A value-added forest management policy reduces the impact of fire on timber production in Canadian boreal forests

Forest Policy and Economics 97 (2018) 21–32

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Forest Policy and Economics journal homepage: www.elsevier.com/locate/forpol

A value-added forest management policy reduces the impact of fire on timber production in Canadian boreal forests

T

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Baburam Rijala, , Frédéric Rauliera, David L. Martellb a b

Centre d'Étude de la Forêt, Faculté de foresterie, de géographie et de géomatique, Université Laval, 2405 rue de la terrasse, Québec G1V 0A6, Canada Faculty of Forestry, University of Toronto, 33 Willcocks Street, Toronto, ON M5S 3B3, Canada

A R T I C LE I N FO

A B S T R A C T

Keywords: Boreal forest Fire Revenue Risk analysis Strategic supply planning

When fire rates are sufficiently high, fire disturbances can have negative impacts on industrial timber supplies. One can mitigate such problems at the strategic level by accounting for potential fire losses in the timber supply planning process by reducing harvest levels to maintain a buffer stock of timber. With a forest planning model based on a timber volume maximizing policy, reducing the harvest level will lead to a reduction in the harvested timber volume and likely, of revenues. One possible solution is to change the policy to increase the value of the wood that is harvested so as to minimize such reductions with less risk. We have evaluated alternative policies for three commercially-managed forests that have different burn rates in northeastern Canada. When compared with a volume-maximization policy, a revenue-maximization policy that considers sustained production and the sale of sawmilling wood products (lumber, chips and sawdust) increased mean revenues by 130% (36–770%) with > 0.90 probability and substantially decreased the area and volume harvested by 27% (11–38%) and 28% (14–36%), respectively. By reducing the harvest volume, the total number of jobs associated with forest operations decreased by 20% (10–27%) but the number of jobs per unit area harvested and volume increased. The policy also increased the harvest age and thereby enhanced the retention of a greater proportion of old-growth stands. Our study indicated that a tighter link between strategic planning and wood product processing helped identify better compromises between harvesting activities and revenues, despite the occurrence of natural disturbances.

1. Introduction Many forest ecosystems, including the boreal forest, which represents the world's second-largest forest biome, coevolved with natural disturbances. Natural disturbance history, together with climate, surficial deposits, drainage and forest successional dynamics, generate a complex mosaic of ecosystems. As a result, the boreal forest is rich in economic (e.g., both timber and non-timber), environmental (carbon sequestration, water regulation, wild flora and fauna) and social resources (e.g., employment and recreation) (Brandt et al., 2013). The Canadian boreal forest represents 32% of forests worldwide and encompasses half of the forests of North America (Schlesinger and Bernhardt, 2013). It contributes 40% of Canada's wood supply (Bogdanski, 2008). Commercial exploitation of wood in Canada increased by 70% from 1970 to 2004. Though harvest levels began to decrease in 2005 and reached the 1970 level (120 Mm3 y−1) in 2009, they resumed their increase and reached 148 Mm3 y−1 in 2013 (Natural Resources Canada, 2015). Consequently, harvesting activities have

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expanded northwards into less productive and fire-susceptible boreal regions (Powers et al., 2013). Harvesting and transportation costs in remote northern forests have made the forest products industry less profitable and more vulnerable to timber supply disruptions caused by natural disturbances (Gauthier et al., 2014). Forest planning consists of a three-step hierarchical process (strategic, tactical and operational steps) with an increasing level of detail and a decreasing time horizon at each step (Davis et al., 2001). The first step, strategic planning, is designed to assess the sustainability of harvesting and silviculture policies and practices over periods of up to one and a half rotations in length (Baskent and Keles, 2005) by forecasting wood supply based on data, models (e.g., stand-level yield curves), and assumptions concerning harvest and regeneration (e.g., succession rules). The objective of such analyses is to devise a forest management strategy that is designed to reduce the likelihood that ecological, social and economic resources are depleted by harvesting activities (Bettinger et al., 2009). At this step, the specific requirements of the forest industry are coarsely and conventionally described by maximizing the

Corresponding author. E-mail address: [email protected] (B. Rijal).

https://doi.org/10.1016/j.forpol.2018.09.002 Received 21 March 2018; Received in revised form 30 August 2018; Accepted 4 September 2018 1389-9341/ © 2018 Elsevier B.V. All rights reserved.

