lumber. The alternative 

mix would increase the total cost only by about $3 

($14,140 compared to $14,137, as shown in Table 1). 

For a more complete discussion of the interpretation 

of the range and sensitivity analysis and how it can be 

used as a decisionmaking tool, .. see . USDA Forest Service Research Paper NE-563 entitled "OPTIGRAMI: 

Optimum Lumber Grade Mix Program for Hardwood 

Dimension Parts." 

Cutting Instructions 

The last section of the WALNUT printout is the cutting 

instructions (Table 2) for obtaining the required furniture cuttings from the proposed least-cost mix. This 

section is normally given to the rough-mill foreman for 

use in assigning lengths to specific saw operators. 

Table 1.-Least-cost grade mix solution (Nov. 30, 1985: china cabinet No. 

7335--walnut) 

Total 

Selected lnput CosV Gross production Board feet of Percent 

grade M bf volume cost cuttings yield 

Dollars M bf Dollars Number 

No. 2 

Common 575 15,210 8,746 7,141.8 47.0 

No. 1 

Common 1,110 3,798 4,216 2,267.2 59.7 

First and 

Seconds 1,792 656 1,174 483.5 73.7 

Total 19,664 14,137 9,892.5 50.3 

RANGE AND SENSITIVITY ANALYSIS 

Selected Input cost and Associated 

qrade IevelsIM bf aross volumes 

No. 2 

Common 

No. 1 

Common 

First and 

Seconds 

- - 

Dollars M bf 

Upper 577.28 

575.00 

Lower 571.78 

Upper 1,112.36 

1,110.00 

Lower 1,108.34 

Upper 1,796.31 

1,792.00 

Lower 1,785.88 
Table 2.-Optimum solution cutting information (Nov. 30, 1985: china 

cabinet No. 7335--walnut) 

Gross Cutting size Type of Cuttings Net board Board feet 

volume Length Width cuttinga feet shorts 

19,664 15,383 9,892.5 61 3.0 

"R = random; S = specified. 

b4/4 lumber thickness. 

It provides the input volume for each grade according 

to the least-cost mix, the cutting sizes that are to be 

obtained from each grade, and the number of pieces 

that are expected from that volume of lumber. 

The computer evaluates all combinations of cutting 

requirements and yield per grade to determine the 

least-cost combination. The results are not always according to tradition. For example, in the cutting instructions shown (Table 2), the longest length in the cutting 

order (73.375 inches) is obtained exclusively from 1C 

and not FAS. Instead, FAS is used to supplement 

the requirements for the 62.5, 37.875, 16.5, and 

13.875 cutting lengths. However, this combination of 

lengths results in a 73.7-percent yield of cuttings from 

FAS (Table 1). 

The cutting instructions also include the value "board 

feet shorts." This represents the net board feet of 

unused volume that would be available as 1 O-inchlong, random-width cuttings. As such, it provides an 

indication of how well the raw material is being utilized. 

In addition to information on each grade, there is a 

summary for the entire cutting order. Included are the 

total gross volume of lumber required, the total net 

board feet of cuttings to be obtained, the total board 

feet of shorts anticipated, and the total number of 

pieces required. 

WALNUT as a Decisionmaking Tool 

Because walnut lumber is an expensive commodity, 

relatively small adjustments in the grade composition 

of the lumber going to the rough mill can have significant effects on the cost of the dimension produced. 
WALNUT can be a valuable tool in determining the 

best, or least-cost, combination of grades to use for 

specific cutting orders. If an adequate quantity of a 

specific grade recommended in the least-cost mix is 

not available, WALNUT can be rerun using the volume 

constraints feature to determine the next best alternative. 

The upper and lower input cost levels shown in the 

range and sensitivity analysis are an indication of the 

relative value of each grade in relation to the value 

of the other grades when used in a particular cutting 

order. Consequently, decisions regarding the allocation of lumber to several cutting orders can be made. 

