Optimal decisions for salvage logging after wildfires

Abstract

Strategic, tactical, and operational harvesting plans for the forestry and logging industry have been widely studied for more than 60 years. Many different settings and specific constraints due to legal, environmental, and operational requirements have been modeled, improving the performance of the harvesting process significantly.

During the summer of 2017, Chile suffered from the most massive wildfires in its history, affecting almost half a million hectares, of which nearly half were forests owned by medium and small forestry companies. Some of the stands were burned by intense crown fires, which always spread fast, that burned the foliage and outer layer of the bark but left standing dead trees that could be salvage harvested before insect and decay processes rendered them unusable for commercial purposes. Unlike the typical operational programming models studied in the past, in this setting, companies can make insurance claims on part or all of the burnt forest, whereas the rest of the forest needs to be harvested before it loses its value. This problem is known as the salvage logging problem. The issue also has an important social component when considering medium and small forestry and logging companies: most of their personnel come from local communities, which have already been affected by the fires. Harvesting part of the remaining forest can allow them to keep their jobs longer and, hopefully, leave the company in a better financial situation if the harvesting areas are correctly selected.

In this work, we present a novel mixed-integer optimization-based approach to support salvage logging decisions, which helps in the configuration of operational-level harvesting and workforce assignment plan. Our model takes into account the payment from an insurance claim as well as future income from harvesting the remaining trees. The model also computes an optimal assignment of personnel to the different activities required. The objective is to improve the cash position of the company by the end of the harvest and ensure that the company is paying all its liabilities and maintaining personnel. We show how our model performs compared to the current decisions made by medium and small-sized forestry companies, and we study the specific case of a small forestry company located in Cauquenes, Chile, which used our model to decide its course of action.

Full text

Optimal decisions for salvage logging after wildfires
Gianluca Baselli, Felipe Contreras, Mat´ıas Lillo, Magdalena Mar´ın, Rodrigo A. Carrasco∗
Faculty of Engineering and Sciences, Universidad Adolfo Ib´a˜nez, Santiago, Chile
Abstract
Strategic, tactical, and operational harvesting plans for the forestry and logging industry have been
widely studied for more than 60 years. Many different settings and specific constraints due to legal,
environmental, and operational requirements have been modeled, improving the performance of the
harvesting process significantly.
During the summer of 2017, Chile suffered from the most massive wildfires in its history, affecting
almost half a million hectares, of which nearly half were forests owned by medium and small forestry
companies. Some of the stands were burned by intense crown fires, which always spread fast, that
burned the foliage and outer layer of the bark but left standing dead trees that could be salvage
harvested before insect and decay processes rendered them unusable for commercial purposes. Unlike
the typical operational programming models studied in the past, in this setting, companies can
make insurance claims on part or all of the burnt forest, whereas the rest of the forest needs to be
harvested before it loses its value. This problem is known as the salvage logging problem. The issue
also has an important social component when considering medium and small forestry and logging
companies: most of their personnel come from local communities, which have already been affected
by the fires. Harvesting part of the remaining forest can allow them to keep their jobs longer and,
hopefully, leave the company in a better financial situation if the harvesting areas are correctly
selected.
In this work, we present a novel mixed-integer optimization-based approach to support salvage
logging decisions, which helps in the configuration of an operational-level harvesting and workforce
assignment plan. Our model takes into account the payment from an insurance claim as well as
future income from harvesting the remaining trees. The model also computes an optimal assignment
of personnel to the different activities required. The objective is to improve the cash position of
the company by the end of the harvest and ensure that the company is paying all its liabilities and
maintaining personnel. We show how our model performs compared to the current decisions made
by medium and small-sized forestry companies, and we study the specific case of a small forestry
company located in Cauquenes, Chile, which used our model to decide its course of action.
Keywords: salvage logging, forest harvesting, wildfires, workforce allocation
∗Corresponding author
Email addresses: gbaselli@alumnos.uai.cl (Gianluca Baselli), felcontreras@alumnos.uai.cl (Felipe
Contreras), malillo@alumnos.uai.cl (Mat´ıas Lillo), magmarin@alumnos.uai.cl (Magdalena Mar´ın), rax@uai.cl
(Rodrigo A. Carrasco)
Final version available at https://doi.org/10.1016/j.omega.2019.06.002
2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
http://creativecommons.
org/licenses/by-nc-nd/4.0/
Preprint submitted to Omega, v.3.0(190607113034) Friday 7th June, 2019

