Development of a 3D log sawing optimization system for small sawmills in central Appalachia, US

15 Pages·2011·1.29 MB·English

by  Lin, Wenshu

DEVELOPMENT OF A 3D LOG SAWING OPTIMIZATION SYSTEM FOR
SMALL SAWMILLS IN CENTRAL APPALACHIA, US
Wenshu Lin{
GraduateResearchAssistant
E-mail:[email protected]
Jingxin Wang*{
Professor
WestVirginiaUniversity
DivisionofForestryandNaturalResources
Morgantown,WV26506
E-mail:[email protected]
Edward Thomas
ResearchScientist
USDAForestService,NorthernResearchStation
Princeton,WV24740
E-mail:[email protected]
(ReceivedApril2011)
Abstract. A3Dlogsawingoptimizationsystemwasdevelopedtoperformloggeneration,openingface
determination,sawingsimulation,andlumbergradingusing3Dmodelingtechniques.Heuristicanddynamic
programmingalgorithmswereusedtodetermineopeningfaceandgradesawingoptimization.Positionsand
shapesofinternallogdefectswerepredictedusingamodeldevelopedbytheUSDAForestService.Lumber
gradingprocedureswerebasedonNationalHardwoodLumberAssociationrules.Thesystemwasvalidated
throughcomparisonswithsawmilllumbervalues.Externalcharacteristicsoflogs,includinglength,large-
endandsmall-enddiameters,diametersateachfoot,anddefectswerecollectedfromfivelocalsawmillsin
centralAppalachia.Resultsindicatedthathardwoodsawmillshavethepotentialtoincreaselumbervalue
throughoptimalopeningfaceandsawingoptimizations.Withtheseoptimizations,averagelumbervalue
recoverycouldbeincreasedby10.01%usingtheheuristicalgorithmor14.21%usingthedynamicprogram-
mingalgorithm.Lumbergradewasimprovedsignificantlybyusingtheoptimalalgorithms.Forexample,
recoveryofselectorhighergradelumberincreased16-30%.Thisoptimizationsystemwouldhelpsmall
sawmilloperatorsimprovetheirprocessingperformanceandimproveindustrycompetitiveness.
Keywords: Heuristic,dynamicprogramming,gradesawing,modeling,optimization.
INTRODUCTION (Zhuetal1996;Leeetal2001).Thisprocessis
limited by the decision-making ability of the
Maximizing profits gained from the conversion
operators. Because most log defects are at
of hardwood logs into lumber is a primary con-
unknown internal locations within the log, it is
cern for both large and small forest product
difficult to give an optimal decision (Sarigul
companies. Increased operating costs caused by
et al 2001). Problems that arise from manual
higher fuel and electricity prices coupled with
log defect detection and conventional log saw-
lowerlumberpricesareforcingwoodprocessors
ing practices include low lumber yields, less
to become more efficient in their operations.
than adequate lumber quality with respect to
Conventional log sawing practices rely heavily
grade, and slow production, all of which result
onmanualinspectionofexternallogdefectsand
in inefficient use of forest resources (Thomas
arebasedonmaximizingeithervolumeorgrade
2002).
Log scanning and optimization systems can
*Correspondingauthor
{SWSTmember be used in lumber production (Thomas et al
WoodandFiberScience,43(4),2011,pp.379-393
#2011bytheSocietyofWoodScienceandTechnology
380 WOODANDFIBERSCIENCE,OCTOBER2011,V.43(4)
2004). Preliminary studies have shown that implemented the latest sawing and optimization
implementinganautomatedlogscanninginspec- technologiestoincreaselumberyieldandvalue.