For instance, assume that in scheduling the daily cutting orders to be processed by the rough mill, there 

was not enough 1C available to satisfy the least-cost 

grade mix for two separate cutting orders. By comparing the upper input cost level for 1C lumber in each 

cutting order, the manager could elect to allocate the 

available 1C to the cutting order with the highest upper limit because that is where 1C would have its 

highest value use. The remaining 1C would be used in 

the other cutting order, which would be reevaluated 

using the volume constraints feature in WALNUT. By 

allocating the available 1C lumber in this manner, 

the total cost of processing the pair of cutting orders 

would be at a minimum. More than two orders would 

be handled in the same way, always giving priority 

to the cutting order providing the highest valued use of 

a particular grade. 

WALNUT, and its companion programs OPTlGRAMl 

and YELLOPOP ("Producing Yellow-Poplar Furniture 

Dimension at Minimum Cost Using YELLOPOP," 

USDA Forest Service Research Paper NE-592, in 

press), can provide valuable insight into numerous 

other management decisions besides specific leastcost grade mixes. OPTlGRAMl is used to evaluate 

cutting orders from all species graded by the standard 

National Hardwood Lumber Association rules and 

YELLOPOP is used for yellow-poplar. As management 

tools, they can help in making decisions regarding the 

grades of lumber that should be purchased, scheduling of lumber to be dried, improving rough-mill efficiency, or improving yields through changes in design. 

Creative managers will find additional applications. 

Using WALNUT 

WALNUT is designed for use on any IBM mainframe 

computer with a mathematical programing system 

(MPS) in its program library. The program can be accessed through an on-site computer or through a remote terminal. 

Remote Terminal 

For users wishing to use a remote terminal, WALNUT 

has been placed on the Computerized Management 

Network (CMN)-a national time-sharing computer 

service managed by the Virginia Cooperative Extension Service. Access to CMN can be made with any 

ASCII terminal and a modem, or with a microcomputer 

with a communications program. 

CMN is accessed through normal long distance telephone lines. To LOG ON, you will need to obtain a 

CMN user identification number (userid) and password 

by contacting: 

Virginia Polytechnic Institute & State University 

Virginia Cooperative Extension Service 

Extension Computing Resources 

Plaza I, Building D 

Blacksburg, VA 24061 

703-961 -51 84 

There is no initial fee or hookup charge for CMN, but 

there is a small monthly userid ownership charge. 

To use the program, simply dial the computer telephone number and LOG ON with your CMN userid 

and password. The computer will then ask you what 

program you would like. Enter "WALNUT." The Main 

Menu (Fig. 4) will ask what you would like to do. By 

pressing one of the four function (PF) keys, you can 

request a file for editing or analysis, determine if a 

submitted analysis has been returned to your userid, 

get the HELP file, or exit the program. If you wish 

to make a WALNUT analysis, press the PF4 key. A 

File Specification screen will ask you to enter a file 

name (Fig. 5). The file names that you have previously run also will be listed. To enter a file name, enter a name of from one to eight characters in the file 

name field and press the ENTER key, or position the 

cursor at the name of one of your existing files and 

press ENTER (this copies the name at the cursor to 

the file name field at the top of the screen); press 

ENTER again to validate the name you have selected. 

A message will appear at the bottom of the screen 

indicating that the requested file is an old file. 

Now that you have selected your file, press the PF8 

key to proceed to the File Options screen (Fig. 6). 

Press a PF key to select whether you want to edit the 

select file (PF4), submit the file for processing (PF5), 

or specify your job priority (PF6). Since we are interested in making an analysis, we would press PF4 

to proceed to the Data Entry screen (Fig. 1). You can 

move the cursor with the cursor controls or skip from 

field to field with the TAB key. 
ress a PF key to indioate your choice 

PF4 - Specify a file for editing or analysis. 

P95 - Determine if submitted analysis bas been returnad to your userid. 

PFl = Help PF3 = Exit 

Figure 4.-Main Menu screen. 

/ 

Enter file nw: ----------- 

Files: 

CCABIWET 17335 

PF1 z Help PF3 s Exit PF7 = Hain Menu Screen PFB = File Options Screen 

(i?dit/Submit 

Filea) 

Figure 5.-File Specification screen. 

On the completed Data Entry screen (Fig. 7), we have 

specified 414 thickness and the lumber grades of 2C, 

1 C, and FAS. The input costs of $575, $1,110, and 

$1,792 reflect estimates of the total of costs for each 

grade through the rough mill. The 87- and 96-percent 

yield adjustments for 2C and 1C are for demonstration 

purposes only. Since no volume constraints were 

used, the program assumes that there are unlimited 

volumes available for each grade. We would now 

press PF8 to move to the Cutting Order screens (Figs. 