1. Introduction
The forestry industry is one of the most important industries in Chile. In 2016, it represented
2.1% of the annual GDP and 8.7% of Chilean exports, being most common in the southern regions of
the country [
7
]. Among the forestry companies in the country, there are more than 1,400 small and
medium-sized companies (according to the Chilean Income Tax System, small and medium-sized
companies are those with revenues between US 99,000 and US 4,000,000). For these companies,
developing optimal production plans is of great relevance since doing so allows them to efficiently
use their resources to compete with much larger companies.
Between January and February of 2017, the most significant wildfires in Chilean history took
place in the southern part of the country, burning 467,537 hectares of urban and rural zones in over
six geographical regions [
6
]. In some days, there were more than 100 active wildfires simultaneously,
overwhelming the response capacity available. Within the affected areas, it was common to see
forests from both large and small forestry companies. In particular, 227,627 hectares of insignis pine
(Pinus radiata) forests burned in these fires, critically impacting the affected area’s flora and fauna.
These fires also had a strong economic effect in the forestry industry, which reported more than
USD 370 million in losses for both the government and private companies [
6
]. These fires had a
profound impact on the affected regions: forestry companies hire mostly local personnel, which now
not only had their homes and towns affected by the flames, but also the companies they worked for
had no work for them anymore.
Due to these awful circumstances, forestry companies had to change their course of action to use
their remaining resources efficiently after the wildfires. In many cases, due to high winds, crown fires
and high-intensity surface fires affected the forest. Those fires consumed much of the foliage and
outer layer of the bark of the trees and left standing dead trees that could be salvage harvested before
insect and decay processes rendered them unusable for commercial purposes. The complication is
that there was a limited time to do so since, after about 12 months, the wood might start to lose its
value due to stains or decomposition. What makes the problem seemingly straightforward is that
most companies had fire insurance. Hence, the decision was straightforward: make insurance claims,
and move on. However, this course of action implies that there is no more work for the company’s
workforce, even though some of the trees could still be harvested. If the amount of wood is large
enough, harvesting the remaining trees can provide a better future cash position compared to only
processing the insurance claims, making the decision more complicated. Now, companies need to
decide how much of the forest plantation will be compensated by the insurance company and what
to harvest, if anything. Furthermore, companies also need to allocate their personnel correctly and
decide what kind of work will they do: which squads will harvest, which will manage the sawmills,
and to which sawmill to send the harvested trees to. In this setting, making an optimal operational
harvesting schedule is greatly relevant and time-sensitive.
It is important to note one additional difficulty with using insurance claims in the Chilean
setting. First, the deductibles for these types of insurance policies are between 10% and 25% of
the commercial value of the total forest insured. This implies, in some cases, depending on the
policy, that at least 10% of the forest must have suffered from the fires to make the insurance claim
helpful. Furthermore, such claims are time-sensitive since companies have only four weeks to make
them, and the payment depends on the duration of the fire. If the fire lasts less than 72 hours, the
insurance company pays the commercial value of the trees before the fire. If the fire lasts for more
than 72 hours, the forest is assessed by the insurance company personnel, and a new value will be
determined, which can be significantly smaller than the former value [8].
Given the difficult situation in which forestry companies are left, the standard course of action
after wildfires for most of these companies is to collect the compensation for the entire forest. It
2

is the easiest and fastest method to recover some of the company’s value. However, as was the
case in 2017, wildfires can affect the forest plantation by only burning the tree bark, thus leaving
in each tree a considerable amount of wood available for harvesting and commercialization. This
available wood could return a more substantial profit than the payment of the insurance claim.
Hence, forestry companies need, in a brief amount of time, an operational program to salvage as
much wood as possible, if economically viable, to sell it while deciding what sections of the forest,
called forest stands, to claim to the insurance company.
Inspired by this problem, we developed an optimization model that helped companies to efficiently
make these decisions with the current information they had. In this work, we present the resulting
mixed-integer optimization approach used, which computes an optimal harvesting plan and workforce
assignment for the previous problem, named the salvage logging problem. Our objective is to help
the forestry company take the right set of decisions to maximize its final cash flow position and
limit the need for layoffs or at least provide the workers with time to find new jobs.
1.1. Previous Work
Operations research (OR) tools have been applied to forestry-related problems since the early
1960s [
13
]. Since then, OR has been used in a plethora of issues and challenges that are continually
emerging, whether by searching for efficiency within the industry or by environmental and social
pressures [
29
]. In particular, OR has been very successful in defining management strategies for
different time horizons.
Strategic forest management has been studied for a long time. From the operations research
perspective, it was first tackled in [15], where the authors addressed the construction of long-term
plans for forest management, which include investments, harvesting, road construction, and forest
growth [
11
,
20
,
28
]. A description of the main problems in forestry and the current approaches to
solving them is available in [
2
]. Tactical forest planning deals with shorter time frames and includes
supply-chain decisions and workforce assignment [
4
,
5
,
14
,
16
,
17
,
31
]. Operational planning involves
the day-to-day harvesting decisions and allocation of personnel. This is the setting of our problem
since we are interested in defining a weekly operation for salvage logging. For this short-term plan,
researchers have focused mostly on harvesting decisions, i.e., when to harvest each of the forest stands
(the minimum unit of contiguous trees considered for collection) [
12
,
21
,
25
,
26
]. Environmental
concerns have had a significant impact on these decisions and models, adding additional constraints
to the problems due to new regulations [
3
,
23
]. Although workforce assignment is considered
in some of these works, to the best of our knowledge, no models deal specifically with postfire
harvesting, where we must include that, after some time, the value diminishes due to carbon stains
and, eventually, the decomposition of the wood.
When considering wildfires, researchers have usually focused their attention on the environmental
effects of these fires, such as soil fertility damage and the difficulty for animal species to reappear
[
22
], or on providing procedures and precautions that should be taken to avoid massive damage
[
27
]. From an operations research standpoint, the main topic that researchers have addressed is how
to plan the forest harvest to prevent wildfires [
1
,
2
,
18
,
24
] and how to deal with the actual fires
[
10
,
19
]. Only the work of Martell [
18
], who extended the stochastic regeneration approach in [
32
]
to include post-fire salvage value in a stand-level model, addresses the topic of postfire effects in
forest value. To the best of our knowledge, postfire salvage harvesting has not been addressed.
Salvage logging problems have been addressed from a supply-chain point of view [
9
,
30
]. Even
though these papers address the need of salvage logging, their focus is centered on environmental
concerns, considering long-term forest regeneration and ecological survival. To the best of our
knowledge, no work has been done that addresses contingency plans that focus on the operational
programming of forestry companies, nor has any work addressed the social impact on company
3

