The economic impact of green-up constraints in the southeastern United States

The economic impact of green-up constraints inthe southeastern United States

Kevin Bostona,*, Pete Bettingerb

aWarnell School of Forest Resources, University of Georgia, Athens, GA 30602, USAbDepartment of Forest Resources, Oregon State University, Corvallis, OR 97331, USA

Received 27 December 1999; accepted 21 March 2000

Abstract

Green-up, or adjacency, requirements are a common constraint in forestry. The American Forest and Paper Association has

developed a Sustainable Forestry Initiative that includes a green-up constraint which limits the average clearcut opening to

48 ha for 3 years or until the average height of the regenerated trees is >1.4 m. In addition to constraining the average clearcut

size, many forestry companies in the southeastern USA voluntarily limit their maximum clearcut size to between 60 and 90 ha.

In this research, a heuristic algorithm was used to develop tactical forest plans that consider both the maximum and average

clearcut sizes. Economic effects of the green-up constraints were estimated for situations where intensive management can

reduce the length of the green-up time from 3 to 2 years on a 21 600 ha ownership in Georgia (USA). For a 60-ha maximum

opening size, this reduction in green-up time from 3 to 2 years resulted in an additional US$ 66 600 in present net worth

(PNW) over a 10-year analysis period. This corresponds to a US$ 10 per harvested ha, or a 0.8% increase in PNW. The bene®t

gained by reducing the length of the green-up period is less with a 90-ha maximum clearcut size, where PNW increases by

US$ 45 600, or US$ 6.70 per harvested ha, a 0.5% increase. While the total volume per period was near the volume goal

produced by a strategic forest plan, the spatial restrictions and the desire to maximize net present value resulted in lower

volume of timber products (sawlogs and chip-and-saw logs) from older forest stands. A sensitivity analysis showed that an

increase in price or yield further reduced the economic incentive for the reduction of the length of the green-up constraint. As

price or volume decreased below expectations, however, the incentive to use intensive forest management practices to reduce

the length of the green-up constraint became more attractive, since the differences between a 2-year and 3-year green-up time

requirement may be large enough to pay for more intensive management practices. # 2001 Elsevier Science B.V. All rights

reserved.

Keywords: Green-up constraints; Economic effects; Forest management

1. Introduction

Increasing competition from international pine-pro-

ducing regions is forcing forest industry organizations

in the southeastern United States to adopt intensive

forestry practices, including extensive site prepara-

tion, weed control, and fertilization. It is well accepted

that these practices can accelerate forest growth rates

(Knowe et al., 1985; Bacon and Zedaker, 1987), but

they also add to the operational costs of growing trees.

Forestry ®rms are under increasing pressure to pro-

duce higher returns for their shareholders and may

only adopt practices that improve their overall pro®t-

ability. Activities are often selected on their ability to

Forest Ecology and Management 145 (2001) 191±202

* Corresponding author.

E-mail addresses: [email protected] (K. Boston),

[email protected] (P. Bettinger).

0378-1127/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 3 7 8 - 1 1 2 7 ( 0 0 ) 0 0 4 1 7 - 5

improve pro®ts, not just improve growth rates and

reach sustainability.

In addition to increased competition from interna-

tional producers, most forest products companies in

the southeastern United States have adopted the Amer-

ican Forest and Paper Association (AF&PA) Sustain-

able Forestry Initiative (SFI). The initiative is a

voluntary agreement among AF&PA members to

promote sustainable forestry practices. One compo-

nent of the SFI guidelines is a green-up constraint that

restricts the average clearcut size to <48 ha for either 3

years or until the average height of the regenerated

trees is >1.4 m. Additionally, many companies have

developed an internal policy to voluntarily limit their

maximum clearcut size to 60±90 ha. Estimating the

effects of the combination of these land manage-

ment constraints poses a challenging combinatorial

problem.

The ®nancial impact of various green-up con-

straints has generally been estimated by using rela-

tively long periods of time for adjacent stands to

`green-up'. For example, in Canada, three different

green-up periods (10, 20, and 30 years), three differ-

ent maximum opening sizes (20, 40, and 80 ha), and

three different rotation lengths (80, 100, and 120

years) were used to compare the cost of various

harvesting restrictions (Daust and Nelson, 1993).