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periods will increase, which will reduce the probability of occurrence of timber supply disruptions caused by fire (Leduc et al., 2015). A change in forest policy from maximizing timber volume to maximizing product value during strategic planning should therefore indirectly help mitigate the impact of fire. In order to examine this, we simulated the application of four different policy models. These policy models maximized: (1) timber harvest volume - a commonly-used planning objective (Davis et al., 2001; Gunn, 2007) in many countries including Canada (BFEC, 2013; Natural Resources Canada, 2015), (2) timber revenue from timber directly sold to the mills (Boychuk and Martell, 1996) and (3 and 4) revenue of primary-processed wood products - a vertically integrated model (Gunn and Rai, 1987; Rijal and Lussier, 2017). We developed timber harvest optimization models to design harvesting plans congruent with each policy. We then developed a landscape simulation model to simulate the implementation of those plans with a replanning process in interaction with fire. We used three forest management units with different mean annual burn rates located in the boreal forest region of Quebec (Canada) and compared the policies prescribed by models in terms of the impact of fire on several performance metrics. We identified risk zones corresponding to a range of outputs of performance metrics occurring with a specified probabilities produced by our simulation models.

harvest of timber volume (Weintraub and Romero, 2006; Gunn, 2007), which can lead to uneconomic harvesting (Gunn, 2007). The ability to account for risk and uncertainty in forest planning requires information which may or may not be available (Eyvindson and Kangas, 2018). Contrary to uncertainty which relates to lack of knowledge, risk is defined as an exposure to quantifiable losses. Risk analysis is a methodology designed to account for unexpected events and depends on the understanding of the potential impacts of a loss in terms of probability and their effects (Gardiner and Quine, 2000). Managers of public forests usually attempt to avoid risks, which implies that they select plans that have a high probability of success, i.e., with a high probability of achieving targeted levels of outcomes (Weber and Milliman, 1997; Savage et al., 2010) (e.g., p ≥0.90). The integration of fire risk in strategic planning has been investigated since the 1980s (van Wagner, 1983), but its inclusion in strategic planning remains uncommon (Hanewinkel et al., 2011). One of the problems is the resulting size and complexity of the planning problems that need to be solved (Bettinger et al., 2009). As a risk mitigation strategy, the inclusion of fire effects in the planning process can result in a reduction of the harvest level (Armstrong, 2004; Savage et al., 2010) which forest managers are reluctant to implement because such reductions immediately affect potential income and regional economic activity (Patriquin et al., 2008; Raulier et al., 2013). Nevertheless, for the last 10 years, interest in applying risk analysis in forest fire management and strategic planning has been steadily growing (Savage et al., 2010, 2011; Miller and Ager, 2013; Gauthier et al., 2014). In Canada, each province is responsible for the management of its forests on public land (Haley and Luckert, 1990). Forest tenure agreements on public land are negotiated in terms of volume in the provinces of Quebec and British Columbia (Rotherham and Armson, 2016). Consequently, timber supply calculations in these two provinces are based on the maximization of timber volume. The maximization of timber volume is still a guiding rule in forest management in many countries including Canada (Davis et al., 2001; Gunn, 2007). The objective of our study was to explore alternative policies with respect to their potential to reduce the impact of fire on timber supply economics through strategic planning. We hypothesized that one possible solution would be to deal with this by focusing on timber that can be used to produce high-value-added products. Increasing the value-added timber harvest is not by itself, a mitigation strategy against fire loss, but it may indirectly contribute to minimizing the loss of product value because it is positively related to log size-based wood quality recovery (Liu and Zhang, 2005). Since the harvested tree size depends on rotation age and longer rotation ages decrease the harvest flow at the forest scale (Cissel et al., 1999), the amount of timber available for harvest in successive

