Originalscientificpaper
Examining the Optimal Bucking Method
to Maximize Profits in Commercial
Thinning Operations in Nasunogahara Area,
Tochigi Prefecture, Japan
Chikara Nakahata, Kazuhiro Aruga, Masashi Saito
Abstract
Optimal bucking methods were applied to two operational sites of the Nasu-machi Forest
Owners’ Co-operative to maximize profits, with and without taking log size into consideration,
and to maximize revenues considering a new subsidy system and higher unit prices of smallsized logs. Corresponding optimum extraction rates and small-sized log prices were examined.
Extraction rates from stands using the optimal bucking method to maximize profits considering log sizes were similar to the actual values, unlike the estimations obtained using other
methods, e.g. without considering log sizes or maximizing revenues. However, the differences
in extracted volumes and economic balances among these estimations were small and can be
said to be within the error limits traditionally seen for forests and forestry conditions in the
stands. The stands were about 50 years old, with an average diameter at breast height (DBH)
of about 20 cm. Differences in extraction rates from stems with a DBH exceeding 20 cm were
small. However, extraction rates from stems with a DBH less than 20 cm were significantly
different. Therefore, the optimal bucking method to maximize profits considering log sizes
could help determine the optimal extraction rates of younger stands with smaller DBHs. Possible effects of the new subsidy system and different unit prices for small-sized logs were also
discussed. Both the new subsidy system and the unit prices with feed-in tariff contributed to
an increase in extracted volumes of small-sized logs.
Keywords: Optimal bucking, maximum profit, extraction rate, economic balance, small-sized
logs, subsidy
1. Introduction
Facilitiessuchasbiomasspowerplants,chipproductionfactories,andpelletplantsinTochigiprefecturerequirewoodybiomassresources.Theseresource
requirementsaremainlyfulfilledbysawmillresidues
and construction waste woods. However, there are
concerns about the future adequacy of supplies of
thesematerials,becauseoftheincreasednumberof
entrepreneurswhohavesetupbiomasspowerplants
asameasureagainstclimatechangeandtoimprove
energysecurity.Furthermore,theFeed-InTariff(FIT)
schemewasintroducedinJapanstartingJuly1,2012.
InFIT,thepurchaseprice(withouttax)ofelectricity
Croat. j. for. eng. 35(2014)1
generatedwithunusedmaterialssuchassmall-sized
logsandloggingresidue,generalmaterialssuchas
sawmillresidue,andrecycledmaterialsuchasconstructionwastewoodare0.32USD/kWh,0.24USD/kWh,
and0.13USD/kWh,respectively(AgencyforNatural
ResourcesandEnergy2012).Powergenerationwith
unusedmaterialswasincentivized.Therefore,theuse
ofsmall-sizedlogsandloggingresiduemustbepromotedinthenearfuture.
Tochigiprefecturemeasures640785ha,ofwhich
about54.5%iscoveredbyforests(TochigiPrefectural
Government 2009).About 45% of these forests are
man-made,constitutingavolumeof42255000m3
45
C. Nakahata et al.
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
(62.4%).Giventhedelayinthinning,whichwasaseriousproblemforman-madeforeststhroughoutJapan,
theTochigiPrefecturalGovernmentintroducedanew
regulationinApril2008,alongwithsubsidiesforthinning operations, aimed at making forests healthy
(TochigiPrefecturalGovernment2010a).Asaresult,
thinningoperationswereconductedon2663haof
forest in 2009. However, large amounts of thinned
woodwereleftintheforests,becausenearlyallthe
thinningoperationsconductedwerepre-commercial
forsmall-sizedtreesandaffectedprofitability.
TheNasu-machiForestOwners’Co-operativeextractssmallerdiameterlogsforpelletsorpulpinaddition to larger diameter logs for saw timber or laminated
lumber.However,theextractionofsmallerdiameter
logswouldincreaserevenue,butalsoincreasecosts,
and subsequently, decrease profitability. Numerous
studieshaveexaminedoptimalbuckingforincreasing
revenues(Akayetal.2010,HaynesandVisser2004,
Nagumoetal.1981,Nakajimaetal.2008,Nakajimaet
al.2009,Olsenetal.1991,Sessionsetal.1989a,Wanget
al.2009,YoshidaandImada1989).However,thebuckingmethodsaffectedtheefficienciesofthebuckingand
extractingoperations,therebyincreasingcostsandloweringprofitability.Therefore,itisessentialtoconduct
optimalbuckingwithaconsiderationofcostsandprofitabilityaswellasrevenues.
The optimum bucking problems can be categorizedintothreelevels:(1)stem-levelproblemstodeterminetheoptimumbuckingforeachsteminaway
thatmaximizesthetotalstemvalue;(2)stand-level
problemstodeterminethebestpossiblebuckingresultswithmaximumaggregateproductionvalue;and
(3)forest-levelproblemstomaximizetheglobalprofit considering demand constraints, merchandising
restrictions,andforest-estate(Laroze1999).Network
analysistechniques(Sessions1988)andDP(Nasberg
1985)havebeeneffectivelyusedtosolvestem-level
optimumbuckingproblems.Atstand-level,optimum
buckingproblemshavebeengenerallyformulatedas
two-leveloptimizationproblemsutilizingbothLPand
DP(Sessionsetal.1989b,LarozeandGreber1997).The
optimization procedures involving heuristic techniquessuchasTabuSearch(Laroze1999)andGenetic
Algorithm (Kivinen 2004) have been used to solve
forest-levelbuckingproblems.Uusitalo(2007)developedaGeneticAlgorithmbasedmethodtointegrate
transportation cost and product values into forestleveloptimumbuckingproblem.
