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,--., United States .&%: Department of -1P-" Agriculture OPTIG RAMI: Optimum Lumber 

Forest Service Grade Mix Program for 

Northeastern Forest Hardwood Dimension Parts 

Experiment Station 

Research Paper 

NE-563 David G. Martens 

1985 Robert L. Nevel, Jr. 
d 

I 

B 

: 

The Authors 

1 David G. Martens received a B.S. degree in forest products from Iowa 

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 4 improve the efficiency of wood use. 

Robert L. Nevel, Jr., forest products industry specialist, received a B.S. 

degree in forest technology from The Pennsylvania State University in 1965 

i and an M.F. degree in wood technology from Yale University in 1968. He 

then joined the Northeastern Forest Experiment Station's Forestry Sciences Laboratory at Princeton, West Virginia. In June 1978, he transferred 

to the Forest Inventory and Analysis unit, Broomall, Pennsylvania, where he 

is assigned to the timber removals group. 

9 6 Abstract 3 

With rapidly increasing lumber prices and shortages of some grades 

and species, the furniture industry must find ways to use its hardwood 

lumber resource more efficiently. A computer program called OPTlGRAMl 

is designed to help managers determine the best lumber to use in producing furniture parts. OPTlGRAMl determines the least-cost grade mix of 

lumber required to produce a given cutting order of dimension parts. If the 

optimum grade mix is not available, the program can determine the best 

alternatives. It also can be useful in procurement and allocation planning. 

A description of the pronram and examples of its use are included. 
Introduction 

As mid-1984 arrived, lumber 

prices for No. 1 Common 414 plainsawed northern red oak topped $600 

per thousand board feet (M bf). The 

FAS grade, with premium, topped 

$950 per M bf. Cherry and tough ash 

were not far behind. 

With spiraling lumber prices and 

shortages of some grades and 

species, the furniture industry must 

find ways to improve efficiency of 

lumber use. A computer program 

called OPTlGRAMl is a management 

tool that can do just that. With it 

you can determine the optimum, or 

least-cost, mix of lumber grades 

required to produce a given cutting 

order in a furniture rough mill; if this 

mix is not available, the next best 

mix can be determined. OPTlGRAMl 

also can be used in making decisions on improving lumber use 

practices. 

In this paper, I discuss the OPTIGRAMl program and provide 

examples of how the program can 

be used to help solve day-to-day 

rough-mill decisions. Ahother report 

entitled "OPTIGRAMI Users' 

Manual" provides the users of OPTIGRAMl with step-by-step instructions for performing an analysis. It 

can be obtained from tbe Northeastern Forest Experiment Station's 

Forestry Sciences Laboratory, P.O. 

Box 152, Princeton, West Virginia 

24740; or from the USDA Forest 

Service's Northeastern Area, State 

and Private Forestry, 370 Reed 

Road, Broomall, Pennsylvania 19008. 

OPTIGRAMI 

OPTlGRAMl is a computer 

program that was written for the 

person with little or no computer 

experience. Input to the program is 

straightforward and includes 

numerous prompts for the user's 

benefit. 

Because the program is designed 

for use on any IBMmainframe computer with a mathematical programing system (MPS) in its program 

library, access can be through an 

on-site computer or through a 

remote terminal. 

For users wishing to use a remote 

terminal, OPTlGRAMl has been 

placed on the Computerized 

Management Network (CMN), a 

national time-sharing computer 

service managed by the Virginia 

Cooperative Extension Service. The 

CMN software library consists of 

many problem-solving programs and 

resides on the computer at Virginia 

Polytechnic Institute and State University, Blacksburg, Virginia. 

Access to CMN can be made with 

any ASCII terminal and a modem. 

You also can use a microcomputer 

with a communications program as 

a terminal. You can access CMN by 

dialing the computer directly and 

paying the long-distance charges on 

your monthly telephone bill. 

Anyone can use CMN. Directions 

for obtaining a CMN userid and 

password are presented in the 

OPTlGRAMl Users' Manual. 

For its data base OPTlGRAMl 

uses the predicted yields of dimension parts from standard grades of 

kiln-dried lumber developed at the 

USDA Forest Service's Forest 

Products Laboratory (Englerth and 

Schumann 1969). These yields were 

developed for hard maple, but they 

can be applied to most species 

graded by the same standard 

National Hardwood Lumber Association rules. 