tion system has the potential toimprove produc- However,smallhardwoodsawmillsarelessable
tivity and quality, or grade, of the hardwood to implement advanced technologies because of
lumber being produced (Zhu et al 1996). Hard- highinitialcost,longpaybackperiod,andmod-
wood lumber value can be increased 11-21% by ifications to current operations (Occen˜a et al
using optimal sawing strategies gained through 2001).Tosurviveinthehighlycompetitivemar-
the ability to detect internal log defects (Sarigul ketplace under current turbulent economic con-
etal2001).Althoughinternaldefectsaredifficult ditions, developing appropriate cost-effective
to detect, any improvements in defect detection milling technology for these smaller mills is
cancontributetorecoveryofhigherqualitylum- essential for them to improve profitability and
ber, increased profits, and better use of forest competitiveness. Therefore, the objectives of
resources (Thomas 2002). Currently, most avail- this study were to 1) design optimization algo-
able scanning systems are based on external rithmstodetermineopeningfaceandlogsawing
models that use a laser-line scanner to collect patterns to improve lumber value recovery;
rough log profile information. These systems 2) develop a 3D visualization computer-aided
were typically developed for softwood (pine, log sawing simulation system for small hard-
spruce, fir) log processing and for gathering wood sawmills to implement optimal computer
information about external log characteristics algorithms; and 3) validate the optimal sawing
(Samson 1993) but are becoming more common systembycomparingcomputer-generatedresults
in hardwood mills. The USDA Forest Service in withactualoutputatexistingsawmills.
cooperation with Concord University and Vir-
ginia Tech has developed a full shape 3D log
LITERATUREREVIEW
scannertodetectseverelogsurfacedefectsusing
relativelylow-costequipment($30,000plusinte- Sincethe1960s,therehavebeenongoingefforts
grationlaborcost)(Thomas2002,2006).Inaddi- to improve lumber value or volume recovery
tion, internal log defect prediction models also througheithercomputersimulationormathemat-
weredevelopedbasedonmeasurementsofexter- icalprogramming(Tsolakides1969;Hallockand
naldefects(Thomas2006,2008).Arecentstudy Galiger1971;Richards1973;Hallocketal1976;
has shown that the models can accurately pre- Richards et al 1979, 1980; Lewis 1985; Occen˜a
dict about 81% of internal knot defects for red and Tanchoco 1988; Harless et al 1991; Steele
oak(Thomas2011).Therearealsoseveralinter- et al 1993, 1994; Occen˜a et al 1997, 2001;
nal log scanning technologies being developed Guddanti and Chang 1998; Chang et al 2005).
(X-ray, computed tomography, MRI, etc); how- For example, Tsolakides (1969) reconstructed a
ever,noneofthemareefficientandcost-effective log as a cylinder and developed a digital com-
forsmall-scalehardwoodsawmills. puter analytical technique to study effects of
alternativesawingmethods.HallockandGaliger
Small hardwood producers are key contributors (1971), Hallock et al (1976), and Lewis (1985)
to the hardwood industry in the central Appala- developed Best Opening Face (BOF) systems to
chian region. In West Virginia, 68.52% of the maximize the volume of lumber produced from
hardwood sawmills produce less than four mil- small-diametersoftwoodlogs.TheBOFprogram
lion board feet (9440 m3) of green hardwood is a computer simulation model of the sawing
lumber per year (West Virginia Division of process for recovering dimension lumber from
Forestry2004).InPennsylvania,50%ofrespon- small, straight logs. The sawing algorithm deter-
dents in a hardwood sawmill profile survey mines the initial opening face to produce the
produced less than 3.2 Mm3 of lumber per smallestacceptablepiecefromagivenlog.Once
year (Smith et al 2004). Most large softwood the opening face is found, consecutive cuts are
mills and many large hardwood mills have made and the yield for the log is determined.
Linetal—3DLOGSAWINGOPTIMIZATIONSYSTEMFORSMALLSAWMILLS 381
Then, the opening face is moved toward the sawing system for optimal lumber production.
center of the log by arbitrarily selected incre- Thesystemprovidesoptimalopeningfacedeter-
ments and the sawing process repeated. At last, mination,mathematicalmodels,andheuristicand
all possible sawing results are compared and the dynamic programming algorithms for lumber
BOF determined. The program was widely production optimization. External log defect
adopted during the 1980s, and many softwood information is used to obtain internal log defect
sawmills still use it today to produce lumber. data, which are used to maximize lumber value
However, application of BOF in hardwood saw- recovery. The system can be used in decision-
millsisverylimited. making for hardwood lumber production and as
atrainingtoolfornovicesawyers.
