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Scandinavian Journal of Forest Research
ISSN: 0282-7581 (Print) 1651-1891 (Online) Journal homepage: http://www.tandfonline.com/loi/sfor20
Valuation and production possibilities on a
working forest using multi-objective programming,
Woodstock, timber NPV, and carbon storage and
J. P. Roise, K. Harnish, M. Mohan, H. Scolforo, J. Chung, B. Kanieski, G. P.
Catts, J. B. McCarter, J. Posse & T. Shen
To cite this article: J. P. Roise, K. Harnish, M. Mohan, H. Scolforo, J. Chung, B. Kanieski, G.
P. Catts, J. B. McCarter, J. Posse & T. Shen (2016) Valuation and production possibilities on
a working forest using multi-objective programming, Woodstock, timber NPV, and carbon
storage and sequestration, Scandinavian Journal of Forest Research, 31:7, 674-680, DOI:
To link to this article: http://dx.doi.org/10.1080/02827581.2016.1220617
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Published online: 01 Sep 2016.
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Valuation and production possibilities on a working forest using multi-objective
programming, Woodstock, timber NPV, and carbon storage and sequestration
J. P. Roise
, K. Harnish
, M. Mohan
, H. Scolforo
, J. Chung
, B. Kanieski
, G. P. Catts
, J. B. McCarter
, J. Posse
and T. Shen
Operations Research Program, North Carolina State University, Raleigh, NC, USA;
Department of Forestry and Environmental Resources, North
Carolina State University, Raleigh, NC, USA
This study analyzes the trade-off between net present value (NPV) of timber resources, and carbon
sequestration and storage for a working forest, the Hofmann Forest in North Carolina, USA. Multi-
objective optimization is used to determine the production possibility curves showing the
relationship between NPV and carbon. We then perform a sensitivity analysis to explore alternative
management strategies. For carbon yields we used aboveground pools: branches, leaves, tops and
bole as estimated by the Forest Vegetation Simulator (FVS) and LOBDSS using the California
Carbon Market Protocols, including product carbon. Timber yields of sawtimber, chip-n-saw and
pulpwood were estimated by LOBDSS for planted stands less than 49 years of age, and FVS was
used for all natural stands and planted stands 49 years and over. Our results reveal that NPV
opportunity costs associated with increasing carbon sequestration at Hofmann Forest are less than
the current California carbon market price.
Received 15 December 2015
Accepted 28 July 2016
Multi-objective; carbon; net
present value; Woodstock;
The modern approach to forest management planning not
only involves timber production, but also includes multi-objec-
tive integrated management criteria and goals (Baskent &
Keleş2009). As forest ecosystems serve as possible sinks of
carbon dioxide (CO
), terrestrial carbon sequestration
through reforestation, avoided land-use conversion, afforesta-
tion and improved forest management (IFM) practices are
been viewed as methods to mitigate the issues related to
global climatic change (Hoen & Solberg 1994; Newell &
Stavins 2000; CARB 2015). Although water vapor contributes
more to the greenhouse effect, CO
is considered the most
important among anthropogenic gases (Hoen & Solberg
1999; van Kooten et al. 1999) and forests in this sense can
help in mitigating CO
emissions through carbon uptake and
storage in forest biomass and forest soil, substitution of fossil
fuel with biofuel and substitution of wood products for more
energy demanding materials (Dixon et al. 1994; Brown et al.
1996; Backéus et al. 2005). As an attempt to reduce the dra-
matic increase in CO
emissions, several guidelines for the
inclusion of forest-sector carbon sequestration in the national
greenhouse gas balance have also taken form in the last
few decades (Díaz-Balteiro & Romero 2003; Penman et al.
2003). In United States, atmospheric carbon sequestered by
forests was about Tg C yr
in year 2004 and it was found to
have a potential for reducing CO
emissions from burning
fossil fuels by approximately 10% (Heath & Smith 2004;
Birdsey et al. 2006).