workers after wildfires. Although fire management is one of the highlighted problems given in [
29
],
postfire harvesting has not been addressed.
It is important to note that none of the previous work considers the use of financial instruments,
which allow for the management of the company’s cash flow, by receiving financial income at the
same time as sales revenue to deal with liabilities. We are not aware of any work that addresses this
issue, which is relevant to the problem we describe in this work.
1.2. Our Contributions
The main contribution of this work is to present a novel mixed-integer optimization model that
synchronizes both personnel allocation and postfire harvesting in forestry. Due to the social impact
that wildfires provoke, this model incorporates social awareness by including the cost of maintaining
the workforce and taking advantage of such labor to harvest selected forest stands. Thus, not firing
the current personnel is a hard constraint.
Our model determines the optimal set of decisions on which parts of the forest to cover through
insurance claims and which forest stands to harvest, together with how to allocate personnel correctly.
We also incorporate a financial model to manage the cash flow at each time step and thus improve
the company’s future wealth and match income and liabilities at each time step. To the best of
our knowledge, this problem has not been addressed before in the literature and has become very
relevant due to the wildfires that have occurred in other parts of the world.
As an additional contribution, we have analyzed the performance of our model by using real
data from Forestal Hueicolla, a small-sized forestry company located in Cauquenes, in southern
Chile, which was severely affected by the fire. This company provided historical data on inventories
and sales as well as on the performance of its workers and of the sawmill companies with which it
works. Furthermore, the use of our model improved the company’s financial position significantly
and was used by the company to decide what proportion of each forest stand to make insurance
claims for (if any) and determine the allocation of some of its workers.
The rest of this paper is organized as follows. Section 2explains the different concepts used
in the forestry industry and describes in detail the problem tackled through this work. Section 3
presents a case study with the experimental results of using our model at Forestal Hueicolla. Finally,
Section 4describes our conclusions and the future lines of research that are left open.
2. Problem Formulation
In this section, we describe the specific setting for our problem and the model used to compute
the optimal decisions for the salvage logging problem.
The main difficulty observed in medium to small forestry and logging companies is the lack of
operational harvesting programs that allow them to decide quickly and efficiently what procedures
to follow to diminish the economic and social impact of the wildfires. The quickest solution, which
is chosen by the majority of the forestry companies, is to collect the insurance compensation of the
whole forest controlled by the company. Even though it is a feasible option, there are many more
factors that need to be evaluated. For example, in Chile, the expected returns of the insurance
payments are gravely affected if the fires last more than 72 hours. Another aspect to consider is the
effect it has on the company’s workforce. Since the insurance company will deal with managing
the claimed forest, the company’s workforce is paralyzed, which may cause worker dismissals. This
not only has an adverse effect on the forestry’s economy but also a considerable social impact on
the region. Finally, as mentioned previously, the damage done by the fires sometimes only affects
the tree bark, keeping part of the trees’ commercial value intact. This opens an opportunity of
maintaining or even improving the future cash position of the company by harvesting the forest
with the current workers, instead of claiming the insurance payments on the whole forest.
4

The general setting we considered is as follows. We consider a medium or small forestry company,
which has a forest plantation of up to 500 hectares, divided into small forest stands. Each forest
stand has its own specific characteristics such as how steep the land is, its soil acidity, the age of the
trees, and the particular amount of wood available for harvest, among others. We first assume that
there is a good estimation of the amount of wood available on each forest stand after the wildfires.
We show, in our case study, the effect of errors in this parameter over the optimal allocation. We
define a squad to be the basic personnel unit to harvest a forest stand or complete any other task.
In our case study, each squad is made up of up to 3 workers. Since there might be more than one
squad working on a specific task, we also need to define teams of squads that will be assigned to a
specific job.
The overall production process has three main steps: harvesting, which includes cutting the trees
of a designated forest stand; then moving all the wood logs from the stands to the sawmills; and,
finally, the sawmilling process, which consists of producing the final products that will be sold, such
as wooden posts or wood planks. Regarding the workforce, the company has its personnel, which
we call internal squads, who are multiskilled and thus able to do harvesting or sawmilling activities.
These squads have a legal contract with a fixed salary and need to be grouped and assigned to tackle
the several tasks available (such as managing the sawmills or chopping down trees). The company
can also work with external teams, who work for variable fees, which depend on their production
rate in the assigned task. Due to this option, one of the challenges is workforce allocation.
Furthermore, there are also precedence constraints in the tasks since, to start sawmilling, it is
necessary to have the harvested wood logs available. Hence, the company needs to decide how to
allocate its internal squads, as well as external ones, and define a harvesting plan for the forest
stands, making sure all operational constraints are satisfied. This plan includes the option of making
insurance claims over some part or all of each forest stand at the beginning and defining how to
manage the cash obtained in each week through low-risk financial instruments. For the related cash
position problem, we consider that the company has access to three different financial instruments:
commercial papers with 30-, 60-, and 90-day maturity at a fixed rate. These financial instruments
can be useful to hedge for future liabilities (mainly workforce salaries), which are known in advance.
2.1. Parameters and Decision Variables
We use the following notation for the parameters in our optimization problem:
I: set of forest stands.
G: set of worker squads, where Giare internal squads and Geare the external ones.
J
: set of work teams formed as a result of the combination of squads, where
Ji
is the set
of teams with internal squads and
Je
is the set of teams with external squads. Team 0 is
considered the insurance company.
Ek: set of squads contained in team k.
F
: set of sawmills, where
Fi
are the ones operated by the internal squad, whereas
Fe
are
external squads rented and managed by external personnel.
T: number of weeks after which the unharvested timber has no value.
R1: interest rate for a time deposit with a 30-day maturity [%].
R2: interest rate for a time deposit with a 60-day maturity [%].
5