Thisstudyintegratedforwardingcostsintostemlevel optimum bucking problem. Nakahata et al.
(2013)investigatedcommercialthinningoperations
aroundNasunogaharaarea,wheretheNasu-machi
46
Forest Owners’ Co-operative is located. They analyzedtherelationshipsbetweenlogsizesandoperationalcostsofprocessingaswellasforwarding,and
developedequationstoestimateoperationalcostsaccordingtologsizes.Theoperationcostsestimated
withtheequationswereincreasedaccordingtothe
extractionofsmallerdiameterlogs.Thus,wedetermined the optimal bucking methods to maximize
profitsandtheoptimumextractionratesofsmallsized logs. Here, we examine optimum extraction
ratesusingdifferentoptimalbuckingmethodsand
small-sizedlogprices.
Table 1 Study sites
A
B
Japanese
Japanese
Japanese
cedar
cypress
cedar
55
55
52
5.25
1.87
6.70
Slope angle, °
19
16
23
DBH*, cm
32
24
25
19.9
18.7
22.2
Stem volume, m /stem
0.80
0.46
0.62
Stand density, stem/ha
937
1 169
1 054
749.60
537.74
653.48
26
19
20
Thinned wood tree height, m
18.5
17.7
20.1
Thinned wood volume,
m3/stem
0.49
0.27
0.36
Thinning rate of stem, %
27.6
35.4
33.3
Thinning rate of volume, %
17.1
20.5
19.3
668.27
207.75
844.23
Species
Stand age, year
Area, ha
Tree height, m
3
Stock, m3/ha
Thinned wood DBH, cm
3
Thinned volume, m
3
606.97
311.08
Extracted rate, %
69.3
36.9
Road density, m/ha
300.3
229.7
Extracted volume, m
Rate of bunching area, %**
83.0
88.2
43.9
Forwarding distance, m***
120.0
247.6
111.9
* DBH: Diameter at Breast Height
** Rate of bunching area to stand area. Bunching area was assumed to be
within 20 m from the roads
*** Forwarding distances were estimated from landing to each stand by the
Dijkstra method
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Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
2. Optimal bucking method to maximize
profits
Theoptimalbuckingmethodtomaximizeprofits
wasdeterminedasfollows:1)estimatethinningvolumes,2)determinethetapercurveformula,3)estimate
extractedvolumes,4)estimaterevenues,5)estimate
expenses,6)estimateeconomicbalances,and7)determinetheoptimalbuckingmethodtomaximizeprofits.
2.1 Study sites
Theoptimalbuckingmethodswereappliedtotwo
commercialthinningoperationsiteswheresmall-sized
logswereextracted,inadditiontosawlogsandlogs
forlaminatedlumber(Table1,Fig.1).Forestryoperations included chainsaw felling, grapple-loader
bunching,processorprocessing,andforwarderforwarding,withahigh-densityroadnetwork,morethan
200m/haofrelativelysteepterrain,around20°(Fig.
2).Roadwidthwas3.5m.Before2008,smaller-sized
machineswereused,andtheroadwidthwas2.0m.
Before2008,theforestryoperationsystemincluded
chainsawfellingandprocessing,minigrapple-loader
bunching, and mini-forwarder forwarding. Using
largermachinesafter2008,operationalefficienciesimprovedfrom2.3–3.8m3/person-dayto3.9–5.3m3/person-day,anddirectoperationcostswerereducedfrom
59–76USD/m3to37–44USD/m3(Arugaetal.2013).
SiteAincluded55-yearoldJapanesecedarandJapanesecypressstands,withanareaof7.12haandaslope
angleof19°.CommercialthinningoperationswereconductedbytheNasu-machiForestOwners’Cooperative
betweenJanuary28andMarch9,2010.Theforestroad
C. Nakahata et al.
was268mlong.Thestriproadwas3.5mwideand
1870mlong.Therefore,theroaddensitywas300.3m/ha.
Grapple-loaderbunchingoperationswereconducted
within20mfromtheroads,andthinnedwoodsbeyond
20mfromtheroadswereleftintheforest(pre-commercialthinningoperationswereconductedintheforest
beyond20mfromtheroads).Therefore,theextraction
isassumedtobewithin20mfromtheroads.Therates
ofthebunchingareastothestudysiteareawere83.0%
forJapanesecedarand88.2%forJapanesecypress.
SiteBwasa52-yearoldJapanesecedarstand,with
anareaof6.70haandaslopeangleof23°.Commercial
thinning operations were conducted by the NasumachiForestOwners’Co-operativebetweenNovember12andDecember10,2010.Theforestroadwas587m
long.Thestriproadwas3.5mwideand952mlong.
Therefore,roaddensitywas229.7m/ha.Grapple-loaderbunchingoperationswereconductedwithin20m
fromthestriproadsonly.Therefore,therateofthe
bunchingareatothestudysiteareawasonly43.9%.
2.2 Results of the study
Inordertoestimatethinningvolumes,thediameteratbreastheight(DBH)distributionsofthethinned
woodswereestimatedtoapplytheWeibulldistribution(Kinashi1978)totheresultsoftheplotdata(Fig.
3).ThetreeheightsH(m)wereestimatedasfollows.