OPTlGRAMl uses linear programing techniques to correlate the 

input cost for each lumber grade 

with the predicted yields of various 

dimension part sizes to determine 

the least-cost combination of 

grades required to satisfy a given 

cutting order. The sensitivity of that 

combination to changes in the cost 

associated with each grade also is 

evaluated. 

The OPTlGRAMl printout provides 

detailed information on production 

cost, yields by grade, and the size, 

number, and net board footage of 

cuttings obtainable from each 

grade. 

The program is fast, simple to 

use, and inexpensive, usually 

costing less than $5 per analysis. It 

provides a quantitative basis for 

making decisions based on input 

information applicable to each 

specific situation. 
lnformation Required 

The only input information 

required is a description of what 

you want OPTlGRAMl to evaluate. In 

general, this consists of the cutting 

order to be evaluated; the grades of 

lumber you want considered and 

costs for each; and any conditions 

or limitations you may impose. 

Cutting Order lnformation 

Cutting order information 

typically includes some type of 

identification or furniture model 

number; the date and species for 

future reference; the thickness of 

lumber required; and the cutting 

order itself, which is a listing of the 

cuttings by length, width, type, and 

number required. Up to 50 different 

sizes of cuttings can be evaluated 

at one time. The yield tables 

accommodate lengths from 10 to 96 

inches and specified widths up to 6 

inches. A random-width description 

is used when the parts are to be 

glued into panels. 

Lumber Grades and Costs 

You can select up to three grades 

of lumber to be considered for possible inclusion in the least-cost mix. 

These can be picked from First and 

Seconds (FAS), Selects (SEL), No. 1 

Common (No. 1 C), No. 2 Common 

(No. 2 C), or No. 1 Common and Better (No. 1 C and Better). The input 

cost for each grade, expressed in 

dollars per M bf, is the sum of all 

costs through the rough mill. Cost 

items to be included are at the discretion of the user but could 

include costs for lumber purchase, 

delivery, drying and handling, roughmill cut-up, inventory, inspection, 

and overhead (Table 1). 

Table 1.-Cost items to consider when determining production cost per lumber grade 

Pur- Drying Inventory Overhead 

Lumber chase and and and 

grade price Delivery handling Cut-up storage other Total 

--------------- DollarslM bf - - - - - - - - - - - 

2C 292 20 100 80 8 70 570 

1 C 588 20 100 50 10 75 835 

FAS 768 20 100 40 12 80 1020 

Volume Limitations and Yield 

Adjustments 

The volume limitations and yield 

adjustments are simply options you 

can use to tailor the OPTlGRAMl 

analysis to fit your specific situation. You can limit the volume of a 

grade being considered by placing a 

volume constraint on that grade. 

The resulting OPTlGRAMl 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. 

You also can adjust the predicted 

yields of any of the grades with a 

yield adjustment factor. Acting as 

multipliers, yield adjustment factors 

can be used to adapt the basic 

yields for individual species, admissible defects, heavy thicknesses of 

lumber, and general rough-mill 

efficiency. 

What's the Best You Can 

Do? 

The OPTlGRAMl printout consists 

of four sections: (1) the input 

information that you have evaluated; 

(2) the optimum of least-cost grade 

mix; (3) the range and sensitivity 

analysis; and (4) the cutting instructions to obtain the desired cuttings. 

The first three sections usually 

would be retained by the plant 

manager and filed for future 

reference. The last section would 

go to the rough-mill foreman for 

use in establishing the cutting 

instructions. 

Input lnformation 

The first section is strictly for reference purposes. It records the 

input information you have asked to 

be evaluated. Appendix I includes 

our cutting order identification, 

species, and date, and the grades 

we wanted evaluated, lumber cost, 

yield adjustment factor, volume constraints, and lumber thickness. 
Next we have the cutting order 

that we have evaluated. The length, 

width, type, and number of pieces 

were input. The net board feet of 

each cutting was calculated by the 

program. The cutting bill does not 

need to be entered in any giveq 

I order; the program will arrange it by 

type of cutting, whether random or 

specified, and by longest length 

first. 

Least-Cost Grade Mix 

The second section provides the 

least-cost grade mix solution 

(Appendix 11). In addition to the cutting order identification, the printout 

shows which grades were being 

considered, the input cost for each 

grade, and the least-cost grade mix. 