R3: interest rate for a time deposit with a 90-day maturity [%].
Pv: wood log selling price [ /inch].
Pw: wooden post selling price [ /unit].
Vi: wood logs available in stand i[unit/m3].
Wi: wooden posts available in stand i[units/m3].
Cv: wood log operational cost for an external squad [ /unit].
Cw: wooden post operational cost for an external squad [ /unit].
PI
i: insurance payment for forest stand i[ /m3].
Rij : squad j’s estimated production rate in stand i[m3/week].
Lt: liabilities (fixed costs at time t– these are the internal squads’ salaries) [ ].
Ii0: initial wood inventory in stand i[m3].
Cm: cost for moving wood logs from a stand to a sawmill [ /m3].
Kl: maximum input capacity of sawmill l[m3].
Ql: performance of sawmill l[inches/m3].
Cs
l: variable cost of sawmill lper inch [ /inch].
We use the following decision variables:
Continuous Variables
xijt : amount of harvested wood from stand iby team jat time t[m3].
blt: amount of wood that comes into sawmill lat time t[m3].
st: inventory in transit on time t[m3].
ut: amount of money to be invested at a time deposit with a 30-day maturity at time t[ ].
vt: amount of money to be invested at a time deposit with a 60-day maturity at time t[ ].
wt: amount of money to be invested at a time deposit with a 90-day maturity at time t[ ].
fh
t: net cash at time tassociated with the harvesting process [ ].
fm
t: net cash at time tin wood transportation from forest stands to sawmills [ ].
fs
t: net cash at time t, which includes all income and costs during the sawmill process [ ].
ft: net cash flow at time t[ ].
ct: total cash position at time t[ ].
Binary Variables
6

zijt is 1 if squad jharvests stand iat time t, and 0 otherwise.
αlt is 1 if sawmill loperates during time t, and 0 otherwise.
βjlt is 1 if squad j, of only internal workers, works on sawmill lat time t, and 0 otherwise.
yit is 1 if forest stand ihas no wood left to harvest at time t, and 0 otherwise.
2.2. Objective Function
Since we want to maximize the company’s cash position (cash on hand) by the end of the
harvesting period, the cost function we want to maximize is as follows:
max cT(1)
2.3. Problem Constraints
The following are the operational constraints required by the problem.
Squad: A squad cannot work in more than one forest stand at a given time, and hence,
X
i
X
j∈Ek
zijt ≤1,∀k∈Ge,∀t. (2)
Additionally, for internal squads, we need to add the following:
X
i
X
j∈Ek
zijt +X
l∈Fi
X
j∈Ek
βjlt ≤1,∀k∈Gi,∀t. (3)
Teams: One forest stand may only be harvested by one team, and thus,
X
j∈Je
X
i
zijt ≤1,∀t. (4)
Additionally, for every team jwith only internal squads,
X
j∈Ji
X
l∈Fi
βjlt +X
j∈Ji
X
i
zijt ≤1,∀t. (5)
Harvesting forest stands
: If one forest stand starts being harvested, it will continue to be
until harvesting is completed, i.e., no preemption is allowed. Thus,
X
j
zij(t+1) +yit ≥X
j
zijt ,∀i, ∀t. (6)
For every forest stand, harvesting must stop when there is no more inventory left to harvest.
yi(t+1) ≥yit ∀i, ∀t. (7)
A squad will be available once the forest stand has no more inventory left to harvest.
Ii0−X
j
t−1
X
u=0
xiju ≤Ii0(1 −yit )∀i, ∀t. (8)
7