The smallest maximum size and the longest green-

up time resulted in a 29% reduction in harvest volume

compared with an optimal solution from a linear

programming effort, which did not contain the spatial

constraints. In Oregon (USA), increasing the green-

up period from 20 to 30 years showed a 34±40%

reduction in the present net worth (PNW) (Yoshimoto

and Brodie, 1994). In California (USA), increasing

the green-up period from 10 to 20 years reduced PNW

by 13% for a 4-ha maximum opening size. As the

minimum patch size increased to 32 ha, there was

smaller difference for increased exclusion period

(Barrett et al., 1998).

A variety of heuristic techniques can be used to

solve problems that consider management options

with green-up size constraints, or spatially con-

strained harvest scheduling problems. Van Duesen

(1999) was able to solve numerically-large spatially

constrained problems by using a simulated annealing

algorithm, but did not compare the quality of his

solutions. Two problems based on a smaller spatial

scale showed no signi®cant difference in the objec-

tive function values for a random starting location

hill-climbing algorithm, Monte-Carlo integer pro-

gramming, simulated annealing, and tabu search

(Murray and Church, 1995). Four problems of larger

spatial scales were used to compare Monte-Carlo

integer programming, simulated annealing, and tabu

search. Simulated annealing found the best solution

to three of the four problems while tabu search found

the best solution to the fourth (Boston and Bettinger,

1999).

Most of the tabu search algorithms used to solve

harvest scheduling problems have a single search

neighborhood. Bettinger et al. (1999) describe a tech-

nique that expands this by allowing two search neigh-

borhoods to change their status simultaneously. This

technique produces signi®cant improvements in the

objective function value, but at the cost of longer

processing times. Tabu search also tends to ®nd solu-

tions that are concentrated in one portion of the

solution space (Glover et al., 1995). The development

of a technique that can combine several local optimal

solutions into a single new solution may yield better

results (Glover et al., 1995).

This paper begins by describing a heuristic tech-

nique that combines tabu search and genetic algo-

rithm techniques. Then, the heuristic technique is

used to develop several tactical forest management

plans and, subsequently, estimate the ®nancial effects

of reducing the green-up time and maximum clearcut

size constraint. The economic effects are estimated

for situations where the green-up time is reduced

from 3 to 2 years, and where the maximum clearcut

size ranges between 60, 70, 80, and 90 ha. The change

in revenue, if positive, could provide additional

®nancial incentive for companies to adopt intensive

forest management practices. The goal is to deter-

mine whether variations in green-up parameters mat-

ter ®nancially in forest planning. Obviously, this can,

and has been, shown to be true for long green-up

times and small maximum clearcut sizes. However,

it has not been shown for shorter differences in

green-up times and larger maximum clearcut sizes.

If there is an economic bene®t for reducing the length

of the green-up time in areas where tree species can

be more intensively managed, this will provide

further incentive for using intensive management

techniques.

192 K. Boston, P. Bettinger / Forest Ecology and Management 145 (2001) 191±202

2. Methods

We ®rst develop the problem formulation for eval-

uating green-up constraint parameters, then present

the heuristic technique used to develop the tactical

forest plans. Then, a database from a southeastern

United States (Georgia) forest industry organiza-

tion, representing �21 600 ha, is used to evaluate

the economic effects of variations in green-up

requirements.

2.1. Model formulation

Two models were used to solve this problem, one

for a strategic 30-year plan, and one for a tactical 10-

year plan. The strategic plan provides the target

harvest goals for the tactical plan, and it can be

considered a `relaxed' problem, since the spatial

constraints for green-up are absent. The results from

this plan provide a theoretical upper-bound on the

solution. The objective function consists of maximiz-

ing the net present value of revenue from harvests less

logging costs:

maximizeXJ

j�1

XN

n�1

XT

t�1

�Revnt ÿ Lcnt�VjntXnt (1)

where J is the number of products, j the product type,

N the number of harvest units, n the harvest unit; T

the number of time periods, t the time period; Revnt

the revenue per cubic meter for unit n harvested in

time period t; Lcnt the logging cost per cubic meter

for unit n harvested in time period t, Vjnt the volume

per hectare of product j in unit n harvested

during time period t, Xnt the continuous variable

indicating whether unit n is harvested during time

period t.