StandAJapanesecedar:
H=5.342D0.382 (R2=0.53)
(1)
StandAJapanesecypress:
H=8.817D0.239 (R2=0.56)
(2)
StandBJapanesecedar:
H=5.065D0.46 (R2=0.56) (3)
Fig. 1 Study sites (Left: Stand A, Right: Stand B
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Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
ThinnedvolumesinthestandsVT (m3) were estimatedasfollows.
VT =
Dmax
∑
j = Dmin
(4)
VTj
where VTj denotes thinned volumes in the jDBHclass
(m3),andDmax and Dmin are the maximum and minimumDBHclassofthinnedwoods,respectively.VTj
wasestimatedasfollows.
VTj = Vnj ´ N j ´ A ´
RTj
(5)
100
where Vnj denotes stem volumes of thinned woods in
the jDBHclass(m3/stem),Nj refers to the number of
thinned woods in the jDBHclass(stem/ha),A is the
standarea(ha),andRTj is the thinning rate of stems in
the jDBHclass(%).
2.3 Determination of the taper curve formula
Stemdiameterd (cm) at the height h (m) above the
groundwasestimatedwiththefollowingtapercurve
formula(InoueandKurokawa2001).
 

1.2 
− 0.9 a + 1.8 ´
a  1.0 −


H

d= 
 

h
a  1.0 −  − 0.9a + 1.8 ´
H
 


h
 1.0 − H 

1.2 
 1.0 − H 
´ D (6)
Coefficientawasestimatedasfollows.
a=

21.6 
7
 18.0 − H  − 12.6 10 f

2.4  
8.4 
7
 2.0 − H  −  0.7 − H  10 f
(7)
where f denotes the breast height form factor estimatedasfollows.
f=
Fig. 2 Operational system with grapple-loader bunching (A), processor processing (B), and forwarder forwarding (C)
where DdenotesDBH(cm).Stemvolumesofthinned
woods Vn (m3/stem) were estimated with the two-way
volume equation (ForestryAgency of Japan 1970).
48
4Vn
 HD 2p 
 10 000 


(8)
AverageRootMeanSquaredErrors(RMSEs)between the measured and estimated stem diameters
were1.1cmforbothJapanesecedarandJapanesecypress.Logdiameterswereusuallyroundedby2cm.
Therefore,theseRMSEswerewithinallowableranges.
2.4 Estimation of extracted volumes
Extractedlogswereclassifiedassawlogs,logsfor
laminatedlumber,andsmall-sizedlogs(Table2).Saw
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C. Nakahata et al.
Fig. 3 DBH distributions (Left: Survey results, Right: Weibull distribution)
Croat. j. for. eng. 35(2014)1
49
C. Nakahata et al.
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
logswere3.00–6.00mlong,withthetop-enddiameter
exceeding10cm.Logsforlaminatedlumberwere2.00m
long,withthetop-enddiameterexceeding16cm.Correspondingvaluesforsmall-sizedlogswere2.00m
andover3cm.Small-sizedlogsweresoldtoapellet
plantorachipproductionfactory.Loglengthswere
assumedtobe2.00m,3.00m,3.65m,and4.00mfor
Japanese cedar and 2.00 m, 3.00 m, and 4.00 m for
Japanesecypress(interviewwiththeNasu-machiForest Owners’ Co-operative). Cutting height was assumedtobe20cmabovetheground(IeharaandKurokawa 1990). Possible combinations of log length
buckedfromathinnedwoodwereestimated,andlog
volumes v (m3/log) were estimated with log length l
(m)andtop-enddiametersoflogsusingestimated
stem diameter d(cm).
v=
d2l
10 000
Table 2 Log unit prices
Species
Diameter
m
cm
Stand A
Stand B
11–14
69.50
92.70
16–20
116.60
141.00
22–28
112.20
135.10
18–28
127.40
142.90
>30
127.40
150.40
10–14
75.90
120.10
16–20
107.90
125.70
22–28
127.50
133.20
>30
125.90
145.70
11–14
66.40
94.40
16–28
179.80
223.10
>30
170.00
260.40
10–14
94.00
128.40
16–20
197.30
237.50
22–28
225.00
257.30
>30
–
390.50
3.00
3.65
Japanese
Cedar
4.00
Saw logs
(9)
Then,extractedvolumesVl (m3/stem) were estimatedasfollows.
Vl =
n
∑v
i =1
VE =
∑
j = Dmin
VEj
RTj
100
´
RS
100
Small-sized
logs
Japanese
Cedar
2.00
Japanese
Cypress
2.00
Japanese
Cedar
16–18
50.00
>20
55.00
16–18
70.00
>20
90.00
>3
30.00
2.00
Japanese
Cypress
(12)
where Vlj refers to extracted volumes of thinned woods
in the j DBH class (m3/stem), and RS is the rate of
bunchingareatostandarea(%).
2.5 Estimation of revenues
Logpricesp (m3/log) were estimated with log volumeandunitprices(Table2).Unitpricesofsawlogs
weresourcedfromtheunitpricesintheOotawaralog
market,wheretheNasu-machiForestOwners’Cooperativesellssawlogs.Unitpricesoflogsforlaminatedlumberandsmall-sizedlogsweresourcedfrom
theunitpricesofalaminatedlumberfactory,thepellet
50
Logs for
laminated
lumber
(11)
where VEj denotes extracted volumes in the jDBH
class (m3).VEjwasestimatedasfollows.
VEj = Vlj ´ N j ´ A ´
Japanese
Cypress
4.00
where vi is the i-thlogfromthebuttend(m3/stem),and
nisthenumberoflogsfromathinnedwood.Extractedvolumeswereestimatedwithpossiblecombinationsofloglengthbuckedfromathinnedwood.