The printout contains, for each lumber grade, the predicted lumber 

volumes required; each grade's 

contribution to the total production 

cost; the net board feet of cuttings; 

the percent yield; and the totals of 

these for the entire cutting order. In 

our example, the least-cost grade 

I mix had a total cost of $14,538 and 

contained 7.268 M bf of No. 2C, 

5.298 M bf of No. 1 C, and 5.855 

I M bf of FAS (Appendix 11). For the 

conditions we have imposed, that is 

the best we can do. There is no 

I other combination of grades that 

will result in a lower total cost. 

I Range and Sensitivity Analysis 

The range and sensitivity section 

provides information on how 

responsive our optimum grade mix 

is to changes in the input cost of 

the various grades being considered 

(Appendix 11). For decision purposes, it is probably the most 

important part of the OPTlGRAMl 

printout. 

By varying the input cost of one 

grade while holding the others 

constant, OPTlGRAMl determines at 

what level of input cost there would 

be a change in how the grades are 

used to obtain the cuttings 

required. In essence, the program 

says that if the input cost of a given 

grade were to change to this new 

level, assuming that the cost of 

others remains the same, there 

would be another combination of 

volumes that would be as good as 

the least-cost grade mix we have 

now. In other words, at those input 

costs both volume combinations 

would have the same total cost. The 

program also calculates the amount 

of that grade that would be used in 

the alternative least-cost grade mix 

associated with that level of input 

cost. 

Another way to consider these 

cost limits for a grade is that within 

the cost range between them, 

assuming that the cost of other 

grades remains constant, the leastcost grade mix will not change. 

True, the total cost will change 

depending on the level of input cost 

being considered; but the specific 

volumes of the grades given in the 

least-cost solution always will 

provide the lowest total cost for 

those conditions. 

For example, consider the cost of 

No. 1 C in our range and sensitivity 

analysis (Appendix 11). Although the 

input cost is $835.00 per M bf, it 

could range from a low of $834.23 to 

a high of $851.64 per M bf without 

changing the least-cost grade mix. 

However, at an input cost of 

$834.23 per M bf, less than a dollar 

per M bf from our current cost, 

there would be another combination 

of grades with the same total cost, 

but it would use 10,281 board feet 

of No. 1 C. That is nearly twice as 

much as our current optimum mix. 

In linear programing, the range 

values often are referred to as 

critical points, representing the 

intersection of two limiting constraints in the optimal solution. 

Consequently, they provide two 

equal solutions. 

In our example, the alternate 

solution would use 4,983 board feet 

more No. 1 C. Since it must have 

the same total cost as the original 

grade mix, it stands to reason that it 

will use less of the other grades. 

Note that the associated volume for 

No. 2 C drops from 7,268 board feet 

to 5,785 board feet, and FAS drops 

from 5,855 board feet to 2,609 board 

feet. 

By comparing the total cost for 

the two solutions, you can confirm 

their equality: 

No. 1 C No. 2 C FA S Total 

1 

Current 

solution ($834.23 x 5.298)+($570 x 7.268)+($1020 x 5.855) = $14,535 

Alternative 

solution ($834.23 x 10.281)+ ($570 x 5.785) + ($1020 x 2.609) = $14,535 I 

This particular cutting bill is 

sensitive to input price, especially 

that of No. 1 C. Information 

regarding the alternative grade mix I 

can be of tremendous value to the 

rough-mill manager. 
If You Can't Have 

Optimum, What Is Next 

Best? 

Cutting Information 

The last section of the OPTIGRAMl printout is the cutting information for obtaining the required 

furniture parts from the proposed 

grade mix (Appendix Ill). This is 

the section that would be given to 

the rough-mill foreman. It provides 

the input volume of each grade 

according to the optimal grade mix, 

the part sizes that should be 

obtained from each grade, and the 

number of pieces that are expected 

from that volume of lumber. 

This section also provides a value 

called "board feet shorts." In the 

case of No. 2 C, it shows 625 board 

feet, or the net board feet of volume 

that would be available in 10-inchlong, random-width cuttings. This 

value was included in the program 

to provide an indication of how well 

the resource is being used. In our 

example cutting order, the shortest 

length is 19-112 inches. Consequently, there would be substantial material availablelfor 10-inch 

cuttings. 

As you would expect, the longer 

pieces are from the better grades 

while the short pieces are from all 

grades. For our cutting order, all of 

the requirements for 87-314-inch, 80- 

318-inch, and 56-inch cuttings would 

be obtained from FAS, as would 

some of our shorter pieces. 