A minimum harvest age of 19 years was assumed

for each timber stand, and individual product volumes

could not change by >5% per time period, except

sawlog volumes, which were set to 10% per period.

1ÿPN

n�1�VjntXnt� ÿPN

n�1�Vjnt�1Xnt�1�PNn�1�VjntXnt�

��

� deviation j 8j; t � 1; . . . ; t ÿ 1 (2)

The formulation for the tactical planning problem is

similar to the strategic plan, and to the objective

function found in Boston and Bettinger (1999). The

objective function for the problem is:

maximizeXJ

j�1

XN

n�1

XT

t�1

�Revnt ÿ Lcnt�VjntXnt

ÿXJ

j�1

XT

t�1

�Vpjtdujt� ÿXJ

j�1

XT

t�1

�Vpjtdljt� (3)

where Xnt�0,1 is a variable indicating whether unit n

is harvested during time period t; Vpjt the volume

penalty per cubic meter of product j during time period

t, dujt the positive deviation from volume goal of

product j during time period t, and dljt the negative

deviation from volume goal of product j during time

period t. The volume goals we used were those that

resulted from the strategic plan.

Penalties were used to force the heuristic search

process towards solutions which would emulate the

strategic planning solution. A three-part step function

was used to penalize deviations from the volume goal

for each product. For deviations <10% from a volume

goal, the penalty value is 50% of the product price

(Table 1). For deviations between 10 and 25% from a

volume goal, the penalty value is equal to the price.

For deviations >25% from the volume goal, the pen-

alty value is 150% of the price.

Three main constraints were considered. The ®rst is

a volume constraint, which is an accounting constraint

used to sum the volume harvested in each period and

determine the deviations from the goal for each pro-

duct:XN

i�1

�VjntXnt� ÿ dunt � dlnt � volume goal 8j; t (4)

The second constraint is a singularity constraint,

which limits each unit to one treatment during the

planning horizon:XT

t�1

Xnt � 1 8n (5)

Table 1

Prices assumed for forest products

Products Price ($/m3)

Sawlogs 46.24

Chip-and-saw logs 32.12

Pulpwood 12.00

K. Boston, P. Bettinger / Forest Ecology and Management 145 (2001) 191±202 193

The third constraint defines a maximum opening size

for each logging unit n and its set of adjacent neigh-

bors (Un). For a 3-year green-up constraints, we define

a set (Tm) of near-time periods (mz, where m1�tÿ3,

m2�tÿ2, m3�tÿ1, m4�t, m5�t�1, m6�t�2, and

m7�t�3; all mz�0, otherwise not in Tm; all mz�T,

otherwise not in Tm). We define a similar set for a 2-

year green-up constraint (mz, where m1�tÿ2,

m2�tÿ1, m3�t, m4�t�1, m5�t�2; all mz�0, other-

wise not in Tm; all mz�T, otherwise not in Tm). There-

fore, an opening is not just the harvests that occur in

time period t, but also includes those around each unit

n that have occurred during the near-time periods. The

maximum opening size constraint is:XUn

k�1

XTm

m�1

�AkXkm�" #

� �AnXnt�

� Maximum opening size 8n where Xnt � 1; t

(6)

where Un is the set of adjacent neighbors to unit n, k

the adjacent neighbors to unit n, Tm the set of near-

time periods, m a near-time period, Ak the area of unit

k; Xkm is 0,1, a variable indicating whether unit k is

harvested during near-time period m; An the area of

unit n; and Xnt is 0,1, a variable indicating whether unit

n is harvested during time period t.

A maximum average opening size can be de®ned

for each time period. If each opening is centered

around a focal unit (f) during a time period (t), we

can de®ne the size of the opening (Oft) as:

XUn

k�1

XTm

m�1

�AkXkm�" #

� �Af Xft� � Oft (7)

where Un is the set of adjacent neighbors to focal unit

f, k the adjacent neighbors to focal unit f, Tm the set of

near-time periods, m a near-time period, Ak the area of

unit k, Xkm the 0,1 variable indicating whether unit k is

harvested during near-time period m, Af the area of

focal unit f, and Xft is 0,1, a variable indicating whether

focal unit f is harvested during time period t.