Extracted volumes in the stands VE (m3) were estimatedasfollows.
Dmax
3.00
(10)
i
Unit prices, USD/m3
Length
plant,andthechipproductionfactory,wheretheNasu-machiForestOwners’Co-operativesellslogsfor
laminatedlumberandsmall-sizedlogs.Then,revenue
from a thinned wood was estimated with the number
oflogsperthinnedwoodandeachlogprice.
Revenues in the stands S(USD)wereestimatedas
follows.
S=
Dmax
∑
j = Dmin
Sj
(13)
where Sj denotes revenues in the jDBHclass(USD).Sj
wasestimatedasfollows.
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Sj =
n
∑
n
∑
i =1
Pij ´ N j ´ A ´
RTj
100
´
RS
100
Table 3 Standard unit costs for strip road construction (3.5 m wide)
(14)
Pij isthelogpriceinthejDBHclass(USD/
where
stem). i =1
Inadditiontorevenuesfromlogsales,subsidies
wereestimatedwithstandardunitcosts,areas,assessmentcoefficients,andthesubsidyrateofferedbythe
Tochigi Prefectural Government (2010b). Standard
unit costs were determined by age class, thinning
rates,andwhetherextractionoccurred(Fig.4).Anextractionrateofatleast50%wasrequired.Theassessmentcoefficientandthesubsidyratewereassumedto
be1.7and4/10,respectively.InJapan,subsidiesfor
striproadestablishmentarealsoprovidedforstands
withsubsidizedthinningoperations.Standardunit
costsforstriproadestablishmentweredeterminedusingtheaverageslopeangle(°)androadwidth(Table
3).Subsidieswereestimatedwithstandardunitcosts,
length,assessmentcoefficients,andthesubsidyrate
offeredbytheTochigiPrefecturalGovernment(2011).
Theassessmentcoefficientandthesubsidyratewere
assumedtobe1.7and4/10,respectively.
2.6 Estimation of revenues
CostsinthestandsC(USD)wereestimatedasfollows.
C=
Dmax
∑
j = Dmin
OEj + OC
(15)
Fig. 4 Standard unit costs for subsidy for 30% stem thinning rate
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C. Nakahata et al.
Slope angle, °
Standard unit costs, USD/m
35 –
43.97
30 –
12.50
25 –
7.02
20 –
4.06
15 –
3.38
10 –
2.81
5–
2.34
where OEjdenotesdirectexpensesinthejDBHclass
(USD),andOCreferstootherexpenses(USD).OEj was
estimatedasfollows.
(
)
OEj = OEF + OES ´ RS VTj + (OEP + OEE ) VEj
(16)
where OEFdenoteschainsawfellingcosts(USD/m3);
OES,grapple-loaderbunchingcosts(USD/m3);OEP,
processingcosts(USD/m3);andOEE,forwardingcosts
(USD/m3).
Costs of chainsaw felling and grapple-loader
bunchingwereestimatedusingtheequationsinNakahataetal.(2011).Theseequationsweredeveloped
withoutconsideringlogsizes,becausetheseoperationswereconductedwithwholetreesbeforeprocessingoperations,andthecostswerenotaffectedbylog
sizes(Table4).CostsofprocessorprocessingandforwarderforwardingwereestimatedusingtheequationsdevelopedinNakahataetal.(2013),whichconsideredlogsizes.RMSEsbetweenmeasuredvalues
andestimationsusingtheequationsinNakahataetal.
(2013)thatconsideredlogsizes,estimationsusingthe
equationsinNakahataetal.(2011)andIshikawaetal.
(2008)thatdidnotconsiderlogsizes,werecompared.
Forprocessingoperations,theRMSEof1.29USD/m3
obtainedfromtheequationsinNakahataetal.(2013)
waslowerthanthatobtainedfromtheequationsin
Nakahataetal.(2011)(2.14USD/m3)andIshikawaet
al.(2008)(6.12USD/m3)(Fig.5).Forforwardingoperations,theRMSEof0.85USD/m3usingtheequations
inNakahataetal.(2013)wasalsolowerthanthatusing
theequationsinNakahataetal.(2011)(2.31USD/m3)
(Fig. 6). RMSEs in Nakahata et al. (2013) were the
smallestofallestimations.
Inadditiontothesedirectexpenses,striproadexpenses,trucktransportationexpenses,machinetransportationexpenses,insurancecosts,handlingfeesof
theForestOwners’Co-operativeandthelogmarket,
51
C. Nakahata et al.
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
Table 4 Direct expenses, USD/m3
Nakahata et al.
(2011)
Nakahata et al. (2013)
Chainsaw
felling
Whole
tree
0.91/Vn + 1.12
0.91/Vn + 1.12
Grapple-loader
bunching
Whole
tree
12.41
12.41
Processor
processing
Log
2.88/Vl + 2.66
{(2.42Vla + 0.22) n +
1.90}/Vla · n
Forwarder
forwarding
Log
0.0060LF + 7.08
{(-34.30Vla + 16.77) +
0.012 LF}/(1.74Vla + 1.71)
Vn – Stem volume, m3/stem;
Vl – Extracted volume, m3/stem;
Vla – Average log volume, m3/log;
n – Number of logs per stem, logs/stem;
LF – Forwarding distance, m.
Fig. 6 Forwarding distances, m and operational costs, USD/m3
backhoe,agrapple-loader,aprocessor,andtwoforwarders.Insurancecostswereestimatedtobe18.4%
ofdirectexpenses.HandlingfeesoftheForestOwners’Co-operativeandthelogmarketwereestimated
tobe5%and5%,respectively.Pilingfeesinthelog
marketwereestimatedtobe7.00USD/m3.