In this context, several forest management optimization
models with carbon sequestration as a complementary
objective were developed. For example, Hoen and Solberg
(1994,1999) developed a multi-objective management
model for determining the transformation curve between
net present value (NPV) of timber and CO
the planning horizon. For these models, the classic methods
to determine optimal forest rotation age were found ineffec-
tive (Díaz-Balteiro & Romero 2003) as they were considering
conflicting bi-objective goals. This study investigates the
trade-off between NPV of timber resources, and carbon
sequestration and storage for a working forest, the
Hofmann Forest in North Carolina, USA. Multi-objective
optimization was employed for determining the production
possibility curves between NPV and Carbon. Adding to that,
alternative management strategies were explored using a
For our case study, the economic cost for carbon seques-
tration was quantified by estimating the NPV opportunity
cost associated with the buildup of carbon storage from har-
vested merchantable timber. For obtaining net greenhouse
gas credits from forest management projects, one has to
show additional carbon storage and sequestration above
what would have been achieved without the project. Recent
research findings suggest that the additionality requirement
of carbon will result in high economic costs to private land-
owners, which can only be mitigated by a corresponding
high price paid for carbon credits. Whereas public land is a
different story, because they typically do not have a profit
motive and they could feasibly be called on to sequester
and store additional carbon, for the public good. The oppor-
tunity cost of carbon sequestration depends on the
© 2016 Informa UK Limited, trading as Taylor & Francis Group
CONTACT J. P. Roise email@example.com Department of Forestry and Environmental Resources, North Carolina State University, Box 8008, Raleigh, NC
SCANDINAVIAN JOURNAL OF FOREST RESEARCH, 2016
VOL. 31, NO. 7, 674–680
contribution margins of the sold timber, and thus varies from
place to place and time to time (Ndjondo et al. 2014). Even
though several authors have written about carbon sequestra-
tion, it can be hard to compare studies due to differences in
objectives, products and substitutions included, and non-
decision variables (Gharis et al. 2015). There is no specific
management practice that can be applied to every situation,
but we can make better trade-offs depending on our needs,
if we are able to comprehend the situation and understand
the variables behind it efficiently.
Materials and methods
The geographic focus of this study is the Hofmann Forest, a
major landholding of the Forestry School at North Carolina
State University, USA (Figure 1). It encompasses approxi-
mately 32,000 contiguous hectares in the coastal plain of
North Carolina ranging from 12 to 20 meters above sea
level with an average slope of ≤1%. For this study, we ana-
lyzed only the 24,000 ha of operational land, consisting
mostly of loblolly pine (Pinus taeda L.) plantations. Figure 2
shows the associated age class distribution and other land-
Multi-objective management approach
In this paper, we present a forest management model
designed to optimize the combination of two objectives:
NPV, and carbon sequestration and storage, on the Hofmann
Forest in North Carolina. For growth-and-yield estimates, we
used both LOBDSS and the USDA Forest Vegetation Simulator
(FVS). LOBDSS (Amateis et al. 2000,2001) is an expert system,
with FastLob2.1 as the underlying growth-and-yield model
used to determine intensively management treatment
effects of short (<49 years) rotation options (Amateis et al.
2000,2001). FVS is used to simulate longer (≥49 years) rotation
effects on forest outcomes and conditions. FVS is a family of
models that simulate growth and yield in an individual-tree
and distance-dependent fashion. Considerable investments
have been made by the United States Forest Service to
include as many forest outputs and conditions as science will
support (Dixon 2002). We spliced these two models together
to produce realistic short-rotation plantations which maximize
NPV and long-rotation estimates that are assumed to be
needed to maximize carbon sequestration and storage. Our
prescriptions included three levels of management intensity
over a 100-year planning horizon using 5-year planning
periods. Through sensitivity analysis, we explore the effects
of changes in carbon storage and NPV, and compared our
final values to the current markets (ARBOCS
) to evaluate
their feasibility to produce a change in management practices.