The longest length to be obtained 

from No. 1 C would be 64-318 

inches. However, the full requirement, 200 pieces, would be 

obtained from No. 1 C, as would the 

full requirement for the 48-114-inch 

random cuttings. 

The requirements for the 33-118- 

inch cuttings were split between 

FAS and No. 1 C, and the 23-112- 

inch cuttings were split between 

No. 1 C and No. 2 C. The shortest 

two lengths would be obtained from 

all three grades. lnformation 

regarding specific lengths and 

number of pieces to be derived from 

each grade can have a major impact 

on improving yields from the raw 

material. 

Optimum is best, and we always 

would conduct as unconstrained 

OPTlGRAMl analysis as our first 

step. Because most furniture rough 

mills do not have unlimited supplies 

of every species, grade, and thickness, OPTlGRAMl is useful in helping the rough-mill manager allocate 

the available raw material most 

efficiently. 

The key to determining the next 

best alternative for lumber allocation is the range and sensitivity 

analysis section. In general, when 

the upper or lower cost limit is near 

the current input cost and is accompanied by a major change in the 

associated gross volume, our leastcost solution would be considered 

sensitive. By contrast, if a major 

change in the input cost would 

result in a relatively minor change in 

the associated gross volume used 

in the alternative solution, our 

current solution would be considered relatively insensitive to the 

cost of that grade. Essentially, 

everyone would agree with these 

definitions of sensitivity at the 

extremes. However, between these 

extremes is a gray area of what is 

sensitive and what is not. Sensitivity 

is really a measure of what is of 

practical importance; it is at best a 

subjective judgment. As a result, 

changes in the total cost of our 

cutting order or in the volume of a 

grade of lumber used that seem 

important enough for us to take 

advantage of today might be considered a nuisance 6 months from 

now. 

Use of the range and sensitivity 

analysis of OPTlGRAMl can be helpful in determifling our next best 

alternatives when we have a limited 

supply of a grade, or are trying to 

conserve a grade that is in short 

supply, or have run out of a grade 

entirely. 

Limited Supply of a Grade 

With all of the different species, 

grades, and thicknesses required to 

operate a modern rough mill, occasionally there will be an insufficient 

supply of available dry lumber of a 

given grade and thickness needed 

for the least-cost grade mix. 

However, the fact remains that 

whatever other option we decide to 

take, the total cost will be greater 

than if we had the optimum mix of 

grades. 

Certain types of cutting orders 

appear to have certain grades or 

grade mixes that are most appropriate for them. For instance, 

cutting orders for dining room 

chairs typically require a high 

proportion of No. 2 C in the leastcost mix. Buffets, on the other 

hand, call for mostly No. 1 C. An 

indication of the appropriateness of 

a given grade to a cutting order can 

be derived from the upper and lower 

cost limits in the range and sensitivity section. For example, if OPTIGRAMl has been used to evaluate a 

cutting order for dining chairs, the 

upper cost limit for No. 2 C might 

be $80 or $90 above the current 

input cost that was used. This 

would be interpreted to mean that if 

the cost of the other grades remains 

unchanged, the input cost level of 

No. 2 C could increase by $80 or $90 

without changing the amount of the 

No. 2 C used in the least-cost solution. Therefore, No. 2 C would be 

considered well suited to this cutting order. In other words, this cutting order is insensitive to the cost 

changes of No. 2 C. It also means 

that if there is a shortage of No. 

2 C, this would not be a good cutting order to be forced to substitute 

No. 1 C to fulfill the total lumber requirements. 

Although OPTlGRAMl evaluates 

each cutting order individually, the 

printouts from these individual 

analyses can be helpful in making 

decisions that involve a number of 

cuttin.g orders. 
With this in mind, assume that we 

were evaluating the OPTlGRAMl 

solutions with unconstrained 

lumber volumes for three individual 

cutting orders that together required 

a total of 60 M bf of No. 2 C 414 

pecan. From our inventory records 

we determined that only 40 M bf are 

available. Therefore, we must substitute some of our higher grades, 

probably No. 1 C, to complete the 

orders. Our problem becomes: 

Where can we substitute most 

effectively? By looking at the 

individual range and sensitivity 

analyses for No. 2 C, we note the 

following: 

Associated 

Cutting Input cost gross 

bill and levels volumes 

Our logic would be as follows: On the basis of the upper 

limits shown, we might consider 

that No. 2 C could be worth as 

much as $497 per M bf to us relative 

to the costs of the other grades 

ahen it is being used in cutting order B. Consequently, cutting order 

B provides our highest value use of 

No. 2 C and should receive all of the 

No. 2 C it requires-30 M bf. In 

other words, B is the most insensitive to changes in the cost of No. 