2.7 Estimation of economic balances
Economic balances were estimated with revenues
and costs of possible combinations of log length
buckedfromathinnedwood.Then,buckingmethod
andextractionratewithmaximumprofitsweredeterminedastheoptimalbuckingmethodandtheoptimal
extractionrate,respectively.Extractionratefromstems
RESwasestimatedasfollows.
RES =
3
3
Fig. 5 Extracted volumes, m /stem and operational costs, USD/m
andpilingfeesinthelogmarketwerealsoestimated.
Striproadexpenseswereestimatedassuminglabor
expensesof25.50USD/h,backhoemachineryexpensesof46.39USD/h,andstriproadconstructiontimes
of117and33hoursforStandAandB,respectively.
Trucktransportationexpenseswereestimatedtobe
13.00 USD/m3 for saw logs, 0 USD/m3 for logs for
laminated lumber (because of landing sales), and
15.00USD/m3forsmall-sizedlogs.Machinetransportationexpenseswereestimatedtobe50.00USD/machine.Therewerefivemachinestobetransported:a
52
Vl
´ 100
Vn
(17)
Extraction rate on the stands RE was estimated as
follows.
RE =
VE
´ 100
VT
(18)
3. Results and discussion
3.1 Optimal bucking method to maximize profits
By the optimum bucking method to maximize
profits, maximum four to five logs were made for
StandAandB,respectively(Tables5,6,and7).The
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C. Nakahata et al.
Table 5 Results of the optimal bucking method to maximize profits in Stand A of Japanese cedar
Thinned trees
DBH
Height
Stem volumes
Extracted volumes
Stem/ha
cm
m
10
18
16
0.210
0.176
31
20
17
0.270
39
22
17
42
24
39
Direct
expenses
Economic balance
No. of
logs
Revenues
83.6
3
91.69
43.80
47.89
0.218
80.7
3
97.40
39.64
57.77
0.320
0.257
80.3
3
114.49
36.98
77.51
18
0.400
0.349
87.3
4
107.05
34.37
72.68
26
19
0.490
0.426
87.0
4
117.41
32.03
85.38
32
28
19
0.550
0.490
89.0
4
121.33
30.60
90.73
24
30
20
0.660
0.578
87.6
4
121.49
28.92
92.56
17
32
20
0.740
0.652
88.1
4
121.97
27.80
94.17
10
34
21
0.870
0.749
86.1
4
123.82
26.53
97.29
7
36
21
0.960
0.841
87.6
4
122.67
25.53
97.14
4
38
21
1.050
0.962
91.6
4
126.57
24.42
102.15
2
40
22
1.210
1.082
89.4
4
126.67
23.39
103.28
1
42
22
1.330
1.206
90.7
4
125.86
22.48
103.37
259*
25.9
18.5
0.495
0.429
86.6
3.7
116.91
31.22
85.69
Direct
Economic
m3/stem
Rate
%
USD/m3
*Total value. The other values refer to averages
Table 6 Results of the optimal bucking method to maximize profits in Stand A of Japanese cypress
Thinned
trees
DBH
Height
Stem
Extracted
volumes
volumes
3
m /stem
Rate
%
No. of
logs
Revenues
expenses
balance
3
USD/m
Stem/ha
cm
m
29
12
16
0.100
0.000
0.0
0
–
–
–
62
14
16
0.130
0.000
0.0
0
–
–
–
72
16
17
0.180
0.127
70.4
2
93.38
48.27
45.11
70
18
17
0.220
0.160
72.7
2
159.81
43.09
116.73
60
20
18
0.290
0.232
79.9
3
154.66
35.59
116.08
46
22
18
0.340
0.295
86.8
3
179.67
35.20
144.47
32
24
19
0.430
0.350
81.3
3
180.35
32.84
147.51
20
26
19
0.490
0.448
91.5
4
193.73
31.57
162.16
13
28
19
0.560
0.523
93.4
4
198.89
30.00
168.89
7
30
20
0.670
0.574
85.6
4
200.30
28.97
171.33
4
32
20
0.770
0.677
87.9
4
212.11
27.45
184.66
414*
18.8
17.5
0.266
0.195
73.3
2.1
168.04
36.67
131.37
*Total value. The other values refer to averages
Croat. j. for. eng. 35(2014)1
53
C. Nakahata et al.
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
Table 7 Results of the optimal bucking method to maximize profits in Stand B of Japanese cedar
Thinned
trees
DBH
Height
Stem
Extracted
volumes
volumes
m3/stem
Rate
%
No.