A model II multi-objective forest management linear pro-
gramming formulation was used involving different levels of
management intensity and rotation ages from 15 to 150
years. The model uses 5-year periods and a 100-year planning
horizon. The Remsoft Spatial Planning System™provided the
modeling structure. Equation (1) expresses the trade-off
between the weighted total NPV from timber and weighted
additional tons of carbon. The decision land management
variables are hectares allocated to each combination of plant-
ing density, thinning timing and intensity, and rotation length.
Besides timber volumes and values of sawtimber, chip-n-saw
and pulpwood, we track tons of carbon in standing timber, in
harvest residuals and slash, in product classes, and in landfill.
We did not include carbon used as a substitution for fossil
fuels or in soils, down woody debris, snags, understory, litter
and duff. The model formulation is:
MAX WnpvNPV + WcC, (1)
(bijkrijk) , (2)
(vijk xijk )+
(vijk rijk )+
(viNk riNk ),
xiNk =Aii=1...24, (4)
rjlk j=1...20 , (5)
hijk rijk =Hjj=1...20, (6)
Hj+1−(1 −flow)Hj≥0 for j=1 to 19 (lower bound), (7)
Hj+1+−(1 +flow)Hj≤0 for j
=1 to 19 (upper bound), (8)
xijk ≥0 for i=1...24, j=1... 20, k=1...5 , (9)
rijk ≥0 for i=1...17 j=3...20 k=1...12 , (10)
are the existing stand decision variables, (i) is exist-
ing landclass, jis harvested period, following prescription k.
are existing stands not harvested by period N(=20). x
are existing stands at time = 0. r
) are the regenerated
stand decision variables (hectares planted in period i(j),
regen-harvested in period j(l), using prescription k). r
regenerated stands not harvested by period N.
A prescription is a combination of planting and thinning
activities as listed below. Existing stand options are thin (if
young enough) or not using same options as specified in (5, 6,
7, 8 and 9) below, and clear-cut at any time from ages 15 up
to 150 years, which leaves the option of doing nothing over
the 100-year planning horizon. Regenerated stand options
rotation ages from 15 to 150 years and the following options:
SCANDINAVIAN JOURNAL OF FOREST RESEARCH 675
(1) Planting and site preparation: shear, bed and plant at
1.5 × 6 meter spacing or 1077 trees ha
(5 × 20 feet
spacing or 436 trees ac
) (no fertilizer);
(2) Planting and site preparation: shear, bed and plant at
1.5 × 6 meter spacing or 1077 trees ha
(3) Planting and site preparation. shear, no bedding, plant at
3705 trees ha
(1500 trees ac
(4) Planting and site preparation. shear, no bedding, plant at
3705 trees ha
(5) Thin at ages 15 and 25;
(6) Thin at ages 10 and 20;
(7) Thin once at age 15;
(8) Thin once at age 20;
(9) No thinning.
NPV (Equation (2)) is the NPV of the whole forest over a
100-year planning horizon.
C (Equation (3)) is the total carbon stored in aboveground
live carbon and harvested wood products (HWPs) over the
100-year planning horizon. C and NPV are the two objectives
used in Equation (1). W
is the weight for NPV and W
weight for carbon. We use weights only to find alternative sol-
utions in each run. Weights are selected to find new solutions
on the production possibility curves (Figure 3).
Figure 1. Hofmann Forest 2015 Operations Map, including 640 km of roads and 2240 km of drainage ditches. Large blue area is Pocosin Swamp (6880 ha). Green
Square in upper blue area is T.E. Maki’s plot arguably changed forest practices in the southern coastal plan.