Richardsetal(1979,1980)designedacomputer
simulationprogramforhardwoodlogsawing.In
this program, a log was represented by a trun-
MATERIALSANDMETHODS
cated cone and each knot was simulated as a
cone with its apex of 24(cid:1) at the pith. Occen˜a DataCollection
andTanchoco(1988)usedagraphiclogsawing
Log sawing practices for five small hardwood
simulator as an analytical tool for automated
sawmills in North Central West Virginia were
hardwoodlogbreakdown.Logsawingoptimiza-
studiedbetweenOctober2009andAugust2010
tion can be defined as a dynamic programming
(Linetal2011).Thesemillsweretypicalsmall-
problem, and recursive equations were
scale hardwood sawmills for this state in terms
established to find optimum total lumber value
of equipment and sawing methods. All the saw-
or volume recovery (Faaland and Briggs 1984;
mills used the grade sawing method to produce
Geerts 1984; Funk et al 1993; Todoroki and
lumber. A total of 230 logs of two species,
Ro¨nnqvist 1997, 1999; Bhandarkar et al 2002,
red oak (Quercus rubra) and yellow-poplar
2008), although Occen˜a et al (1997) and
(Liriodendron tulipifera), were measured on
Thawornwongetal(2003)usedheuristicalalgo-
site, of which 50 logs (25 of each species) were
rithmstooptimizelogsawingpatterns.
selected to test the program. Selected logs were
Although several optimal log sawing programs 2.44-4.27mlongand0.25-0.33minscalingdi-
hadbeendeveloped,theywereeithernotsuitable ameter (Table 1). Log taper was calculated as
for hardwood log grade sawing practices or eco- the difference between large-end and small-end
nomically infeasible for small central Appala- diameter divided by log length. Log profile
chian sawmills. For example, many existing data included log length, large- and small-end
programs did notprovide a practicalsawing tool diameters, and diameters at every foot from the
or training tool with a 3D simulation environ- small end. External log defect data collected
ment.Someprogramsconsideredexteriordefects include defect type (such as adventitious
only or internal defects obtainedby X-ray/CT or knot [AK], heavy distortion [HD], medium dis-
MRIscanningmethods.Thesemethodswerenot tortion [MD], light distortion [LD], overgrown
fast, efficient, and cost-effective for small-scale knot [OK], sound knot [SK], and unsound knot
and portable sawmills. Most optimal log sawing [UK]), distance of defects away from the small
strategies use live sawing guided by heuristic end of the log, defect angle with respect to the
algorithms or mathematical models. However,
live sawing is not commonly used in hardwood Table1. Characteristicsofsamplelogs.
sawmills. Although some researchers used heu- Statistic Length Small-end Large-end Taper
categories (m) diameter(m) diameter(m) (mm/m)
ristic log grade sawing methods in their studies,
Min 2.44 0.25 0.26 0.83
their solutions were not efficient because of
Max 4.27 0.33 0.38 25.83
effects of the log’s rotational orientation and
Mean 2.74 0.29 0.31 6.67
depth of the first opening face. In this study, we SDa 1.62 1.14 1.43 5.83
describe the design and implementation of a log aStandarddeviation.