Squad capacity
: The wood harvested during each period
t
in a forest stand
i
may not be
greater than the squad’s production capacity, and thus,
xijt ≤Rij ,∀i, ∀j, ∀t. (9)
Consistency
: Connect binary and continuous decision variables, where
M
is a large constant.
This is achieved by the following constraints:
xijt ≤M·zij t,∀i, ∀j, ∀t. (10)
Harvesting and initial inventory
: The amount of wood harvested from each stand must
be less or equal to the initial inventory when the decision is to be made. Hence,
X
j
X
t
xijt ≤Ii0,∀i. (11)
Unavailability of forest stands
: Some forest stands are not reachable during parts of the
year. This is because they are located on steep hill slopes, which generally are not accessible
during the rainy season; hence,
xijt = 0,∀jif i∈ {steep stands}, t ∈ {rainy season}.(12)
Inventory in transit
: We create an auxiliary variable named inventory in transit as the
amount of wood harvested but not yet sawmilled. The state variable is defined as
st=st−1+X
i
X
j
xijt −X
l
blt,∀t≥1,(13)
st≥0,∀t. (14)
Sawmilling only what was harvested
: The amount of wood that goes into sawmills must
be less or equal to the amount of wood harvested during period
t
, plus inventory in transit.
Hence,
X
l
blt ≤st+X
i
X
j
xijt ,∀t. (15)
Sawmill capacity
: The amount of wood that goes into sawmills must be less than or equal
to their input capacity, and thus,
blt ≤Kl·αlt,∀t, ∀l∈Fi,(16)
blt ≤Kl,∀t, ∀l∈Fe.(17)
Internal sawmill operation
: Binary decision variables are related to the operation or
shutting down of internal sawmills. This is achieved by the following constraints:
αlt ≤X
j
βjlt ,∀l, t. (18)
Net cash from the harvesting process
: The income comes from wooden post sales,
8

whereas the costs are the variable salary of external squads for their harvesting.
fh
t=X
i
X
j
xijt ·[(Pw·Wi)−(Cv·Vi+Cw·Wi)],∀t. (19)
Net cash from moving logs
: The only cost is related to the logs dispatched from forest
stands to sawmills.
fm
t=−Cm·X
l
blt,∀t. (20)
Net cash from the sawmilling process
: The income of the sawmilling process is the
wood sales by inch, whereas the costs are external squads’ salary for their performance in the
sawmilling process.
fs
t=X
l
blt ·Ql·(Pv−Cs
l),∀t. (21)
Net cash flow
: The net cash flow for a forestry company is the amount of money invested
in time deposits with different maturities, the income from previous time deposits, and the
liabilities payed, which are the internal squads’ salaries.
ft= (1 + R1)ut−4+ (1 + R2)vt−8+ (1 + R3)wt−12 −ut−vt−wt−Lt,∀i, j, t. (22)
Total cash position
: The forestry company must always have a positive cash position to
fulfill all its liabilities and pay its squad’s salary. The company’s cash position at
t
= 0
represents the income from collecting compensation from the insurance company.
ct=ct−1+fh
t+fm
t+fs
t+ft,∀t, (23)
c0=X
i
xi00 ·PI
i,(24)
Final position in commercial papers
: The forestry company must not have any invested
money after the considered time horizon.
T
X
t=T−3
ut= 0,
T
X
t=T−7
vt= 0,
T
X
t=T−11
wt= 0.(25)
All variables must be positive or binary.
xijt ≥0, zij t ∈ {0,1}, αijt ∈ {0,1},∀i, j, t, (26)
yit ∈ {0,1},∀i, t, (27)
βjlt ∈ {0,1},∀j, l, t, (28)
blt ≥0,∀l, t, (29)
st≥0, ct≥0, ut≥0, vt≥0, wt≥0,∀t, (30)
fh
t≥0, f m
t≥0, f s
t≥0, ft≥0,∀t. (31)
9

Figure 1: Remains of the forest.
3. Experimental Results and Case Study
We study the performance of our model using, as a test case, a small forestry company in the
south of Chile, called Forestal Hueicolla, located in Cauquenes in the Maule Region. The company
has 152 hectares of insignis pine trees (pinus radiata), separated into 16 different forest stands. The
company has two internal squads and three commissioned squads (external), owns two sawmills,
and four external banks are available, which work by commission.
The impact after the “firestorm” in early 2017 was substantial, generating enormous losses
for the company, with approximately 95% of the company’s forest plantation burnt. Due to the
duration of the fires, the insurance value of the forest stands postfire fell to 44% of their original
value per hectare, which, in some stands, represents less than the minimum expected return per
hectare that the company obtains by harvesting the land. Figure 1shows the forest remains after
the fires died out a few weeks later.
Because of this drop in insurance payments, it became clear that making insurance claims for
the whole forest might not be the optimal decision. Furthermore, the company owner was interested
in keeping his internal squads for as long as possible since their own houses were affected by the
fires, and they needed the work. This situation is the social component that was captured by adding
the cost of the workers as liabilities in the model and having them as hard constraints. Hueicolla’s
management team was interested in computing an optimal plan for the next 24 months that helped
it decide which forest stands to make insurance claims on and which to harvest. The plan had a
longer time horizon since the team had secured a buyer for its wood, even though the product was
stained. Furthermore, the management team needed to set up teams of internal and external squads
and assign them to the different required tasks, as well as define how to manage cash to ensure the
company can pay all the required salaries.
As a first step, we gathered all the information required in our model. Most of the parameters are
straightforward from the company’s information such as the number of squads, the location of forest
stands, and production rates and capacities, which were estimated from two years of historical data.
The selling prices of products were also predefined by the contracts the company has with its buyers,
whereas the costs are defined in the contracts with workers and external companies. The return rate
of the financial instruments comes from banks in the area and the insurance payments from the
insurance contract and the assessment made by the insurance company. With the help of a forest
engineer, we estimated the amount of wood available in each of the forest stands. This estimation
was done by sampling tree sizes from each forest stand and using past volumes to estimate the
current initial inventory. All this information was compiled in Excel worksheets that served as an
10