8-9). Part sizes do not need to be entered in a particular order, such as from longest to shortest. 

Selected File: CCABINET 

Press the PP key Corresponding to your choice 

PF4 - Edit the Selected File 

PFS - Submit the file for processing. 

PF6 - Specify job priority. 

(Use before submitting a Job.) 

PFl i Help PF3 = Quit PF7 = Return to Pile Specification Panel 

-.-z 

Figure 6.-File Options screen. 

11 / 30 185 China Cabinet 17335 Walnut 4 14 -- -- -- --------------------- -- Date Name of Cutting Order Species Thicknesr 

Input 

Factors 

Lder Grade Information 

(Select only three) 

2C 1C SEL FAS 

PF1 = Help PF3 = Exit PF7 : Prev. screen PF~ = Next screw 

Figure 7.--Completed Data Entry screen. 

Pressing the PF8 key takes us to screen 2 of the cutting order (Fig. 3) and pressing PF8 again takes us 

to the File Options screen (Fig. 6). By pressing PF6, 

we can specify our job priority (Fig. 9). Five levels 

of priority can be selected, from idle (least expensive) 

to urgent (most expensive). If no selection is made, 

the program is set to run on idle priority. Assuming 

that we are satisfied with our priority, we press PF5 to 

submit our file for processing. We will receive a message at the bottom indicating "WALNUT job submitted. Check for results after 10 minutes." 
I CUTTING ORDER 

Item Length Width RIS* No. of Item Length Width R/S@ No. of 

No. (in.) (in.) pieces No. (in.) (in.) pieces ( 1) 36.750 22.000 R 142 ( 2) 22.750 22.000 R 86 

PFl : Help PF3 = Exit PF7 = Prev. Screen PF8 = Next SCreeQ 

Figure 8.--Completed cutting order (screen 1). 

----> WALNUT JOB PRIORITY <==== 

Mark an "Xu next to the priority you want assigned to your job. 

- IDLE (Least expensive) 

- OVERNIGHT 

- STAWARD 

- PRIORITY 

- URGENT (Most expensive) 

PF7 = Return to Menu 

L 

Figure 9.-WALNUT job priority. 

We can now press PF4 to make changes in our file if 

we want to rerun it with different lumber input costs, 

yield adjustments, or volume constraints. lf we want to 

enter another analysis, we press PF7 to return to the 

File Specification screen (Fig. 5). 

To receive our WALNUT output, we return to the Main 

Menu (Fig. 4) and press the 'PF~ key to determine if 

our submitted analysis has been returned to our 

userid. If it has not, we will receive a message at the 

bottom of the screen saying "No WALNUT output has 

been returned. Try again later." When the analysis is 

completed, the output is returned to your "reader." To 

look at the output, press PF11. This makes the entire 

WALNUT output available to you. You can scroll forward or backward by using the PF8 and PF7 keys. 

If you wish to keep the output, press the PF9 key to 

have it recorded onto your CMN' disk space as a permanent record or to have it printed. If you have a 

printer attached to your terminal, you can have the 

results printed by using the command "TPRINT" followed by the file name that you used (Fig. 5). You can 

discard the output by pressing the PF2 key or have it 

printed at Virginia Polytechnic Institute and State University (VPI&SU) by pressing the PF4 key. VPI&SU 

will then send you the results. Pressing the PF3 key 

returns you to the Main Menu. 

On every screen requiring the selection of an option or 

the input of data, the PF1 key has been labeled 

HELP. By pressing it, a help file will be displayed to 

explain each of the options available to you. 

Mainframe 

Users who have access to an IBM mainframe computer can obtain a free copy of our WALNUT program 

library by sending a blank tape to the Forestry Sciences Laboratory, P.O. Box 152, Princeton, West Virginia 24740. The library will be copied onto it and 

returned with documentation. 

If the IBM mainframe does not have an MPS in its 

program library, it will be necessary to obtain it before 

WALNUT will function. An MPSX can be obtained 

from an IBM representative or an MPSlll can be obtained from KETRON, lnc., Management Science System Divisions, 1400 Wilson Boulevard, Arlington, 

Virginia 22209. 