2. Methods 2.1. Study area In order to examine the effects of different fire rates on timber supply and forest sustainability, we selected three forest management units (FMU) that are located in the northern part of the commerciallymanaged forest in the province of Quebec (Canada) (Fig. 1). These three management units are located within the closed black spruce-moss bioclimatic domain (Robitaille and Saucier, 1998), but each has a different fire regime (Chabot et al., 2009; Mansuy et al., 2014), management history, species composition and age structure. Although black spruce (Picea mariana [Mill.] B.S.P.) dominates the forest landscape, jack pine (Pinus banksiana Lamb.) is more abundant in the central part of the study area (FMU 026–65) where the estimated mean annual burn rate during the 20th century was the highest (0.65% y−1, Irulappa Pillai Vijayakumar et al., 2015). Balsam fir (Abies balsamea [L.] Mill.) abundance increases considerably in the eastern part (FMU 094–52), where the historical mean burn rate was the lowest (0.2% y−1, Bouchard et al., 2008). Fig. 1. Study area showing the spruce-moss forest (light grey), and three forest management units (FMUs, dark grey). The bold continuous line bounded polygon is the boreal forest and the doubleline is the northern limit of commercially-managed forests in the province of Quebec (MRNFQ, 2000). The bar plots are the age class distributions of the initial forest condition in the three FMUs (2002–2004).

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Table 1 Total and productive forest area, mean annual burn rate and mean distance to the sawmill for each forest management unit (FMU). FMU

Total Area (km2)

Productive Areaa (km2)

SPF abundanceb (%)

Mean burn rate (% y−1) (1971–2014)

Mean distance (and range) to sawmill (km)

Western (085–51) Central (026–65) Eastern (094–52)

9857 4572 9095

5734 3188 6954

80 92 96

0.137 0.483 0.062

65 (31−120) 162 (131−230) 196 (140–255)

a Area that is producing at least 50 m3 ha−1 of merchantable timber (diameter ≥ 9 cm) over a 150 year planning horizon, with a mean timber stem volume ≥ 50 dm3/tree (Raulier et al., 2013). b SPF denotes spruce, pine and fir cover type.

the harvested volume into lumber, chips and sawdust and each product was sold separately. The 10-year average processing cost of lumber was $106 per thousand board-feet (MBF) (Del Degan Massé, 2010). With an average conversion factor of 4.4 cubic meter of merchantable volume per lumber MBF (Del Degan Massé, 2010), this processing cost is equivalent to $24 m−3 of merchantable volume. Ten years (2004–2013) of selling price data for primary-processed products were obtained from the Quebec Forest Industry Council for lumber ($155 m−3), MFFP for wood chips (Del Degan Massé, 2010 - $52 m−3) and Tembec (Pasturel, 2013) for sawdust ($9 m−3). Lumber, wood chips and sawdust are shipped to different locations. We referenced Montreal as being the closest market from which lumber products can be shipped to national and international destinations. We assumed that wood chips and sawdust are shipped to the closest pulp and paper or panel mill respectively. Transportation mode can vary (truck or rail) depending on mill and market locations and has an impact on the processed-product transportation cost ($0.02 km−1 m−3 for truck and $0.002 km−1 m−3 for train transportation, CPCS, 2013; Laurent et al., 2013). We used a constant discount rate of 4% y−1 (BFEC, 2013) to discount future costs and revenues, and applied it to the middle of each period. In addition to costs and revenues which we used as economic activities in public forests, we evaluated the number of jobs related to forest management and timber processing activities. The three forest management units considered in this study are located on public land and the design of forest management strategies on public land also aims at enhancing the regional employment (MRNFQ, 2009). We therefore used the average number of jobs provided from provincial forest statistics (MFFP, 2015) for the year 2010 as: 4.84 (forest harvesting), 4.11 (lumber processing), 2.23 (chip or sawdust processing) jobs per million dollars of gross revenues (sale of timber or of a processed product). The total number of jobs in a single mill was equated to the sum of the number of jobs required to process the three products, assuming a single mill would process all three products as independent processing units. The fire burn rate was estimated for each forest management unit using past fire events that occurred between 1971 and 2014. The fire data were provided by the Quebec forest fire management agency (SOPFEU). Since forest management units were too small to characterize management unit specific fire burn rates (Boulanger et al., 2012, 2013), we used the fire zones delineated by Chabot et al. (2009), which include the management units in our study area. The area of these fire zones ranged between 48,500 and 51,000 km2.