Revenues
of logs
Direct
Economic
expenses
balance
USD/m3
Stem/ha
cm
m
29
12
16
0.100
0.000
0.0
0
–
–
–
62
14
17
0.140
0.098
69.7
2
120.49
55.62
64.87
72
16
18
0.190
0.136
71.6
2
120.00
46.63
73.37
70
18
19
0.250
0.204
81.4
3
127.55
40.85
86.70
60
20
20
0.320
0.263
82.1
3
136.56
36.72
99.84
46
22
21
0.410
0.373
91.0
4
134.32
33.65
100.67
32
24
22
0.500
0.453
90.5
4
139.97
31.45
108.53
20
26
23
0.610
0.568
93.1
5
140.02
30.25
109.76
13
28
23
0.690
0.685
99.3
5
140.71
28.61
112.10
7
30
24
0.820
0.772
94.2
5
141.16
27.50
113.66
4
32
25
0.940
0.885
94.2
5
141.31
26.35
114.96
4
34
26
1.090
1.019
93.5
5
142.57
25.19
117.38
417*
19.0
19.5
0.312
0.262
83.9
2.9
134.35
35.58
98.77
*Total value. The other values refer to averages
averagenumberoflogswas3.7and2.1fortheJapanesecedarandtheJapanesecypressofStandA,and
2.9forStandB.ThenumberoflogsincreasedaccordingtotheDBH.However,thinnedtreeswithDBH
valuesbetween12and14cmforStandAandof12cm
forStandBwerenotbuckedintologs(i.e.,theywere
leftintheforests),becausethesethinnedtreeswith
small DBH were not profitable with the optimum
buckingmethodformaximizingprofits.Theaverage
extractionratesfromstemswere86.6%and73.3%for
JapanesecedarandJapanesecypressofStandA,and
83.9%forStandB.Theaverageextractionratesfrom
stemsalsoincreasedaccordingtotheDBH(Fig.7).
Revenuesincreasedanddirectexpensesdecreased
accordingtotheDBH(Tables5,6,and7andFig.8).
Therefore,economicbalancesincreasedaccordingto
theDBH.Despitesmallerlogvolumesandlowerextractionrates,theaveragerevenuesfortheJapanese
cypressofStandAwerehigherthanthosefortheJapanesecedarofStandsAandB,becauseoftheformer’s
higherunitprices.Theaveragedirectexpensesforthe
JapanesecypressofStandAwerealittlehigherthan
thosefortheJapanesecedarofStandsAandB,but
almost same. Therefore, the average economic balancesfortheJapanesecypressofStandAwerehigher
thanthosefortheJapanesecedarofStandsAandB.
54
Optimalextractionrateswere70.3%and37.9%for
StandAandB,respectively.Extractedvolumeswith
theserateswere86.48m3/haand47.77m3/ha,respectively(Fig.9).Conversely,actualextractionratesand
volumeswere69.3%and36.9%,or85.25m3/ha and
46.43m3/haforStandAandB,respectively.Estimated
optimalextractionratesandvolumesweresimilarto
theactualvalues.However,small-sizedlogvolumes
differed. The actual values were 1.79 m3/ha and
1.76m3/ha,althoughnosmall-sizedlogswereestimatedwiththeoptimalextractionrate,becausethe
profitabilityofextractingsmall-sizedlogswaslow.
However,theNasu-machiForestOwners’Co-operativehadanannualcontractwithapelletproduction
factorytotransportacertainlogvolume.Furthermore,
estimated and actual log volumes for laminated lumberalsodiffered.Theactualvalueswerelargerthan
theestimations,becausetheNasu-machiForestOwners’Co-operativealsohadanannualcontractwitha
laminated lumber production factory at log prices,
whichweremorestablethanthoseinlogmarkets.
Fig.10showsrevenues,costs,andeconomicbalancesforStandsAandB.Estimatedrevenueswere
largerthanactualvalues,becauseestimatedvolumes
of saw logs, which were relatively higher priced,
werelargerthantheactualvalues,andlogquality
Croat. j. for. eng. 35(2014)1
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
C. Nakahata et al.
Fig. 8 DBH, cm; and revenues, direct expenses, and economic
balances, USD/m3 in Stand A of Japanese cypress
was not considered in this estimation. Estimated
costsweresmallerthanactualcosts,becauseactual
loss times would be larger than 1/4 of productive
timeasassumedinthestudy(KamiiizakaandKanzaki1990,Nakahataetal.2013).Therefore,estimated
economicbalanceswerelargerthanactualvalues.
3.2 Comparison with the optimal bucking
method without considering log sizes
Fig. 7 DBH, cm and extraction rates from stems, %
Croat. j. for. eng. 35(2014)1
Intheprevioussection,theoptimalbuckingmethodtomaximizeprofitswasdeterminedusingequationsdevelopedinNakahataetal.(2013),whichcon-
55
C. Nakahata et al.
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
Fig. 9 Extracted volumes (M: Measurement, 1: The optimum bucking method, 2: Without considering log sizes, 3: With maximum revenues,
4: With the new subsidy, 5: Unit prices of small-sized logs, 40.80 USD/m3, 6: Unit prices of small-sized logs, 68.00 USD/m3)
Fig. 10 Revenues, costs, and economic balances per extracted volume (M: Measurement, 1: The optimum bucking method, 2: Without
considering log sizes, 3: With maximum revenues, 4: With the new subsidy, 5: Unit prices of small-sized logs, 40.80 USD/m3, 6: Unit prices
of small-sized logs, 68.00 USD/m3)
sideredlogsizes.Thissectiondeterminestheoptimal
buckingmethodtomaximizeprofitswithoutconsideringlogsizesusingequationsdevelopedinNakahataetal.(2011)andcomparesthetwooptimalbuck-
56
ingmethods.Theaverageextractionratesfromstems
withoutconsideringlogsizeswere89.3%and81.2%
for the Japanese cedar and the Japanese cypress of
StandA,and92.2%forStandB.Theaverageextraction
Croat. j. for. eng. 35(2014)1
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
Fig. 11 DBH, cm and direct expenses, USD/m3 in Stand A of Japanese cypress
ratesfromstemswithoutconsideringlogsizeswere
higher.Notably,thedifferencesbecamelargerwith
smaller DBHs (Fig. 7), because direct expenses of
small-sizedlogsdidnotincreasewhenlogsizeswere
notconsidered;subsequently,small-sizedlogstended
tobeextractedalthoughthedifferencesindirectexpensesweresmallbetweenthetwocases(Fig.11).For
example,onlyfivelogscouldbebuckedmaximally
fromthethinnedwoodsintheoptimalbuckingmethodconsideringlogsizes.Ontheotherhand,maximum
seven logs were bucked from the thinned woods by
thebuckingmethodthatdidnotconsiderlogsizes.