input for the model.
We implemented the optimization problem (1)-(31) in Python 3.5, using Gurobi 7.0.2 as an
optimization engine and optimization modeling library. The problem information from Forestal
Hueicolla was loaded directly from the company’s spreadsheets to compute all the required parameters.
Then, we used Gurobi to solve the optimization problem and compute the optimal solution in a
Quad Core i7 processor, with 16 Gb RAM. We limited the solver time to five minutes and extracted
the best feasible solution found within that limit.
The solution obtained from the solver was exported in two ways: an Excel workbook, with
sheets showing a harvesting schedule, the personnel assignment, and the cash flow management,
and a color-coded map of the forest and each forest stand, which could be opened in Google Earth,
indicating what action to take for each forest stand. The resulting map for Hueicolla’s instance
is shown in Figure 2, where each color indicates the decision to be made on that specific forest
stand. This output was extremely valuable for the company owner and the operations team since it
allowed for a much better understanding of the solution, as well as for detecting possible problems
and improvement opportunities. The solver required the whole 5 minutes to compute a solution,
after which we obtained a feasible solution with a 3.8% gap with respect to the best lower bound
available at that time.
To evaluate the performance of our model’s recommendation, which we denote as SLMIP, we
compared the solution to two other common policies. The first one, which was considered by most
small forestry companies, was making an insurance claim over the whole forest that was burned.
We call this the ful l insurance policy.
The second option, which was being considered by Hueicolla after the company realized the
steep drop in insurance payments, was only to harvest the older forest stands, which had trees of
more than ten years old. These stands covered approximately 17% of the forest. The company also
decided not to use its sawmills so the internal squads could focus on the logging process, whereas
the external sawmills would perform the sawmilling. The rationale for this decision was that the
older forest stands were the ones that could provide the most significant income and that, by using
internal workers, the company could harvest all the selected forest stands. Initially, the company
wanted an optimization model that could determine the optimal harvesting schedule under this
setting, and the company was not considering any financial instruments to hedge in this setting.
We call this the partial insurance policy.
Due to privacy concerns, we normalize the cash position at time
T
= 24 as 100.00 for the full
insurance policy, which makes an insurance claim over the whole forest and then pays, from there,
the salaries of all the internal workers during the whole period. The partial insurance policy showed
that the owner of Hueicolla had the right intuition: harvesting the oldest forest stands improved
the final cash position to 214.48.
The SLMIP solution is presented in Figure 2and Figure 3. The cash position in this approach is
improved to 255.00, which is %155 more than the full insurance policy and an 18.89% increase over
the partial insurance policy. This course of action determines a harvesting schedule and workforce
assignment, which assigns 26% of Hueicolla’s forest stands for harvesting and the rest to make
insurance claims. Furthermore, given the cost of the external workforce, the optimization model
recommended to only use the internal workforce for harvesting, and thus, there was only one team
of internal workers doing this type of work.
The resulting harvesting sequence is displayed in Figure 3. Since there are no changes in costs
or selling prices for the period of study, the order of the resulting schedule does not change the
total income. Instead, the main reason for this schedule was the operational constraints: there were
several forest stands on steep parts of the plantation, and thus, these stands could only be harvested
during the dry season.
11

Figure 2: Map output: color-coded map indicating which forest stands should be harvested and for which to make an
insurance claim.
The solution also uses financial instruments to slightly enhance the company’s future cash
position. Considering the final cash position, the income related to the financial instruments
represents only 0.4% of the total earnings in our model’s solution, whereas 28.97% of this income
is related to the insurance company’s compensation, with the remaining 70.63% given by the
operational revenue. The main contribution of these instruments was to match the liabilities and
income for each week, storing income in months with larger production and using the insurance
payments to pay future salaries. Without these instruments in the mode, such matching would not
have been possible.
Beyond the financial aspect, there are also social implications for this hard liability constraint.
In our solution, as well as in the partial insurance policy, workers keep their jobs during the whole
harvesting period, after which the company would be able to put them in other recovery processes,
or they could have found new jobs.
Our literature review identifies that the operational harvesting models are, in general, sensitive
to the wood volume estimated for each forest stand. In our case study, we obtained these values
Figure 3: Harvesting schedule for every two weeks.
12