2.2. Forest and timber processing data Four sources of data were used to characterize forest stands in the timber production area of each forest management unit: landscape units, forest stand maps, temporary sample plots, and growth and yield models. Landscape units and forest stand maps were used to stratify the forest into different strata. Strata are aspatial groups of forest stands that share a common cartographic species composition (two most important softwood species, Table 1) and belong to a landscape unit. Landscape units are spatial units that were used to locate approximately, where harvesting occurs in the forest management units, allowing for the estimation of harvesting costs. These units (of a mean size of 6300 km2 in the black spruce-moss domain; Gauthier et al., 2015) are landscapes that are characterized by their relief, elevation, main surficial deposits, hydrography and forest vegetation (Robitaille and Saucier, 1998). They are part of the ecological classification system that is used by the Ministère des Forêts, de la Faune et des Parcs of Quebec (MFFP). Forest stand maps were prepared by the MFFP from the interpretation of aerial photographs taken at the scale of 1:15,000 between 1991 and 2003 during its third regular forest inventory program. The NATURA-2009 stand growth model (Pothier and Auger, 2011), which is currently used by the MFFP, was used to construct yield curves for each stratum for a 150-year planning horizon that was partitioned into five-year intervals. Temporary sample plots that were located within each stratum were used to estimate the individual density, basal area and volume yield per species group curves, which were summed for each stratum and a single yield table was constructed for each stratum with non-parametric smoothing (lowess in R; R Development Core Team, 2014). We considered lumber, chips and sawdust as the products that are produced by primary processing sawmills. Product yield curves were derived from empirical models developed by Zhang and Tong (2005), Liu and Zhang (2005), and Liu et al. (2009) for black spruce (tolerant softwood), jack pine (intolerant softwood) and balsam fir, respectively. We used data that were provided by Tembec (a forest products company) for FMU 085–51 (Pasturel, 2013) in 2007 to estimate all types of costs: forest management, harvest and transportation from stump to mill gate. First, we assigned the closest sawmill to each forest management unit as a simplified supply chain from a publicly available list of mills that were active in 2009 (MRNFQ, 2009). We then estimated the transportation distance between each landscape unit centroid and the assigned mill with a network analysis conducted in ArcGIS 10.2 (ESRI, Redlands, CA, USA) using forest road network data (Adresses Québec, 2015). The same analysis procedure was used to estimate harvesting and transportation costs for FMUs 026–65 and 094–52 based on the distance from the stump to mill entrance. Harvest cost including loading was kept constant by using the average cost for FMU 085–51 ($39.7 m−3). Transportation costs were estimated using the linear relationship between cost and distance that was provided by Pasturel (2013: Fig. H-1). We used a mean selling price for softwood logs at the mill gate of $58.7 m−3 (expressed in merchantable volume) provided by Pasturel (2013). We assumed that the sawmill transformed

2.3. Simulation framework We developed and used a simulation framework that combines a landscape simulation model and a harvest scheduling optimization model to compare the efficiency of four policies, at reducing the economic impact of considering fire risk in the corresponding strategic planning models (Fig. 2). We developed a timber harvest optimization model to design a harvesting plan congruent with each policy. We also developed a landscape simulation model to simulate the 23