As we are attempting to calculate the average open-

ing size, we do not wish to count openings more than

once. This mis-counting could occur if we allow each

unit (n) in an opening (composed of multiple units n)

to be considered the `center'. Therefore, only one unit

(n) can be delineated as the focal center (f) of the

opening in any time period, and the total number of

openings equals the number of focal centers of open-

ings. Thus,Xf �

Xn and

XXft �

XXnt (8)

The average opening size for a set of openings in a

time period (t) can then be constrained with the

following equation:PFf�1Oft

h iF

� average opening size 8t (9)

where F is the total number of openings, f the focal

center of an opening, or an opening itself, and Oft an

opening centered around a focal unit f during time

period t.

Unlike our strategic plan, the tactical forest plans

include the spatial constraints noted in equations (6)±

(9). For Eq. (6), we examined maximum opening size

constraints of 60, 70, 80, and 90 ha. For Eq. (9), we

used the AF&PA SFI maximum average clearcut size

of 48 ha. The strategic plan was developed using linear

programming techniques, and the tactical forest plans

were developed using a heuristic technique.

2.2. Sensitivity analysis

Two types of sensitivity analysis were completed

when developing the tactical forest plans, one for price

and one for volume. Prices for sawlogs and chip-and-

saw logs were increased by 5%, then decreased by 5%.

A similar approach was used to test the impact of

volume sensitivity where a uniformly distributed ran-

dom number generator was used to assign an adjust-

ment factor for each unit to ®rst increase, then

decrease the volume harvested in a unit between 0

and 5%. In each of these analyses, we examined

maximum opening size constraints of 60, 70, 80,

and 90 ha, and used the AF&PA SFI maximum aver-

age clearcut size of 48 ha.

2.3. Heuristic technique

The heuristic technique is a hybrid algorithm con-

sisting of ®ve components (Fig. 1). The ®rst is a

Monte-Carlo integer programming algorithm that

randomly develops an initial solution. This process

selects a logging unit, determines if it meets the


minimum harvest age, and assures that its incorpora-

tion into the solution does not violate the green-up

constraints. This continues until 10% of the sawlog

volume has been achieved in all periods. Because

each new run of the heuristic technique uses a new

seed for a random number generator, this component

will allow an increase in the proportion of the

solution space explored when the program is executed

repeatedly.

The second component is the core tabu search

routine, similar to the algorithms described in Murray

and Church (1995), Bettinger et al. (1997), and Boston

and Bettinger (1999), and is composed of two ele-

ments: (1) a tabu list that maintains a record of the

recent moves; and (2) the aspiration criteria. After

experimentation, 100 iterations were selected as the

tabu list length. For this application, the aspiration

criterion was assumed to be the overall best objective

function value. The best move from the neighborhood

of moves will be considered ®rst, whether or not it

improves the current solution. If the move is not tabu,

it will be accepted into the solution. If the move is

tabu, yet exceeds the aspiration criteria, it too will be

accepted into the solution. If a move is tabu, yet does

not exceed the aspiration criteria, it is not accepted.

The third component is the intensi®cation routine.

The objective of an intensi®cation routine is to explore

a portion of the neighborhood that has already yielded

a good solution to search for better solutions. This

intensi®cation routine begins by recalling the current

best solution from the core tabu search routine. By

using a 2-opt neighborhood search routine described

in Bettinger et al. (1999), two units can simultaneously

change their status. the intensi®cation routine has the

same short-term memory features as the core tabu

search routine, but the tabu list has been reduced from

100 to 20 iterations.

Tabu search ®nds good solutions to large combina-

torial problems, but they tend to be concentrated in a

small portion of the solution space (Glover et al., 1995).

Thus, the fourth and ®fth components of the heuristic

technique have the goal of forcing the search to new

parts of the solution space. The fourth component

(Fig. 1) is a diversi®cation routine that schedules those

units with the lowest frequency of entering the solution,

while maintaining the minimum harvest age and not

violating the green-up constraints. This diversi®cation

will force the algorithm to the least explored portion of

the solution space. The resulting solution becomes the

starting point for the core tabu search routine.