676 J. P. ROISE ET AL.
= net discounted value for stands harvested period j,
landclass i, and prescription k(interest = 6.5%);
= net discounted value for stands born in i, regen-
harvest in jusing prescription k;
= carbon tons sequestered and stored in variables x
are tons of carbon at start;
= harvest volume for period j, for respective variable;
= the total harvest for period j;
= the area of landclass i.
Flow is the allowable increase or decrease in harvest
volume between periods (0, 0.2 or constraint deleted) and is
used in Equations (4), (7) and (8) to control period to period
variation in harvest volume.
Equation (1) is the objective function. Equation (2) is used
to calculate the NPV.
Equation (3) is a set of equations used to calculate the
carbon stored and sequestered for an optimization run.
Initial carbon amount for a model run is calculated at year
). The estimate of total carbon stored for that run is
is the difference between the carbon stocking in
period xand period x−1 for each hectare. Initial carbon
) were included for time 0 in the total carbon
stocks calculation. HWPs were calculated by taking the differ-
ence between HWP period xand HWP period x−1. Total
carbon stock (Equation (3)) was calculated as the summation
over the 100-year period of from each hectare for each period,
including standing carbon and HWP. This formula was derived
from the California Air Resources Board quantification meth-
odology for an IFM project (CARB 2015). The estimate
“additional”carbon storage comes after the optimizations.
We first measure the total carbon storage at the Max NPV con-
Wc = 0
), business as usual. Then we subtract C
Wc = 0
Wc > 0
(carbon storage under improved management).
Equation (4) is the existing landclass areas. Equation (5) is
the area transfer rows. Equation (6) is the harvest accounting
rows. Equations (7) and (8) are the harvest flow constraints.
Equations (9) and (10) are non-negativity constraints. The
Remsoft Spatial Planning System™provided matrix gener-
ation and report writer. The approach was designed to evalu-
ate the trade-off between NPV and carbon by maximizing the
weighted total NPV from timber and tons of carbon. The
decision variables are hectares allocated to each combination
of planting density, thinning timing and intensity, and
The current inventory is the result of 80+ years of mana-
ging the Forest to Maximize NPV, acknowledging that over
the first 50 years, classical methods were used and only
over the last 30 years was the modern planning methodology
applied. Timber prices for estimating NPV were obtained from
For IFM projects, all protocols require
that parties applying for carbon credits must certify addition-
ality. It is based on how similar forests are being managed,
rather than guessing how a particular landowner would act.
Figure 2. Land-use age class distribution of the Hofmann Forest in March 2015.
The five columns are pine plantations. Not shown are Natural Pine and Hard-
wood operational categories. There are also 2.64 ha (6 acres) of 70+ slash
pine (Pinus elliottii), which are too small to show up on the graph.
Figure 3. Optimal combinations NPV and CO
presented as production possibility curves for NPV and carbon under the three harvest flow constraints. These are the
multi-objective optimization results from Woodstock. Note that each curve starts with 0 additional carbon when NPV is maximized (0 weight for carbon).
SCANDINAVIAN JOURNAL OF FOREST RESEARCH 677
After completing the calculation process and applications,
there are very specific processes for monitoring the accom-
plishment. Some of these procedures require independent
third party verification with consequent expenses. Monitoring
is a way of demonstrating that the carbon pool estimated has
not been reversed, and it accounts for both onsite and offsite
carbon (basically products). The products considered were
pine sawtimber, pine chip-n-saw and pine pulpwood, and
the product units were in green tons. Details on carbon con-
version can be found in Appendix C Estimating Carbon (CARB
It should be noted that in a multi-programming model, the
relative importance of each objective will vary depending on
the decision-maker’s interests, and even the non-decision
variables such as weights, discount rates, site indices, costs
and prices do affect the cost of carbon and efficacy of man-
agement practices (Prodanovic & Simonovic 2003). In other
words, the value of a forest is directly related to management
Results and analysis
The multi-objective formulation was evaluated under three
different constraint scenarios; unconstrained harvest flow,
20% variation from period to period harvest flow and even
harvest flow. The results are summarized in Figure 3 which
displays production possibility curves of the relation
between optimal NPV and additional CO
storage. Each curve is a non-inferior set of points, with each
point on a curve being equally valid depending on the
decision-maker preferences, while each point below the
curve is inferior because you can always increase both NPV
by moving to the curve. Each point above the
curve is non-feasible given the capabilities of the land base
and the policies being applied. In each case, when optimizing
for carbon stored over the entire 100-year planning horizon,
the model selected stands with the highest available planting
density (3705 trees ha
), and extended harvest rotations.