382 WOODANDFIBERSCIENCE,OCTOBER2011,V.43(4)
predetermined initial zero degree, defect size, modeling, sawing optimization, and lumber
and defect surface rise. Bark distortion usually grading (Fig 1). The data input/storage compo-
indicates a knot that has been overgrown to the nent includes data acquisition, data standardiza-
point of being completely encapsulated within tion,anddatastorage,whereasthe3Dmodeling
the log. Bark distortions are classified as light, component handles 3D image display and 3D
medium,orheavy(Carpenteretal1989).Exter- image transformation. The sawing optimization
nal log defect data format is the same as that component determines opening face, log saw-
obtained with the 3D log laser scanner devel- ing, and cant resawing optimization, whereas
opedbytheUSDAForestService,whichallows thelumbergradingcomponentprocesseslumber
future integration of the laser scanning data grades during the optimization process. A com-
process with the developed sawing system. ponent object model (COM) was used to inte-
Internal log defect locations were predicted grate the system and was designed using the
using models by Thomas (2008). Recorded log principles of object-oriented programming. The
and predicted data were stored in a MS Access system was programmed using Microsoft Foun-
(Microsoft,Redmond,WA)database. dation Classes and Open Graphics Library
(OpenGL) using MS Visual Cþþ. ActiveX
Alllogsweremarkedwithuniquenumbers,and
Data Object was used to retrieve data from
corresponding boards sawn from each log were
and save sawing results to a Microsoft Access
labeled to track the source of the lumber after
database.
completing the sawing process for the sample
log. Logs were sawn according to the sawyer’s
choice, and the sawyer chose to use the grade
3DLogModeling
sawing technique. All lumber sawn was 4/4
(25.4 mm) thickness with a saw kerf of 0.125 3D modeling techniques together with OpenGL
and0.305forbandsawandcircularsaw,respec- primitivedrawingfunctionswereusedtogener-
tively. After edging and trimming, lumber ate 3D log visualization (Wang et al 2009). A
length (m), width and thickness (mm), and vol- logwasreconstructedasacircularcross-section
ume (m3) were measured (Table 2). Grade and model (Zeng 1995). The cross-section model
surfacemeasureoflumberweredeterminedbya
certified National Hardwood Lumber Associa-
tion (NHLA) grader at each sawmill. Lumber
prices were based on Hardwood Market Report
for Appalachian Hardwoods (April 11, 2009).
Collectedlumberdatawerecomparedwithopti-
mallogsawingsystemsimulationresults.
SystemStructureandDesign
The optimal sawing system consists of four
major components: data input/storage, 3D
Table2. Characteristicsoflumberfromsamplelogs.
Statistic Length Width Thickness Volume Value
categories (m) (mm) (mm) SMa (m3) (US$)
Minimum 1.82 90 25 0.19 0.01 0.86
Maximum 4.27 214 54 0.65 0.03 6.93
Mean 2.75 155 36 0.37 0.01 2.27
SDb 1.52 1.12 0.16 0.08 1.44 0.88
aSurfacemeasure(m2).
bStandarddeviation. Figure1. Flowchartofoptimallogsawingsystem.
Linetal—3DLOGSAWINGOPTIMIZATIONSYSTEMFORSMALLSAWMILLS 383
2 3 2 3
usesaseriesofcross-sectionsatafixedinterval x0 x0 x0 x x x
along the log length. This model is closer to a 6 1 2 37 6 1 2 37
4y0 y0 y0 5¼R ðaÞ(cid:4)4y y y 5
real log shape because log sweep and crook 1 2 3 x 1 2 3
were considered at each cross-section. A cone z01 z02 z03 z1 z2 z3
model was used to represent an internal defect TS0 ¼R ðaÞ(cid:4)TS
x
(knotonly),anditsapexwasassumedatthepith
ð2Þ
(central axis) of the log. Geometry of internal
defects was described by a mathematical model where TS is the coordinate matrix for one trian-
developed by Thomas (2008). When a sawing gle strip on the surface of a log before transfor-
plane passed through an internal defect, a 2D mation and TS0 is the coordinate matrix after
rectangledefectareawasexposedonthelumber transformation. Similarly, the coordinate matri-
surface. Location and size of the defect area ces for the triangle strip can be rotated around
were determined using mathematical proce- the y- and z-axes. These transformation proce-
dures. OpenGL functions such as translation, dures can be applied to all triangle strips that
rotation,andscalingwereusedtofacilitatevisu- forma3Dlog.