2 C and, therefore, least suited for 

substitution. Cutting order A would 

be next and should receive the remainder. However, since there is 

not enough No. 2 C to fulfill A's 20 

M bf requirement, it should be reanalyzed by OPTlGRAMl but this 

time with a 10 M bf volume constraint on No. 2 C. OPTlGRAMl will 

then give the least-cost grade mix 

for A based on this limitation. Cutting order C is the most sensitive to 

the cost of No. 2 C, and OPTIGRAMI 

automatically would reduce the 

amount of No. 2 C used if the level 

of input cost increased by as much 

as $9 per M bf. Therefore, cutting 

order C should be reevaluated by 

OPTlGRAMl and not include No. 2 C 

in the grades to be evaluated. By 

using the 40 M bf of No. 2 C pecan 

in these combinations for the three 

individual cutting orders, our combined cost for all three will be at a 

minimum for the conditions that 

exist. 

Conserving Grades in Short Supply 

If a given grade and thickness of 

a species is expected to be in limited supply over a prolonged period, 

OPTlGRAMl can help determine 

ways to conserve it. In this case, 

each time an OPTlGRAMl evaluation 

indicates the use of this grade in 

the optimum mix, the range and 

sensitivity analysis should be examined for possible alter~atives. If the 

analysis indicates that the optimum 

solution is sensitive (i.e., upper or 

lower cost limits are close to input 

cost), then that cutting order may 

be a good place to elect to substitute at least some of another grade 

and thereby conserve the one in 

short supply. By being sensitive, it 

points up the opportunity to be able 

to change the grade mix from optimum at a relatively small sacrifice 

in increased total cost. It is less 

costly in the long run to substitute 

some of another grade at each 

opportunity rather than to run out of 

a grade and then be forced to substitute in a cutting order that clearly 

is suited to the grade that is no 

longer available. 

This is where sensitivity becomes 

subjective. How much are we willing to increase the total cost of a 

given cutting order to conserve a 

specific grade of lumber? In the 

case of our example cutting order, 

there would be little additional cost. 

As an example, suppose we wish to 

conserve No. 2 C. From the printout 

in Appendix II, we could determine 

that the next best grade mix would 

use 5.785 M bf of No. 2 C instead of 

7.268 M bf. Since at the input cost 

of $572.59 per M bf both mixes 

would have the same total cost, we 

can determine that we could conserve 1,483 board feet of No. 2 C at 

a sacrifice of $3.84 in increased 

total cost. This is calculated by 

multiplying the change in input cost 

by the change in volume at the limit 

([$572.59 - $5701 x [7.268 - 5.7851 

= $3.84). Is it worth $4 to us to save 

1,480 board feet of No. 2 C? 

If it is, then we also might want 

to consider going beyond the limits 

of this OPTlGRAMl evaluation and 

rerun it with a constrained volume 

for No. 2 C below the current limit 

volume of 5.785 M bf. This would 

provide another alternative for saving the grade that we might wish to 

consider. 

What Is Next Best if You Run Out of 

a Grade 

When you are out of one of the 

grades contained in the least-cost 

mix, you should first rerun 

OPTIGRAMI, omitting this grade 

from those being considered, and 

then compare the total cost of the 

two evaluations. If the additional 

cost is not considered serious, then 

you have the next best solution. 

If the additional cost is considered prohibitive, OPTlGRAMl can 

be used to help you evaluate other 

possibilities, such as purchasing 

additional dry lumber or purchasing 

some or all of the parts in the 

cutting bill. 

Cutting Orders with Low Yields 

When evaluating a cutting order, 

OPTlGRAMl also provides the 

expected percent yield of cuttings 

and the expected residual of 10-inch 

cuttings for each lumber grade in 

the least-cost mix and for the mix 

as a whole. These should be monitored closely. 