The completely unconstrained maximization run resulted
in unrealistic harvest results. Operational and market experi-
ence suggest that no more than 8100 ha (20,000 ac) could
be harvested in a 5-year period. In order to maximize the
annual growth potential of the standing carbon stocks, the
unconstrained model clear-cut unrealistically large areas in
periods 5, 13 and 20. Adding the 20% variation in harvest
flow constraint lowered clear-cut areas to realistic levels and
increased the amount of thinning substantially from 209 ha
(517 ac yr
) to 630 ha yr
(1558 ac yr
A sensitivity analysis revealed that the trade-off between
carbon sequestration and NPV maximization requires only a
slight reduction in carbon sequestration to achieve dramatic
increases in NPV (Figure 3). Under the 20% constraint, carbon
maximization yielded an NPV $48,531,255 and 5,576,235
additional Mg CO
over the 100-year horizon (Point 1, Figure
3). On the other end of the 20% curve, maximum NPV is
$61,552,806 and CO
is at 0 Mg (Point 2, Figure 3). Total CO
sequestered and stored is 15,969,129 Mg but none of this is
additional, since we get this under current management.
However, if we increased CO
to the maximum level (Point 1,
Figures 3 and 4), NPV falls by $13,021,551 yielding a gain of
5,576,235 Mg CO
at an opportunity cost of $2.34 Mg
(Point 1, Figure 4
. Current CARB market prices (over $10 per
) suggest that an IFM plan for large forest owners in
the southeastern United States could effectively improve
both carbon sequestration and profitability.
Our results indicate that pine plantations represent a major
potential carbon pool in the southeastern United States. The
baseline formulation in our model is defined by an NPV optim-
ization condition and this type of baseline approach is impor-
tant as it affects the quantity, credibility and equity of credits
generated from efforts to reduce forest carbon emissions
(Chomitz 1999; Gibbs et al. 2007; Griscom et al. 2009). For
this study, we have not considered the minimum baseline
level (average carbon stocks of forest of the same cover
type in the same region) to be the baseline level of available
carbon stocks as we aimed to assess the net change in CO
sequestration relative to a business as usual scenario, and
not to other forests within the region. From Figures 3 and 4,
we understand that for a small cost per ton we can sequester
and store additional carbon. Although carbon sequestration
in forest might not be a permanent carbon sink, it can buy
us some extra time and thereby help in delaying temperature
increase and related issues (Backéus et al. 2005). Considering
an uncertain future, these methods have an advantage of
being flexible and reversible most of the times (Solberg
1997; van Kooten et al. 1997). Moreover, it is easier to evaluate
the cost of carbon uptake as compared to cost associated with
future damages caused due to changing climatic conditions
(van Kooten et al. 1997; Backéus et al. 2005). There are also
several other mechanisms such as emission trading and
joint implementation, which opens opportunities to pursue
transfer and creation of carbon reduction units through indus-
trial projects at a global scale (Pretty & Ball 2001; Burley et al.
2007). Considering all these factors there is a huge possibility
for landowners following short rotation ages, located in good
wood products markets to alter their management practices
and increase carbon storage capacity of forest, without
costing a large amount of money. However, recent studies
show that these research findings are not accepted by large
segments of the American public for various reasons (Leisero-
witz et al. 2013; Khanal et al. 2016).