by sampling the different forest stands, which could lead to errors in the actual value. Hence, we
performed a thorough sensitivity analysis over this parameter to test the robustness of the solution.
For this analysis, we changed the amount of wood available in each forest stand separately and
computed up to which values the original assignment was still optimal. The results of the sensitivity
analysis are shown in Figure 4.
In this plot, each forest stand indicates the amount of available wood that was estimated (in
m3
), and they are color-coded and ordered from the lowest (stand 14) to highest (stand 13) amount
of wood per forest stand area (i.e., wood density). The dashed boxes indicate the forest stands
for which insurance claims are made, whereas the solid colors indicate that the company harvests
these stands. The whiskers on each bar indicate the upper and lower limit on the amount of wood
available such that the original assignment would still be optimal.
While doing this analysis, we realized that there is a strong relationship between the wood density
on a forest stand and the assignment decision. In a similar fashion to what the forestry company
owner wanted to do, the optimization model selected high-density forest stands for harvesting and
the lower ones for making insurance claims. The reason why stand six is selected for harvesting
but stand seven is claimed to the insurance company, even though it has a higher density, is due to
operational constraints. Forest stand seven is in a steep part of the forest, so it was not feasible to
harvest it in the time available during the dry season.
We have also added a box around the stands that have what we call a critical density, which, in
this case, is of 244.26 m3per hectare.
All stands with less than this critical density (stands 14, 16, 10, 8, 9, and 12) go directly to the
insurance company. For these forest stands, the estimation errors need to be very large (at least
+45%) to be considered for harvesting.
On the other hand, the company will harvest all the forest stands with a higher density than the
critical one, that is, in this case, stands 11, 15, and 13. In this instance, the estimation errors need
to be at least -10% to change the current solution. There is also an upper limit of the estimation,
which is of at least +10%, to change the optimal solution. The reason for this upper limit is that
above it, the available teams are not able to harvest all the forest stands within the time horizon. If
the real amount of wood available in those stands is larger than this upper limit, the least dense
forest stands that were selected for harvesting should go to the insurance company.
For the forest stands within the box (i.e., close to the critical density), the whiskers are very
small. Since all these forest stands have a very similar density, a small error in one would imply that
Figure 4: Sensitivity analysis: decision making under uncertainty of initial inventory on each forest stand with
color-coded density analysis.
13

the optimal decision would change for that forest stand (or another from the box). For example, if
stand seven has 4.3% more wood than other stands, it would be better to harvest it, and stand 6
would go to the insurance company. Hence, if the company wants to make a more certain decision,
these are the stands where the company needs to invest more time in to refine the estimation and
ensure robustness in the solution.
When considering other parameters for the sensitivity analysis, the results are even better:
insurance payments can vary up to
±
30%, internal sawmills’ operational costs can vary
±
20%, and
the harvesting cost may vary between
−
40% and +30% while still resulting in the same optimal
assignment decisions.
4. Conclusions and Future Work
In this work, we have presented a model to tackle the salvage logging problem, which consists
of defining the operational harvesting schedule, the workforce assignment, and the cash flow
management. To the best of our knowledge, this is the first time this problem is addressed in the
operations research literature. Our model can be solved in a reasonable time on a commercial
computer, improving the final cash position significantly when compared to the policies regularly
considered by forestry companies. More importantly, since workforce salary is considered a hard
constraint, we are not firing the company’s personnel and extend the period where they receive
their income and can be reassigned to other recovery efforts or find a new job. This is of particular
importance for large fires such as those that happened in Chile in 2017 and that have regretfully
happened in other parts of the world recently since these fires not only affect forestry companies
but also burn the houses and towns of the people that work in the forest.
By doing a sensitivity analysis on some of the parameters, we were also able to show that the
obtained solution is robust to the most uncertain parameter, namely, the initial inventory level
of each forest stand. Furthermore, our model allows the company to identify the initial inventory
thresholds, in terms of wood available by area, for the decision of which forest stands to harvest
and on which ones to make insurance claims. This information can also be used to determine which
forest stands to sample further to improve the estimation of the wood content and, thus, obtain a
solution with less uncertainty. Improving our model by incorporating the uncertainty in the initial
inventory would certainly be a future line of work, resulting in better action plans for forestry
companies.
The obtained solution allowed Forestal Hueicolla to improve its final cash position, keeping
the current internal personnel, and was used by the company to determine which forest stands to
harvest and on which to make insurance claims. Given the improvements obtained, the Asociaci´on
Chilena de Municipalidades (Chilean Association of Municipalities) decided to take this tool and
use it to help other small and medium-sized forestry companies in the future.
Acknowledgments
The authors would like to thank Mr. Max Wachholtz, the team behind his forestry company,
Forestal Hueicolla, and Mr. Eduardo Gallardo, Municipalidad de Chanco’s forest engineer, for the
time invested and for providing the data required for our work.
This research was partially funded by FONDECYT Project 1151098: Production scheduling:
a mathematical programming approach and applications to natural resource management and by
Universidad Adolfo Ib´a˜nez’ Systems Center.
References
[1]
Acuna, M. A., Palma, C. D., Cui, W., Martell, D. L., and Weintraub, A. Integrated
spatial fire and forest management planning. Canadian Journal of Forest Research 40, 12
14