The ®fth component has the goal of combining two

neighborhoods where good solutions were found with

the hope of ®nding a superior solution. It is based on a

crossover routine used in genetic algorithms. The

genetic crossover routine treats the solution to the

forest planning problems as if they were chromo-

somes, with each unit being a gene on a chromosome.

Fig. 1. Flow chart of the heuristic technique used to develop

tactical forest plans.


The values for the genes, the alleles, become the

periods when the unit is harvested. By using a random

number generator that selects the crossover point, the

two `chromosomes' are recombined into two new

solutions. The solution with the highest objective value

survives the crossover and becomes the starting solu-

tion for a continuation of the core tabu search routine.

This heuristic technique has been shown to produce

good results to similar scheduling problems which

have 3000±5000 0±1 integer variables (companion

paper regarding validation of the heuristic technique

is in preparation), although the heuristic technique

described here uses 2-opt moves. Extending the use of

this solution method to larger scheduling problems

therefore seems reasonable, although the performance

of the solution method cannot be directly compared

against known optimal solutions.

2.4. Data description

The data set, from a forest products ®rm in Georgia

(USA), represents a typical industrial ownership in the

southeastern United States. The data set contains

mostly pine plantations, as well as a mixture of hard-

wood areas, which for this analysis are not managed

for timber production. It contains �1300 logging

units, resulting in �10 000 0±1 decision variables.

Yields were estimated with equations developed by

Harrison and Borders (1996) for three types of wood

products: sawlogs, chip-and-saw logs, and pulpwood.

The product prices that are assumed are shown in

Table 1. We assumed a logging cost of US$ 7.41 per

m3, and an 8% real discount rate. All penalty values

were discounted by using an 8% real discount rate.

3. Results

Production possibility curves for the 3- and 2-year

green-up time when used in conjunction with the

various maximum clearcut sizes are illustrated in

Fig. 2. When applied to the 21 600 ha forest from

the southeastern United States, the heuristic technique

shows that reducing the green-up time from 3 to 2

years had the largest improvement in the objective

function value when used in conjunction with the

smallest maximum opening size, or an improvement

of about US$ 66 600 compared to US$ 45 600 for the

largest opening size. These improvements range from

approximately US$ 10 per harvested ha for the 60-ha

maximum clearcut size to US$ 6.70 per harvested ha

for the 90-ha maximum clearcut size. Again, in all

these analyses, the average opening size was con-

strained to the SFI guidelines of 48 ha.

As expected, the larger maximum opening size

allows the harvested volume to be closer to volume

Fig. 2. Production possibilities over a range of maximum clearcut sizes.


goals generated from our 30-year strategic plan (the

relaxed LP problem formulation). Each maximum

opening size (60, 70, 80, 90 ha) produces similar

results for timber volume in the ®rst years of each

10-year tactical plan, but the larger openings allow for

more volume to be harvested in the later periods.

Figs. 3 and 4 show that the chip-and-saw volume is

>90% of the target volumes in the ®rst few years of the

Fig. 3. Chip-and-saw volume produced in the first 10 years with a 3-year green-up time requirement.

Fig. 4. Chip-and-saw volume produced in the first 10 years with a 2-year green-up time requirement.


strategic plan. The deviations from the sawlog volume

targets are larger (Figs. 5 and 6), and often the tactical

plan is able to only schedule about 75% of the target

volume. The deviations are also consistently larger for

the 3-year green-up constraint than for the 2-year

constraint. The opposite pattern is observed for pulp-

wood volume, where the tactical plan meets or

exceeds the goals of the strategic plan in all time

Fig. 5. Sawlog volume produced in the first 10 years with a 3-year green-up time requirement.

Fig. 6. Sawlog volume produced in the first 10 years with a 2-year green-up time requirement.


periods for both the 3- and 2-year green-up constraints

(Figs. 7 and 8).

The results from the sensitivity analysis showed that

as prices or volumes are decreased the impact of the

green-up constraint becomes more signi®cant (Figs. 9

and 10). As prices are reduced, the magnitude of the

difference between the 3- and 2-year green-up con-

straint increases to US$ 106 per harvested ha for a

Fig. 7. Pulpwood volume produced in the first 10 years with a 3-year green-up time requirement.