alizationofthelog.Forexample,rotationisper-
formed by calling glRotatef (a, x, y, z), which
generates the rotation matrix by defining the SawingAlgorithms
degrees to be rotated (a) and the axis to be
Opening face. There are three steps to deter-
rotated about (x-axis, y-axis, or z-axis). The
mine BOF: 1) identifying four sawing faces by
generic matrix of rotation a angle around the
log rotation (A mathematical procedure was
three axes can be derived and expressed as
developedtoidentifyfourlogfacesafterplacing
(Wooetal2000):
the majority of the defects at the edge of the
2 3
1 0 0 0 cutting planes or on one face.); 2) determining
6 7 thebestface(Itisassumedthattheopeningface
60 cosa (cid:3)sina 07
RxðaÞ¼6640 sina cosa 0775 iestcault2f0r0o3m].tPhreobceesdtusreaswfinogr dfaecteerm[Tinhianwgotrhnewboensgt
face are based on the USDA Forest Service
0 0 0 1
2 3 hardwood log grading rules [Fig 2a] [Rast et al
cosa 0 sina 0 1973]);and3)determiningthedimensionofthe
6 7 openingface.Widthoftheopeningfaceisdeter-
6 0 1 0 07
RyðaÞ¼664(cid:3)sina 0 cosa 0775 ð1Þ mofintheedbaessftoflalocewsis(FM1a,lcthoelmsla1b96w5i)d:thifsthhoeugldradbee
158mm(152mmistheminimumwidthforthe
0 0 0 1
2 3 highest lumber grade board, and 6 mm is the
cosa (cid:3)sina 0 0 width of log sawing kerf) for logs greater than
6 7
6sina cosa 0 07 orequalto0.33minsmall-enddiameter;other-
RzðaÞ¼66 77 wisethelogshouldbeslabbedto108mmwide.
4 0 0 1 05
For all logs that have a best face with grade of
0 0 0 1 F2orF3,slabwidthshouldbe83mm.
To render a 3D log efficiently, simple triangle Heuristic algorithm for log grade sawing. A
strips were used. Let the coordinates of the computer-based heuristic algorithm was devel-
vertices of a triangle be (x , y , z ), (x , y , z ), opedbasedonMalcolm’s(1965)simplifiedpro-
1 1 1 2 2 2
(x , y , z ), respectively. The coordinate matrix ceduresforhardwoodloggradesawing.Cutting
3 3 3
for this triangle after rotating by a degrees from the small end, the opening face is set out
around the x-axis can be expressed as (Wang fulltaperbyusingthesmallendofthelogasthe
etal2009): pivot and unopened faces are parallel to sawing
384 WOODANDFIBERSCIENCE,OCTOBER2011,V.43(4)
Figure2. Proceduresfordeterminingbestfaceandlumbergrades.(a)Bestface.(b)Lumbergrades.
lines. As sawing progresses, the log is not tions1and3ofthelog.Thentheparallelsawing
rotated unless one of the other log faces will planes with orthogonal orientation are
yieldahigher-gradeboardthanthecurrentsaw- conducted on portions 2 and 4. A mathematical
ing face or the current cutting face reaches the model for maximizing lumber recovery value
centralcant.Oncealogfaceissawncompletely, through grade sawing can be expressed by the
the grade of the last board is recorded and this followingfunction:
face will not be chosen again. The algorithm
F¼ðL(cid:5);L(cid:5)ðL(cid:5)Þ;L(cid:5)ðL(cid:5);L(cid:5)Þ;L(cid:5)ðL(cid:5);L(cid:5);L(cid:5)Þ;
then considers the next face. This sawing proc- 1 2 1 3 1 2 4 1 2 3
ess is repeated until a specified size cant is pro- V(cid:5)ðL(cid:5);L(cid:5);L(cid:5);L(cid:5)Þ;S(cid:5)ðL(cid:5)Þ;S(cid:5)ðL(cid:5);L(cid:5)Þ; ð3Þ
1 2 3 4 1 1 2 1 2
duced, indicating that the log sawing process is S(cid:5)ðL(cid:5);L(cid:5);L(cid:5)Þ;S(cid:5)ðL(cid:5);L(cid:5);L(cid:5);L(cid:5)ÞÞ
3 1 2 3 4 1 2 3 4
complete.