Optimalextractionrateswithouttakinglogsize
intoconsiderationwere73.5%and41.1%forStandA
andB,respectively(Fig.9).Thecorrespondingextractedvolumeswithoptimalextractionrateswere
90.44m3/haand51.83m3/ha.Small-sizedlogvolumes
were4.03m3/haand4.04m3/haforStandAandB,
respectively.Thesewerelargerthantheactualvalues
andestimationsmadebytheoptimalbuckingmethod
consideringlogsizes.However,revenuesperm3 decreased,andsubsequently,economicbalancesperm3
alsodecreased(Fig.10).
3.3 Comparison with the optimal bucking
method to maximize revenues
Theoptimalbuckingmethodusuallymaximizes
revenuesandisusedtoestimaterevenues(Ieharaand
Kurokawa1990).Here,theoptimalbuckingmethod
Croat. j. for. eng. 35(2014)1
C. Nakahata et al.
tomaximizerevenuesisdeterminedandcompared.
Theaverageextractionratesfromstemswithmaximumrevenueswere90.0%and90.0%fortheJapanese
cedarandtheJapanesecypressofStandA,respectively,and94.2%forStandB.Theaverageextraction
rates from stems with maximum revenues increased
comparedtothosefromstemswithmaximumprofits.
Notably, the differences became larger for smaller
DBHs(Fig.7),becauserevenuesincreasedaccording
toextractedvolumes.Furthermore,thinnedtreeswith
aDBHbetween12and14cmforStandA,andof12cm
forStandB,wereextractedwiththeoptimalbucking
methodtomaximizerevenues.Aswiththeoptimum
buckingmethodtomaximizeprofits,thesewerenot
buckedintologs(i.e.,theywereleftintheforests),
becausethesethinnedtreeswithsmallDBHwerenot
profitable.Therefore,fortheoptimalbuckingmethod
tomaximizerevenues,directexpensesexceededrevenues,andeconomicbalancessufferedadeficitwith
smallDBHs(Fig.8).
Extraction rates with maximum revenues were estimatedtobe76.0%and41.4%forStandAandB,respectively(Fig.9).Correspondingvaluesforextracted
volumeswithmaximumrevenueswere93.50m3/ha
and 52.22 m3/ha. Small-sized log volumes were
6.14m3/haand4.26m3/haforStandAandB,respectively.Thesewerelargerthantheactualvaluesand
estimationswithmaximumprofits.Therefore,revenuesperhaincreasedaccordingtoextractedvolumes.
However,costsperhaalsoincreasedaccordingtoextractedvolumes.Subsequently,theestimatedeconomicbalancesdecreased.Ontheotherhand,revenuesper
m3decreasedandsubsequently,economicbalances
perm3alsodecreased(Fig.10).
3.4 Comparison with the optimal bucking
method considering the new subsidy system
Thesubsidysystemwaschangedin2011.Until
2010,standardunitcosts(TochigiPrefecturalGovernment2010b)weredeterminedbyageclass,thinningrates,andextraction,ifany(Fig.4).Anextraction rate of at least 50% was required. In the new
subsidysystem,standardunitcosts(TochigiPrefecturalGovernment2011)weredeterminedbyoperation system, thinning rate, and extracted volumes
(Fig.12).Operationsystemswereclassifiedintotwo
types:ground-basedandskylinesystem.Thesitesin
thisstudyusetheground-basedoperationsystem
andhaveathinningrateof30%.Inthenewsubsidy
system,thesubsidywasincreasedaccordingtoextractedvolumes.
Theaverageextractionratesfromstemswiththe
new subsidy system were 89.3% and 79.1% for the
57
C. Nakahata et al.
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
Fig. 12 Standard unit costs for the new subsidy with a groundbased system
JapanesecedarandtheJapanesecypressofStandA,
and88.3%forStandB.Theserateswerehighercomparedtothosefortheprevioussubsidysystem,because the subsidy increased according to extracted
volumes(Fig.13).Extractionratesfromstandswiththe
newsubsidysysteminplacewereestimatedtobe73.3%
and39.9%forStandAandB,respectively(Fig.9).Correspondingextractedvolumeswere90.12m3/ha and
50.29m3/ha.Small-sizedlogvolumeswere3.63m3/ha
and2.51m3/haforStandAandB,respectively.Smallsizedlogvolumeswiththenewsubsidysystemincreasedcomparedtothoseintheprevioussubsidy
system. Consequently, the economic balances increasedwiththeincreaseinextractedvolumes,especiallyinStandB(Fig.10).
3.5 Comparison of optimal bucking methods
with higher unit prices for small-sized logs
Inadditiontotheunitpricesforsmall-sizedlogs:
30.00USD/m3,thefollowingunitpriceswereexamined
assumingnosubsidyforthinningoperationsandstrip
roadestablishments:40.80USD/m3and68.00USD/m3.