(2010), 2370–2383.
[2]
Bjørndal, T., Herrero, I., Newman, A., Romero, C., and Weintraub, A. Operations
research in the natural resource industry. International Transactions in Operational Research
19, 1-2 (2012), 39–62.
[3]
Boukherroub, T., LeBel, L., and Ruiz, A. A framework for sustainable forest resource
allocation: A Canadian case study. Omega 66 (2017), 224–235.
[4]
Bredstr
¨
om, D., J
¨
onsson, P., and R
¨
onnqvist, M. Annual planning of harvesting resources
in the forest industry. International Transactions in Operational Research 17, 2 (2010), 155–177.
[5]
Chinneck, J., and Moll, R. Processing network models for forest management. Omega 23,
5 (1995), 499–510.
[6] CONAF. Descripcion y efectos “Tormenta de Fuego”. Tech. rep., 2017.
[7] de Agricultura, M., and Forestal, I. Chilean forestry sector 2017.
[8] de Justicia, M. Codigo de comercio.
[9]
de las Heras, J., Moya, D., Vega, J. A., Daskalakou, E., Vallejo, R., Grigoriadis,
N., Tsitsoni, T., Baeza, J., Valdecantos, A., Fern
´
andez, C., Espelta, J., and
Fernandes, P. Pode las Heras, J., Moya, D., Vega, J. A., Daskalakou, E., Vallejo, R.,
Grigoriadis, N., . . . Fernandes, P. (2012). Post-Fire Management of serotinous Pine Forests.
In Post-fire Management and Restoration of Southern European Forests, Managing Forest
Ecosyst. In Post-fire Management and Restoration of Southern European Forests, Managing
Forest Ecosystems. 2012, pp. 121–150.
[10]
Dimopoulou, M., and Giannikos, I. Spatial optimization of resources deployment for forest-
fire management. International Transactions in Operational Research 8 (2001), 523–534.
[11]
Epstein, R., Morales, R., Ser
´
on, J., and Weintraub, A. Use of OR Systems Industries
in the Chilean. Interfaces 29, 1 (1999), 7–29.
[12]
Facultad de Ciencias Forestales, U. d. C. Pinus radiata, Eucalyptus globulus y nitens.
Modelo nacional de simulaci´on. Concepci´on, Chile, 2013.
[13]
Haight, R. G., and Weintraub, A. Models and Systems in Forestry. International
Transactions in Operational Research 10, 5 (2003), 409–411.
[14]
Hausman, W. H., and Sepehri, M. An integrated corporate planning model for forest-based
industries. Omega 13, 1 (1985), 29–38.
[15]
Jones, H. The management of timber and related industries in sweden. Omega 5, 6 (1977),
689–697.
[16]
Karlsson, J., Ronnqvist, M., and Bergstrom, J. Short-term harvest planning including
scheduling of harvest crews. International Transactions in Operational Research 10 (2003),
413–431.
[17]
Kong, J., and R
¨
onnqvist, M. Coordination between strategic forest management and
tactical logistic and production planning in the forestry supply chain. International Transactions
in Operational Research 21, 5 (2014), 703–735.
15

[18]
Martell, D. L. The optimal rotation of a flammable forest stand. Canadian Journal of
Forest Research 10, 1 (mar 1980), 30–34.
[19]
Martell, D. L. Forest Fire Management: Current Practices and New Challenges for
Operational Researchers. 2007.
[20]
Martell, D. L., Gunn, E. A., and Weintraub, A. Forest management challenges for
operational researchers. European Journal of Operational Research 104, 1 (1998), 1–17.
[21] Mazza, R. Managing Forests After Fire. Pacific Northwest Research Station, 15 (2007), 12.
[22]
Nappi, A., St
´
ephane, D., Bujold, F., Chabot, M., Dumont, M.-C., Duval, J.,
Drapeau, P., Gauthier, S., Brais, S., Peltier, J., and Bergeron, I. Harvesting in
Burned Forests - Issues and Orientations for Ecosystem-Based Management. 2011.
[23]
Neto, T., Constantino, M., Martins, I., and Pedroso, J. P. A branch-and-bound
procedure for forest harvest scheduling problems addressing aspects of habitat availability.
International Transactions in Operational Research 20, 5 (2013), 689–709.
[24]
Palma, C. D., Cui, W., Martell, D. L., Robak, D., and Weintraub, A. Assessing the
impact of stand-level harvests on the flammability of forest landscapes. International Journal
of Wildland Fire 16, 5 (2007), 584–592.
[25]
Palma, I., and Troncoso, T. Asignaci´on ´optima de equipos en faenas de cosecha forestal.
Bosque 22, 1 (2001), 65–73.
[26]
Ralston, R., Buongiorno, J., Schulte, B., and Fried, J. Non-linear matrix modeling
of forest growth with permanent plot data: The case of uneven-aged Douglas-fir stands.
International Transactions in Operational Research 10, 10 (2003), 461–482.
[27]
Reszka, P., and Fuentes, A. The great valparaiso fire and fire safety management in chile.
Fire Technology 51, 4 (2015), 753–758.
[28]
R
¨
onnqvist, M. Optimization in forestry. Mathematical Programming 97, 1-2 (2003), 267–284.
[29]
R
¨
onnqvist, M., D’Amours, S., Weintraub, A., Jofre, A., Gunn, E., Haight, R. G.,
Martell, D., Murray, A. T., and Romero, C. Operations research challenges in forestry:
33 open problems. Annals of Operations Research 232, 1 (2015), 11–40.
[30]
Saint-Germain, M., and Greene, D. F. Salvage logging in the boreal and cordilleran
forests of Canada: Integrating industrial and ecological concerns in management plans. Forestry
Chronicle 85, 1 (2009), 120–134.
[31]
Troncoso, J. J., and Garrido, R. A. Forestry production and logistics planning: An
analysis using mixed-integer programming. Forest Policy and Economics 7, 4 (2005), 625–633.
[32]
Wagner, H. M. Principles of operations research with applications to managerial decisions.
1969.
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