where L , L , L , L and S , S , S , S are the
1 2 3 4 1 2 3 4
Mathematically based algorithm for log sawing planes and sawing patterns at each por-
gradesawing.Alogisbrokenintofourportions tion, respectively; V is the lumber value; and
at the small end in log grade sawing (Fig 3a). * indicates an optimal value. This proposed
Once the first opening face is determined, the model is based on the optimal log grade sawing
four log sawing faces are fixed. A sequence of proceduredescribedbyBhandarkaretal(2008).
parallelsawingplanesisfirstperformedonpor- The objective of Eq 3 is to find the locations of
Linetal—3DLOGSAWINGOPTIMIZATIONSYSTEMFORSMALLSAWMILLS 385
Figure3. Dynamicprogrammingforloggradesawing.
L , L , L , and L to maximize total lumber determinedusingadynamicprogrammingalgo-
1 2 3 4
value. To generate the candidate flitches, each rithm. Let v*(i) represent the optimal lumber
portion of the log is divided into n equidistant value for each log portion between cutting
sawing planes with resolution c, and a saw- planes 1 and i, g(i, j) be the lumber value from
ing plane is denoted by l at the first por- thecuttingplanesithroughj,arecursivemathe-
1
tion (Fig 3a). Let C¼f1;2;(cid:6)(cid:6)(cid:6);ng be a finite matical equation for the dynamic programming
set of all the potential sawing planes and can be formulated as follows (Bhandarkar et al
S¼fs ;s ;(cid:6)(cid:6)(cid:6);s g be a subset of C that sat- 2008):
0 1 n
(cid:2) (cid:3)
isfiesthefollowingconstraints:
(cid:2) (cid:3) v(cid:5)ðiþ1Þ¼ maxðv(cid:5)ðiþ1(cid:3)Tj(cid:3) k Þ
ðs (cid:3)s (cid:3) k Þ(cid:6)c2T; for1(cid:7)i(cid:7)n ð4Þ j2½0;m(cid:8) c c
i i(cid:3)1 c þgðiþ1(cid:3)Tj;iþ1ÞÞ ð6Þ
c
s ¼1;s ¼n ð5Þ
0 n
where T ¼ðT ;T ;(cid:6)(cid:6)(cid:6);T Þ is a set of lumber CantResawing
1 2 m
thicknesses (mm); m is total number of lumber
The value of the central cant is essential when
thicknesses considered; c is sawing plane reso-
comparing the total lumber value derived from
lution (mm); k is kerf thickness (mm); and
different sawing methods for each log. The 3D
n¼CR=c is total number of sawing planes
optimization system allows the user to make a
withinthecuttingrange.Therefore,thepossible
decision whether to keep the cant or resaw it. If
sawing planes are enumerated as 1,2,...,n,
the central cant is sawn, a usable sawing region
whereas CR is cutting range between opening
for the cant should be defined prior to sawing.
faceandcentralcant(mm).
Because the taper sawing method is used in the
A sawing pattern that satisfies Eqs 4 and 5 was sawing process, the cant will not be square.
consideredafeasiblesolutionforloggradesaw- Thus, the taper must be removed from the cant
ing(Fig 3b). The optimal sawingpattern can be first. It is assumed that the size of the final cant
386 WOODANDFIBERSCIENCE,OCTOBER2011,V.43(4)
is the same as the small end of the unfinished (Lin 2011). For this study, all log sawing simu-
cant. Given lumber thickness and sawing kerf, lations were performed on a desktop PC
the best cutting solution can be determined by equipped with 3.16 GHz CPU, 3.25 GB RAM,
comparingtotallumbervalueobtainedfromtwo anda300GBharddrive.