All features available on the CMN version also are 

available on the mainframe version and they are operated identically. 

Summary 

WALNUT can make a signifcant difference in the total 

cost of walnut dimension parts by selecting the most 

economical combination of grades and volumes required to produce a given cutting order. WALNUT and 

its companion programs, OPTlGRAMl and YELLOPOP, are decisionmaking tools designed to help furniture and dimension rough-mill managers. They are 

easy to use and are adaptable to individual plant situations. 

The computer program described in this publicatior, is 

available on request with the understanding that the 
U.S. Department of Agriculture cannot assure its accu- not assert any proprietary rights thereto nor represent 

racy, completeness, reliability, or suitablity for any it to anyone as other than a Government-produced 

other purpose than that reported. The recipient may computer program. 

Appendix 

Table 3.-Predicted yields of random-width cuttings from FAS grade walnut lumber 

(net board feet per M bf) 

Length of 

subsequent Length of longest cuttings 

cuttings 

(inches) 10 20 30 40 50 60 70 80 90 96 

Table 4.-Reduction values for obtaining predicted yields for cuttings of specified 

widths from FAS grade walnut lumber (net board feet per M b9 

Width of 

cuttings 

(inches) 

Length of cuttings 

10 20 30 40 50 60 70 80 90 96 
Table 5.-Predicted yields of random-width cuttings from SEL grade 

walnut lumber (net board feet per M bf) 

Length of 

subsequent 

cuttings Length of longest cuttings 

(inches) 10 20 30 40 50 60 70 80 90 

Table 6.-Reduction values for obtaining predicted yields for cuttings 

of specified widths from SEL grade walnut lumber (net 

board feet per M bf) -- 

Width of 

cuttings Length of cuttings 

(inches) 10 20 30 40 50 60 70 80 90 

Table 7.-Predicted yields of random-width cuttings from No. 1 

Common walnut lumber (net board feet per M bf) 

Length of 

subsequent 

cuttings Length of longest cuttings 

(inches) 10. 20 30 40 50 60 70 80 
Table 8.-Reduction values for obtaining predicted yields for 

cuttings of specified widths from No. 1 Common walnut 

lumber (net board feet per M b9 

Width of 

cuttings Length of cuttings 

(inches) 10 20 30 40 50 60 70 80 

Table 9.-Predicted yields of random-width cuttings from No. 2 

Common walnut lumber (net board feet per M bf) 

Length of 

subsequent 

cuttinas Length of longest cuttings 

(inches) 10 20 30 40 50 60 70 

Table 10.-Reduction values for obtaining predicted yields for 

cuttings of specified widths from No. 2 Common 

walnut lumber (net board feet per M bf) 

Width of 

cuttings Length of cuttings 
Martens, David G. Reduce dimension costs by using WALNUT. 

Res. Pap, NE-586. Broomall, PA: US. Department of Agriculture, 

Forest Service, Northeastern Forest Experiment Station; 1986. 

10 p. 

A computer program called WALNUT is described that determines the leastcost combination of lumber grades required to produce a given cutting order 

of furniture dimension parts. If the least-cost mix is not available, WALNUT 

can be used to determine the next best alternative. The steps involved in 

using the program are described. 

Keywords: furniture, hardwood dimension; lumber yields; dimension yields 
Headquarters of the Northeastern Forest Experiment Station are in 

Broomall, Pa. Field laboratories are maintained at: 

Amherst, Massachusetts, in cooperation with the University of 

Massachusetts. 

Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of 

Vermont. 

Delaware, Ohio. 

0 Durham, New Hampshire, in cooperation with the University of 

New Hampshire. 

0 Hamden, Connecticut, in cooperation with Yale University. 

0 Morgantown, West Virginia, in cooperation with West Virginia 

University, Morgantown. 

0 Orono, Maine, in cooperation with the University of Maine, 

orono. 

0 Parsons, West Virginia. 

0 Princeton, West Virginia. 

0 Syracuse, New York, in cooperation witb the State University of 

New York College of Environmental &iences and Forestry at 

Syracuse University, Syracuse. 

University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. 

0 Warren, Pennsylvania.