Fig. 8. Pulpwood volume produced in the first 10 years with a 2-year green-up time requirement.


60-ha maximum clearcut size and US$ 92 per har-

vested ha for 90 ha maximum clearcut size. A similar

pattern is shown for a reduction in volume yield with

US$ 157 per harvested ha for 60-ha maximum clearcut

size. It is slightly reduced to US$ 153 per harvested ha

for a 90 ha maximum clearcut size. When volume or

price was increased there was no signi®cant difference

between the 3- and 2-year green-up constraints.

4. Discussion and conclusions

The goal of this analysis was to determine whether

variations in green-up parameters matter ®nancially in

forest planning efforts. Clearly, for relatively short-

rotation pine plantations in the southeastern United

States, shortening the green-up time assumption from

3 to 2 years does make a small difference in the PNW

Fig. 9. Production possibilities when prices are modified.

Fig. 10. Production possibilities when volumes are modified.


of the resulting solutions. While other researchers

(Daust and Nelson, 1993; Yoshimoto and Brodie,

1994; Barrett et al., 1998) have also shown that the

length of the green-up constraint is ®nancially impor-

tant, they do so at much longer temporal scales than

are required by the AF&PA SFI. To reduce the length

of the AF&PA green-up constraint will require the

adoption of intensive forest management techniques

(chemical site preparation, herbaceous weed control,

etc.). From this data set, the increase in PNW repre-

sents only 5±10% of the cost of the average herbicide

treatment in the southern United States (Dubois et al.,

1997). The use of intensive forest management

techniques cannot be justi®ed solely based on the

economic gain that results from a reduction in the

green-up constraint. However, many ®rms in the SE

region are currently using some intensive management

techniques and may require only a marginal increase

in expense to achieve the growth rate that would allow

a reduction of the green-up constraint from 3 to 2

years. Others may have to adopt a full suite of

intensive practices. We recommend that both forest

and stand level analysis should be completed when

evaluating the use of intensive forest management

practices.

We have also shown, at least for one forested area

and ownership in the southeastern United States, that

the maximum opening size assumed does matter.

Variations in the distribution of forest conditions

and the spatial arrangement of the age classes of other

forests may result in different conclusions, but larger

maximum opening sizes should allow more ¯exibility

in the spatial arrangement and timing of harvests. If

forest management organizations are in a position to

develop ¯exible forest policies, such as the maximum

allowable clearcut size, they should examine the costs

and bene®ts of various green-up times as well as

varying the maximum size of forest openings.

The impact of the green-up constraint on the volume

harvest was twofold. First, the products that are

derived from longer rotations, such as sawlogs and

chip-and-saw logs, did not meet the target goals that

we developed in our 30-year strategic plan. Second, a

surplus of pulpwood volume would be produced.

Because the area of older forest stands is limited at

the beginning of the planning horizon, the adjacency

constraint prevents harvesting them at the time indi-

cated by the strategic plan. Thus, stands younger than

desirable will be harvested in order to meet the overall

volume goals of the forest plan, yet they will not be old

enough to produce the desired mix of sawlog or chip-

and-saw log volume.

Sensitivity analysis shows that an increase in price

or yield will further reduce the economic incentive for

using intensive management to reduce green-up time

requirements. However, as prices decrease or the

yields do not meet their expected value, the incentive

to use intensive forest management practices to reduce

the greenup constraint can be justi®ed, as the PNW

differences for this analysis come closer to the cost of

herbaceous weed control.

Organizations that attempt to match forest harvest

scheduling to the needs of wood processing facilities

may need to incorporate the required green-up con-

straints into their planning process if they are to

accurately anticipate the amount and types of products

that will be available. With regard to the heuristic

technique we used to generate solutions to these forest

planning problems, we feel that the hybrid tabu

search-genetic algorithm method can produce better

results than a traditional tabu search technique,

because it allows for both an intensi®cation and a

diversi®cation in the search process, and because it

uses a genetic algorithm to combine local optimal

solutions. We recommend that others developing tabu

search applications should consider combining multi-

ple search strategies into heuristic harvest scheduling

models and move beyond the basic approaches heur-

istics offer.

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The economic impact of green-up constraints in the southeastern United States

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