One of the primary hurdles for including plantations in the
market is the species diversity requirement (CARB 2015). Plan-
tations are inherently monocultures, and currently IFM proto-
cols within the United States, require mixed species,
consistent with natural forest management. Another
concern regarding carbon storage is the saturation issue,
which is a measure of how much carbon forests can carry at
a given time (Marland et al. 2001; Lee et al. 2005; Canadell
et al. 2007; Nabuurs et al. 2013). From our saturation curve,
we can notice that 100 years were not enough for reaching
a steady state in standing volume, which means that there
is less risk of carbon storage over the next 100 years given
the fact that the net growth of our carbon model reflects
carbon sequestration and there are no large-scale
678 J. P. ROISE ET AL.
disturbances happening at the study site. However, it is
advised to understand the actual risk and magnitude of
potential reversals beforehand, so that suitable management
strategies can be incorporated in situations involving inten-
tional or unintentional release of carbon back to the atmos-
phere happening due to storms, fire, pests, land-use
decisions, etc. (Galik & Jackson 2009).
With respect to global climate change and mitigation strat-
egies, a measure of detailed carbon balance is necessary as
the net release or uptake of carbon by forests could have a
large impact on the atmosphere’s CO concentration (IGBP Ter-
restrial Carbon Working Group 1998; Körner 2003). Also, vari-
ation in forest management strategies can have serious
impacts on other carbon pools and this will in turn affect
the overall carbon sequestration capacity of a given forest
land. For example, harvesting, thinning and fertilizer appli-
cations are found to affect the soil carbon dynamics of
forests to a moderate degree (Johnson & Curtis 2001; Luo
et al. 2003; Jandl et al. 2007; Peng et al. 2008; Nave et al.
2010; Noormets et al. 2015). It should be borne in mind that
the carbon inventory used for this study was derived from
merchantable inventory, which does not include carbon
pools, such as soil, standing dead trees and trees below
minimum dbh class. Hence for improving the overall effi-
ciency of current model, further research focused on
implementation of inventory data to include all possible
carbon pools is essential.
Overall our research study suggests that for a small cost per
ton we can sequester and store large amount of carbon in
the pine plantations of southeastern United States.
However, current carbon market standards prohibit forests
with homogeneous species, broadcast fertilization and other
intensive silviculture practices. Further research is needed to
examine the potential for pine plantations located in similar
geophysical regions that adhere to the carbon market stan-
dards in comparison to intensively managed forests like the
Hofmann Forest, so that landowners may better understand
the opportunity cost of managing their property less inten-
sively so that they may enter the market. The current United
States carbon market is hospitable to forest landowners
who are already growing timber for markets that require
long rotation ages and for forest landowners located in
poor forest products markets. With a few changes in market
structure, landowners who currently manage for profit maxi-
mization using short rotation ages and located in good
wood products markets could alter their management and
realize a large increase in carbon sequestration, without
costing a large amount of money.
1. CRT Carbon Credits, Your Vercarbon Guide; Climate action Reserve
Approved to Register Offset Projects for California’s Cap-and-Trade
Program, Business Wire (December 14, 20012).
2. Timber Mart-South Eastern regional averages for the state of North
Carolina for the 1st quarter of 2015 (http://www.timbermart-south.
This research was conducted at the North Carolina State University,
Raleigh, NC 27695, USA.
No potential conflict of interest was reported by the authors.
Figure 4. The opportunity cost per ton in, NPV US dollars, associated with increases in carbon production for the three different harvest flow constraints.
SCANDINAVIAN JOURNAL OF FOREST RESEARCH 679
We would like to thank REMSOFT for use of the Spatial Planning System;
The North Carolina Natural Resources Foundation for use of the Hofmann
Forest, its GIS and database; Buck Vaughan and the Conservation Fund for
helpful insights into carbon projects; and ﬁnally Laura Parker, of American
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