Thesepriceswouldbeconvertedusingabulkdensity
of0.68ton/m3(MikamoForestOwners’Co-operative
andSumitomoOsakaCementCompany2008)from
60.00USD/tonwithadditionalsubsidiestosmall-sized
logprices(JapaneseForestryInvestigationCommittee
2011b)and100.00USD/tonifFITswereintroducedin
Japan (Japanese Forestry Investigation Committee
2011a).
58
Fig. 13 DBH, cm and extraction rates from stems, % with the new
subsidy and higher unit prices
Croat. j. for. eng. 35(2014)1
Examining the Optimal Bucking Method to Maximize Profits in Commercial Operations ... (45–61)
Theaverageextractionratesfromstemswiththe
unitprice40.80USD/m3were86.7%and73.3%forthe
JapanesecedarandtheJapanesecypressofStandA,
and83.9%forStandB.Theaverageextractionrates
fromstemswiththeunitprice40.80USD/m3 were
almost the same as those from stems with the unit
price30.00USD/m3excludingDBHhigherthan38cm
fortheJapanesecedarofStandA(Fig.13).Extraction
ratesfromstandswiththeunitprice40.80USD/m3
were estimated to be 70.4% and 37.9%, and correspondingextractedvolumeswere86.60m3/ha and
47.77m3/ha.Small-sizedlogvolumeswere0.12m3/ha
and0.00m3/haforStandAandB,respectively(Fig.
9).Small-sizedlogvolumesincreasedmarginallyto
0.12 m3/ha with 40.80 USD/m3 for StandA; subsequently,extractionratesfromstandsandextracted
volumesalsoincreasedatalmostthesamerate.Revenuesof40.80USD/m3wererelativelyhigher.However,economicbalancesdecreasedintheabsenceof
asubsidy(Fig.10).
Theaverageextractionratesfromstemswiththe
unitprice68.00USD/m3were91.4%and81.5%forthe
JapanesecedarandtheJapanesecypressofStandA,
and91.5%forStandB.Theseratesarehighercompared
tothosefromstemswiththeunitprice30.00USD/m3.
Notably, the differences became larger for smaller
DBHs(Fig.13).Extractionratesfromstandswiththe
unitprice68.00USD/m3wereestimatedtobe74.5%
and40.4%forStandAandB,respectively,andcorresponding extracted volumes were 91.60 m3/ha and
50.95m3/ha.Small-sizedlogvolumeswere12.14m3/ha
and3.17m3/haforStandAandB,respectively(Fig.9).
Theseincreasedinlinewithunitpriceincreasesfor
small-sizedlogs.Notably,small-sizedlogvolumesin
StandAwerethelargestofallestimations.However,
economic balances decreased in the absence of a subsidy(Fig.10).
C. Nakahata et al.
tionsinthestands.Standinthisstudywereabout50
years old, with an average DBH of about 20 cm.
Among the estimations, differences of extraction
ratesfromstemswithDBHexceeding20cmwere
small.However,extractionratesfromstemswitha
DBH less than 20 cm were significantly different.
Therefore,itislikelythattheoptimalbuckingmethodtomaximizeprofitswhileconsideringlogsizes
canhelpdeterminetheoptimalextractionratesof
youngerstandswithsmallerDBH.Additionalstudiesfordifferentforestsandforestryconditionswould
beuseful.
Small-sizedlogvolumeswiththeoptimalbucking
methodweresmallerthantheactualvalues,because
this model did not consider contracts with factories
concerningannualsupplyobligationsandstableprices.Furthermore,thismodeldidnotconsiderlogquality,andbuckingoperationsshouldbeconductedalso
takinglogqualityintoconsideration.Low-qualitylogs
weresoldtochiporpelletfactoriesratherthantolog
markets. Therefore, future studies should consider
supplyobligationsandlogquality,althoughthelatter
canbedifficulttopredict.
Effectsofthenewsubsidysystemandhigherunit
pricesforsmall-sizedlogswerealsodiscussed.The
newsubsidysystemandunitpriceswithFITsboth
contributed to increased extracted volumes of smallsizedlogs.However,itislikelythatsubsidieswillbe
reducedinthefuture,duetothegovernment’sbudget
constraints.Therefore,alow-costharvestingsystem
shouldbedevelopedtoestablishforestroadnetworks
andimproveforestryoperationsystems.
Acknowledgements
WearegratefultotheNasu-machiForestOwners’
Co-operativefortheircooperationduringthecourse
ofthisresearch.
4. Conclusions
Optimal bucking methods to maximize profits
wereappliedtotwooperationalsitesoftheNasumachiForestOwners’Co-operative,andoptimum
extractionrateswereexaminedwithdifferentoptimalbuckingmethodsandsmall-sizedlogunitprices.
Extractionratesfromstandswithmaximumprofits
weresimilartotheactualvalues,comparedwiththe
optimalbuckingmethodthatdoesnotconsiderlog
sizesandtheoptimalbuckingmethodtomaximize
revenues.However,differencesinextractedvolumes
and economic balances among these estimations
were small and are likely to fall within the error limits traditionally seen for forests and forestry condiCroat. j. for. eng. 35(2014)1
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Authors’address:
Received:July26,2013
Accepted:February3,2014
Croat. j. for. eng. 35(2014)1
GraduateStudent,ChikaraNakahata,MSc.
e-mail:[email protected]
Assoc.Prof.,KazuhiroAruga,PhD.*
e-mail:[email protected]
Assist.Prof.,MasashiSaito,PhD.
e-mail:[email protected]
DepartmentofForestScience,
FacultyofAgriculture,
UtsunomiyaUniversity,
350Mine,Utsunomiya,
Tochigi321-8505,
JAPAN
*Correspondingauthor
61