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including uncertain fire disturbances in such models (Savage et al., 2010). The first model was formulated to maximize timber harvest volume over a 150-year planning horizon subject to even-flow of the harvest volume. By construction, it does not address the real impact of fire on economic values explicitly (Gunn, 2007). Model 2 addresses the economic impact by maximizing the expected net present value (NPV) of forest management activities. To estimate periodic net revenue, different costs need to be subtracted from the timber selling price to account for typical activities that occur in the forest. Optimal solutions from model 2 should therefore avoid harvesting stands that would generate negative revenues, which should reduce the planned harvest area. In this model, we have assumed that the price paid for timber delivered to mill gate is constant. It is expressed in terms of $ m−3 and does not vary by log dimensions. Models 1 and 2 do not consider the value recovery potential to the primary processing mills and are insensitive to the potential value of primary transformation, and its impact on regional economic activity (Patriquin et al., 2008; Dahal et al., 2015). The third and fourth models maximize the NPV of primary-processed wood products produced and sold as a means of linking strategic planning with the supply chain between timber harvest and selling of processed wood products. With a vertically integrated forest management policy (Barros and Weintraub, 1982; Gunn and Rai, 1987), the supply chain is responsible for all types of costs, i.e., forest management, harvesting, transportation, and maximizes the revenue (NPV) from the primary-processed products. At the same time, the integrated structure respects the sustainable management of the forest, which is reflected by an even-flow of harvest timber volume over the planning horizon. We developed two variants of an integrated policy that are represented by models 3 and 4, the last one differing from the third one in terms of a shorter time horizon for the objective function and the addition of two constraints on the even-flow of high-value products. Model 3 maximizes the net present value constrained by an even-flow of harvest volume over the planning horizon. Model 4 maximizes the objective function for only the first two periods because we want to maximize the short- and medium-term economic values (D'Amours et al., 2008; Szaraz, 2014, unpublished), but also ensure the even-flow of harvest volume over the entire planning horizon. Since lumber has the highest value, maximizing the net present value of primary-processed wood products over the entire planning horizon would deplete the timber, which could be used to produce lumber, in the early periods, preferably from stands located near the processing mill. The fourth model addresses these problems by considering two more constraints of even-flow (harvested lumber and distance-weighted harvested lumber) in addition to the constraints of model 3. The mathematical formulations of all optimization models are described in details in the supplementary material SM1. We used the AMPL modeling language (Fourer et al., 2003) to script the models and Gurobi 5.6.0 (Gurobi Optimization Inc., Houston, TX) to solve them.

Fig. 2. Simulation framework of the timber harvest schedule optimization and landscape simulation model. For details please refer to subsections §2.4 and §2.5 and supplementary materials SM2 and SM3.

implementation of those plans in interaction with fire with a replanning process. The model components and procedures are summarized below and details are provided in our supplementary material (SM1-SM3). This simulation framework produced frequency distributions of simulated harvest volumes (m3 ha−1 y−1), number of jobs related to forest harvesting and wood processing (number of jobs (100,000 ha−1) y−1), net revenues for timber and for primary-processed wood products ($ ha−1 y−1) and harvest rates (% y−1) by period. These performance metrics, with the exception of the harvest rate, were expressed per unit area of the timber production area of each forest management unit to ease comparisons. Harvest rates were expressed per unit of terrestrial area of each forest management unit. Planned values were produced by solving the optimization models and the simulated realized values were produced by the simulated replanning implementation of the optimal first period solutions produced whenever the optimization model was run in the landscape simulation model (Fig. 2). A set of performance metrics based upon the statistics of the predicted outcomes from the simulations were used to compare the four policy models. We used six performance metrics, namely, (a) harvest volume, (b) harvest rate, (c) net revenue from the sale of the harvest volume (d), net revenue from the sale of processed wood products, (e) number of jobs related to forest operations, and (f) number of jobs related to wood processing. As an indicator of sustainability, we used median and intra- and inter-period fluctuations (variability) of the examined indicators. In addition to these six performance metrics, we also used other indicators that helped us interpret the simulation results, namely, harvest age, lumber recovery factor, and surplus area available for harvest (Boyland et al., 2006). It provided the area still available for harvest which is related to the size of the available buffer stock of timber.