Low percent yields or high 

amounts of short material indicate 

inefficient use of the raw material, 

which results in higher than normal 

costs. When this occurs, other alternatives should be considered to 

reduce these costs. First determine 

whether the low predicted yields are 

caused by an abnormal distribution 

of cutting sizes or by a small 

number of dimension sizes in the 

cutting bill; when this is determined, consider remedial 

alternatives. 
How Can You Do Better in 

the Future? 

By reviewing OPTIGRAMI printouts of the cutting orders for the 

last 3 months to 1 year, you can 

evaluate instances where other than 

optimum results were achieved. 

Then by recalling the prevailing 

circumstances, you can determine if 

these instances can be avoided in 

the future. 

Literature Cited 

Englerth, George H.; Schumann, 

David R. Charts for calculating 

dimension yields from hard maple 

lumber. Res. Pap. FPL-118. 

Madison, WI: U.S. Department of 

Agriculture, Forest Service, Forest 

Products Laboratory; 1969. 12 p. 

With OPTlGRAMl we can make 

management decisions regarding 

(1) the grades of lumber that should 

be purchased; (2) scheduling of lumber to be dried; (3) improving mill 

efficiency; (4) purchasing dimension 

parts; and (5) improving yields 

through changes in design or size 

requirements. Creative managers 

will discover additional ingenious 

applications for OPTlGRAMl in 

furniture and dimension operations. 

Acknowledgments 

We greatly appreciate the cooperation 

of members of the faculty of the 

School of Forest Resources, North 

Carolina State University, who 

provided guidance and technical 

support during this study. We also 

thank USDA Forest Service 

employees Daniel E. Dunmire Ill and 

Edward K. Pepke for their help in 

demonstrating the concept's validity 

in industrial situations through the 

Rough Mill Improvement Program; 

and Kenneth R. Whitenack for his 

programing efforts. 
Appendix I 

Input Information Section of OPTlGRAMl Printout 

July 10,1984-COUNTRY SQUIRE SUITE-HARD MAPLEa 

LUMBER PRODUCTION 

GRADEb COSTSC 

(DollarslM bf) 

NUMBER 2 COMMON 570.00 

NUMBER 1 COMMON 835.00 

FIRST AND SECONDS 1020.00 

CUTTING SIZE 

LENGTH WIDTH 

(Inches) (Inches) 

GRADE YIELD 

ADJUSTMENT 

FACTORd 

100.0 

100.0 

100.0 

INPUT CUTTING ORDER 

TYPE OF CUTTING 

RANDOM (R) OR 

SPECIFIED (S) 

VOLUME 

CONSTRAINTSe 

(M bf) 

None 

None 

None 

NUMBER 

OF 

CUTTINGS 

LUMBER 

THICKNESSf 

(Inches) 

414 

414 

414 

NET BOARD 

FEET OF 

CUTTINGS 

Total 

aCutting order identification, species, and date. 

bStandard lumber grades chosen to be evaluated. 

CTotal production cost per M bf assigned to each grade. 

dAdju~tment made to the yield of each grade. 

eVolurne constraints imposed on each grade. 

Lumber thickness being considered. 
: Appendix II 

Least-Cost Grade Mix Solution and Range and Sensitivity Analysis 

Information Sections of OPTIGRAMI Printout 

LEAST-COST GRADE MIX SOLUTION 

IN PUT 

COSTIM bfc 

SELECTED GRADESb (Dollars) 

NUMBER 2 COMMON 570 

NUMBER 1 COMMON 835 

FIRST AND SECONDS 1020 

TOTALS 

.COUNTRY SQUIRE SUITE-HARD MAPLEa 

SUMMARY BY GRADE 

TOTAL 

GROSS PRODUCTION BOARD FEET 

VOLUMEd COSTe OF CUTTINGSf 

(M b f) (Dollars) 

7.268 41 42 3541.4 

5.298 4424 3378.1 

5.855 5972 3954.5 

18.421 14538 10873.9 

SELECTED GRADES 

NUMBER 2COMMON 

NUMBER 1 COMMON 

FIRST AND SECONDS 

RANGE AND SENSITIVITY ANALYSIS INFORMATION 

INPUT COST AND 

LEVELSIM bfh 

(Dollars) 

Upper 572.59 

570.00 

Lower 559.27 

Upper 851.64 

835.00 

Lower 834.23 

Upper 1021.18 

1020.00 

Lower 1009.27 

PERCENT 

YlELDg 

48.7 

63.7 

67.5 

59.0 

ASSOCIATED GROSS 

VOLUMES (M bf)' 

a Identifying name or title of the cutting order, species, and date. 

bStandard lumber grades chosen to be evaluated by OPTIGRAMI. 