sawingdirections(horizontalandvertical)using
Sawing begins by determining the BOF. Once
the live sawing method. The problem of central
this is accomplished, the user can choose either
cantresawingcanstillbesolvedbythedynamic
the heuristic or dynamic programming algo-
programming algorithm. Parameters used for
rithm to saw the log. Prior to the interactive
cant resawing are the same as log grade sawing
simulation process, the user needs to specify
withtheexceptionoflogsawingorientationand
some sawing variables (ie kerf width, lumber
cuttingrange.
thickness, cant size, and sawing interval) at the
bottom left area and choose appropriate com-
LumberGrading mands at each group box. When using the
dynamic programming algorithm to optimize
Priortolumbergrading,thesawnflitchmustbe
log grade sawing, a sawing interval must be
resawn into lumber. All the flitches were edged
selected.
to remove wane. To generate this lumber pat-
tern, lumber width was assumed to be the Theloggradesawingprocessusingtheheuristic
narrowest clear area width along the flitch. or dynamic programming algorithm can be
Edged lumber was graded by a computer algo- conducted after the sawing kerf, lumber thick-
rithmbasedonNHLAgradingrulesandahard- ness,cantsize,andsawingintervalarespecified.
wood lumber grading program (Klinkhachorn Then the log can be sawn except for the central
et al 1988) (Fig 2b). NHLA grading rules pro- cant.Theusercanopttosawthecentralcantor
vide both the buyer and seller with a consistent keep it. If the cant is left, its value will be com-
language for conducting hardwood lumber putedbasedonitsvolumeandprice.Allsawing
transactions. NHLA grades are based on per- solutions and results are displayed on the com-
centage of clear defect-free wood on a board puter screen for the user. An easy-to-use inter-
(NHLA 2008). To determine the possible grade face allows users to quickly and easily change
forapieceoflumber,width,length,andsurface settings as desired and compare the results of
measure (SM) of the lumber must be computed differentsawingstrategiesandmethods.
and a potential grade assigned to the poor face.
SMisthesurfaceareaofaboardinsquarefeet.
After these steps, the potential number of clear RESULTSANDDISCUSSION
cuttings and cutting units (CUs) can be calcu-
OpeningFace
lated. By comparing thenumber ofcuttings and
CUs obtained from the lumber and the require- Todetermineiftheoptimalopeningfaceisbetter
ments inNHLA grading rules, afinal grade can thananyfaceschosenrandomly,logsawingwas
be assigned (NHLA 2008). Lumber grades con- simulated using the optimal opening face and
sidered in this study were: First and Seconds, other assumed opening faces with log rotation
FAS-One-Face, Select, 1Common (1COM), angle from 0-85(cid:1) with a 5(cid:1) increment and open-
2Common(2COM),and3Common(3COM). ing face width of 0.083, 0.108, and 0.159 m, re-
spectively (Table 3). Thus, a total of 48 possible
sawingpatternsweretestedbychanginglogrota-
SystemImplementation
tion angle and initial opening face width in the
Theoptimizationsystemcanbeimplementedon assumed log sawing. A sequence of parallel cuts
either a desktop or a laptop and run on a Win- was performed for each log face until a central
dows (Microsoft) platform. Details of the saw- cant remained, which was sawn later by parallel
ing system can be found in the user’s manual cuts. Results showed that total lumber value
Linetal—3DLOGSAWINGOPTIMIZATIONSYSTEMFORSMALLSAWMILLS 387
Table3. Lumbervaluefromoptimalopeningfacecutvsaveragelumbervaluefromotheropeningfacecut.