2.5. Landscape simulation model The landscape simulation model projects the dynamics of forest age structure over time by accounting for fire and harvesting. It uses the same equations as those used for the area accounting constraints to incorporate the effects of fire (Eqs. S4 - S6 in supplementary material SM1), with some differences. First, the periodic burn rate varies from period to period and is generated by random draws of the annual burn rates that were observed between 1971 and 2014 in the fire zone that includes the forest management units we studied. The second difference is with respect to the realized harvest, which is the minimum of the planned harvest area and area that is available for harvest in the same age class and in the same stratum during a period. Our mathematical formulation details are presented in supplementary material SM2. We used AMPL for landscape simulation modeling, and R (R Development Core Team, 2014) for further analyses of the simulated outputs.

2.4. Timber harvest scheduling optimization models We developed four optimization models based upon different policies. They were constructed using a Model III structure (Garcıa, 1984; Reed and Errico, 1986; Gunn and Rai, 1987) because of the ease of 24

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horizon. We constructed and evaluated two more planning policies to explicitly account for economic values (value-added) to wood industry aiming to explore as alternatives to minimize the potential impact of forest fire on the value-added product supply. Therefore, in addition to using sustained harvest volume flows as a classical indicator of performance, we examined the performance of all four planning models against six performance criteria that are presented in the following five subsections (from 3.1 to 3.5).

2.6. Replanning process Periodic replanning requires a process of data exchange between the timber harvest optimization model and the landscape simulation model. With replanning, the optimized solution (i.e., the harvest plan) of a timber supply model is provided to the landscape simulation model at the start of each period. Only the first period of the solution is simulated and two outputs are provided, viz., the starting forest age structure of the next period, which is used as the initial state for a new replanning simulation, and the realized simulated harvest for that period (Fig. 2).

3.1. Basis of model comparison: Harvest volume maximization (Model 1) When the optimal harvest plans produced by model 1 were implemented in the landscape simulation model in interaction with fire, the median realized harvest volumes over the planning horizon varied between 0.80 and 1.02 m3 ha−1 y−1, the median numbers of jobs, between 54 and 64 jobs (100,000 ha)−1 y−1, and the NPV between 533 and 624 $ ha−1. The number of jobs remained fairly uniformly distributed between forest operations (42 to 45%) and wood processing (55 and 58%) (Table 2). Eighty-seven percent of the jobs dedicated to wood processing were related to lumber processing. The median NPV from forest operations (13.6–125.4 $ ha−1) ranged between 3 and 20% of the total NPV. The largest NPV for forest operations (125.4 $ ha−1 for FMU 085–51) was associated with the shortest average distance between harvesting sites and the sawmill (65 km; 31–105 km). The lowest NPV for forest operations (13.6 $ha−1) was associated with the longest distance (196 km; 140–225 km). The variability of the performance metrics was the lowest for the FMU 085–51, which showed the lowest proportion of premature, mature and old stands (ages > 40 years, 49%, vs 57% for 026–65 and 90% for 094–52) (Fig. 1). Revenues and the number of jobs in wood processing associated with lumber recovery and lumber recovery proportions decline through time in FMUs 026–65 and 094–52 (Fig. 3), which indicates a shift in the proportions of wood products processed through time with model 1. This shift in wood product proportions with model 1 is a result of negative revenues beginning in period 15 (75 years from now) for forest management unit 026–65 (Fig. 4). The initial lumber recovery proportion was also the lowest in forest management unit 085–51 (Fig. 3). Some performance metrics varied through the planning horizon and