CTotal production cost per M bf assigned to each grade. 

dQuantities of each grade contained in the least-cost grade mix. 

eTotal costs for the amount of each grade of lumber used in the least-cost mix. 

'Quantity of cuttings expected from each grade. 

QAnticipated percent yield to be obtained from each grade. 

Range of input costs for each grade. 

iVolume of that grade used in the alternate least-cost grade mix at that level of input cost. 
I 

I Appendix Ill 

1 Optimum Solution Cutting Information Section of OPTlGRAMl Printout I 

I OPTIMUM SOLUTION CUTTING INFORMATION 

I July 10,1984-COUNTRY SQUIRE SUITE-HARD MAPLE 

I LUMBER GROSS CUTTING SIZEa TYPE OF NUMBER OF 

SELECTED GRADES THICKNESS VOLUME LENGTH WIDTH CUTTING CUTTINGSb 

I (Inches) (M bf) - - - - (Inches) - - - - 

I NUMBER 2 COMMON 414 7.268 

30.000 19.000 R 608 

28.250 3.000 S 130 

23.500 4.000 S 1117 I 22.750 2.250 S 300 

21.000 4.250 S 172 

~ 19.500 2.750 S 31 1 

NET BOARD FEETIGRADEd = 3541.4 

I BOARD FEET SHORTSe = 625.0 

1 N,UMBER 1 COMMON 5.298 

I NET BOARD FEETIGRADE = 3378.1 

I BOARD FEET SHORTS = 217.2 

FIRST AND SECONDS 

NET BOARD FEETIGRADE = 3954.5 

BOARD FEETSHORTS = 140.5 

TOTAL GROSS VOLUME TOTAL NET BOARD FEET 

(M bf) 18.421 10873.9 

TOTAL SHORTS 

(bf) 

982.8 

N ET 

BOARD FEETC 

TOTAL NUMBER OF PIECES 

7768 

a Cuttings obtained from each grade in the least-cost solution. 

Expected number of each cutting to be obtained from each grade. 

Anticipated quantity of each cutting obtained from each grade. 

Total quantity of all cuttings expected from each grade. 

Cumulative unused net board footage of 10-inch-long cuttings available in each grade. 
1 The computer program described in this publication is 

available on request with the understanding that the US. 

Department of Agriculture cannot assure its accuracy, 

completeness, reliability, or suitability for any other purpose 

than that reported. The recipient may not assert any I proprietary rights thereto nor represent it to anyone as other 

than a Government-produced computer program. For 

cost information, please write: 

Northeastern Forest Experiment Station, Forestry Sciences , Laboratory, P.O. Box 152, Princeton, West Virginia 24740. 
Martens, David G.; Nevel, Jr., Robert L. OPTIGRAMI: Optimum 

lumber grade mix program for hardwood dimension parts. 

Res. Pap. NE-563. Broomall, PA: U.S. Department of Agriculture, Forest Service, Northeastern Forest Experiment 

Station; 1985. 10 p. 

With rapidly increasing lumber prices and shortages of some 

grades and species, the furniture industry must find ways to 

use its hardwood lumber resource more efficiently. A 

computer program called OPTIGRAMI is designed to help 

managers determine the best lumber to use in producing 

furnit'ure parts. OPTIGRAMI determines the least-cost grade 

mix of lumber required to produce a given cutting order of 

dimension parts. If the optimum grade mix is not available, 

the program can determine the best alternatives. It also can 

be useful in procurement and allocation planning..A description of the program and examples of its use are included. 

ODC 836.1 

Keywords: Furniture; hardwood dimension; lumber yields; 

dimension yields 

* U. S. GOVERNMENT PRINTING OFFICE: 1985-505-028 20025 
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. 

0 Berea, Kentucky, in cooperation with Berea College. 

Burlington, Vermont, in cooperation with the University of 

Vermont. 

0 Delaware, Ohio. 

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

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 with the State University of 

New York College of Environmental Sciences and Forestry at 

Syracuse University, Syracuse. 

0 University Park, Pennsylvania, in cooperation with the 

Pennsylvania State University. 

0 Warren, Pennsylvania.