Logno. Lumbervaluea Averagelumbervalueb Logno. Lumbervaluea Averagelumbervalueb
1 12.91 10.59 26 34.72 30.79
2 16.06 15.25 27 40.04 38.6
3 17.01 15.95 28 43.02 45.05
4 14.57 12.97 29 55.23 54.34
5 20.52 19.83 30 43.06 40.7
6 12.48 12.66 31 32.02 28.91
7 27.12 25.39 32 21.05 20.96
8 20.4 19.71 33 32.02 32.51
9 18.93 17.39 34 17.22 15.05
10 20.13 19.8 35 23 22.46
11 30.02 28.58 36 23.35 21.68
12 25.17 24.92 37 35.64 33.83
13 17.5 15.66 38 21.15 18.73
14 16.84 14.7 39 27.69 27.36
15 28.26 26.28 40 26.18 24.04
16 32.76 31.63 41 47.25 45.85
17 35.04 34.29 42 22.15 20.49
18 28.29 26.08 43 24.14 23.47
19 40.38 39.78 44 34.28 33.8
20 18.92 17.91 45 29.67 28.08
21 23.27 22.5 46 29.5 28.62
22 30.56 28.39 47 21.15 20.97
23 37.24 37.24 48 19.82 18.75
24 31.17 30.74 49 33.18 31.83
25 39.09 38.29 50 22.76 21.32
aLumbervaluefromoptimalopeningfacecut
bAveragelumbervaluefromotheropeningfacescut.
using the optimal opening face cut was higher high volume recovery does not always mean
than the average total value derived from any highlumbervaluerecoveryforsomelogs.Also,
other opening face by an average of 4.31%. Log lumber value recovery could be improved sig-
rotation angle and opening face width had nificantly for logs with more defects. For
impactsontotallumbervaluerecovered. instance,forlogswithsixormoredefects,aver-
age lumber value recovery could be improved
by 11.08 and 16.28% using heuristic and
LogSawingComparisons
dynamic programming optimization methods,
Lumber value and volume improvement. If respectively. However, average lumber value
heuristic and dynamic programming optimiza- recoveryimprovedby9.01and12.56%forlogs
tions are used, sawmills have the potential to with five or less defects. Average lumber value
improvetheirlumberrecoveryvalueby10.01% obtained by the dynamic programming algo-
and 14.21% (Figs 4 and 5), respectively. High rithmwasnotalwaysgreaterthanthevaluegen-
volume recovery tends to result in high lumber erated by the heuristic algorithm, because the
valuerecovery.Forexample,whenheuristicand precision of the dynamic programming optimi-
dynamic programming algorithms were used to zation depends on the selected stage interval.
optimize log sawing, average lumber volume However, the more precise solution comes with
was 0.1311 and 0.1331 m3, respectively, and theexpenseoflongercomputingtime.
average lumber value was US $28.18 and US
$29.42, respectively. Average lumber volume Lumber grade improvement. It was found
improved 2.5 and 4.1%, respectively. However, that the distribution of lumber grades differed
388 WOODANDFIBERSCIENCE,OCTOBER2011,V.43(4)
Figure4. Averagelumbervaluefromactualsawmillsandheuristicanddynamicprogrammingalgorithms.
among different sawing methods. About 16, 30, tionalgorithms,resultinginafinallumbervalue
and36%oflumbergradeswereSelectorhigher recoveryincrease.
inactualsawmillingoperation,heuristicoptimi-
zation, and dynamic optimization (Fig 6), re-
LumberValueRecoverybySpecies
spectively. In the actual sawmilling operation,
44, 32, and 9% of lumber was graded as Average lumber value recovery was compared
1COM, 2COM,and 3COM, respectively. When between two dominant species, red oak and
the heuristic algorithm was used to optimize yellow-poplar, in central Appalachia. Internal
thoselogs,48,19,and3%oflumberwasgraded log defect prediction models embedded in the
as 1COM, 2COM, and 3COM, respectively. system were only available for the two species.
When thedynamic programming algorithmwas Other species such as red maple and white
used, 44, 18, and 2% of lumber yielded 1COM, oak may be considered in future analyses once
2COM, and 3COM, respectively. Therefore, prediction models are available. In the saw-
lumber grades can be improved using optimiza- mill, yellow-poplar and red oak lumber values