2.7. Statistical analyses All the descriptive and inferential statistics presented here are based on 1500 outcomes obtained from 50 simulation runs by period over a 30-period planning horizon using a periodic replanning framework (Fig. 2). Our decision to use 50 repetitions was based on an analysis of coefficients of variation (Supplementary material SM3). We compared policies with respect to the potential impact of fire on three performance metrics (harvest volume, net revenue from the sale of processed wood products and number of jobs). We estimated the probabilities of observing greater than or equal to specified values (the complementary cumulative probability distribution function, 1-CDF = p(x) ≥ X) over the planning horizon. Those probabilities serve as a risk measure by identifying risk zones corresponding to a range of outputs occurring with a specified probability. We have defined four such risk zones: a) up to 0.33 as being unlikely to occur, b) 0.33–0.66 as being equally likely or unlikely to occur, c) 0.66–0.90 as being likely to occur, and d) > 0.90 as being very likely to occur (Mastrandrea et al., 2010). As a risk averse strategic planning of public forest management, we chose an indicator of high probability of success (> 0.90) to yield higher revenue over the planning horizon. 3. Results Classical forest management planning policies (e.g., models 1 and 2 in our study) value merchantable timber and deal with the supply of harvest volume by ensuring its even-flow by period over a planning

Table 2 Median values of performance metrics (§2.3) using four harvest policy models for three forest management units (FMUs). The numbers in the parentheses are the interquartile ranges. FMU

Attributes

Model 1

Model 2

Model 3

Model 4

Western (085-51)

Harvest volume (m3 ha−1y−1) Harvest rate (%y−1) NPV ($ ha−1)

0.94 (0.015) 0.82 (0.175) 125.4 (0.3) 498.9 (5.4) 624.3 (5.4) 26.8 (0.4) 37.2 (5.2) 64.0 (5.6) 1.01 (0.034) 1.03 (0.178) 25.8 (2.4) 571.9 (29.5) 597.8 (32.0) 28.6 (1.0) 35.2 (7.8) 63.8 (8.4) 0.8 (0.006) 1.27 (0.254) 13.6 (0.4) 519. 6 (2.3) 533.2 (2.1) 22.6 (0.2) 31.0 (9.9) 53.6 (9.9)

0.93 (0.01) 0.84 (0.146) 135.4 (0. 9) 384.8 (1.0) 520.16 (1.5) 26.5 (0.3) 36.4 (3.3) 62.9 (3.9) 0.71 (0.042) 0.74 (0.079) 44.7 (1.1) 343.2 (6.9) 387.7 (8.0) 20.1 (1.2) 24.4 (5.3) 44.4 (5.9) 0.7 (0.035) 1.17 (0.31) 22.4 (0.1) 455.3 (1.7) 477.7 (1.8) 19.8 (1.0) 26.9 (9.8) 46.7 (10.9)

0.91 (0.018) 0.79 (0.177) 119.6 (0.1) 552.2 (4.8) 671.8 (3.2) 26.0 (0.5) 36.35 (4.4) 62.31(4.9) 0.80(0.076) 0.73 (0.135) 23.4 (0.8) 627.5 (26.0) 651.1 (26.5) 22.9 (2.2) 32.89 (5.2) 55.9 (7.1) 0.75 (0.081) 1.13 (0.31) 17.5 (0.1) 540.7 (0.6) 558.3 (1.7) 21.16 (2.6) 31.00 (10.8) 52.24 (12.6)

0.82 (0.098) 0.76 (0.132) 104.3 (0.4) 369. 9 (3.6) 474.2 (3.1) 23.2 (2.8) 34.3 (2.1) 57.5 (5.0) 0.62 (0.092) 0.59 (0.094) 1.4 (0.8) 361.0 (10.8) 362.4 (9.9) 17.7 (2.6) 28.8 (2.6) 46.4 (5.3) 0.55 (0.144) 0. 94 (0.162) 12.8 (0.1) 315.3 (0.6) 328.2 (0.6) 15.7 (4.1) 25.4 (4.2) 41.1 (8.3)

Jobs (# y−1/ 100,000 ha)

Central (026-65)

Harvest volume (m3 ha−1y−1) Harvest rate (%y−1) NPV ($ ha−1) Jobs (# y−1/ 100,000 ha)

Eastern (094-52)

Harvest volume (m3 ha−1y−1) Harvest rate (%y−1) NPV ($ ha−1) Jobs (# y−1/ 100,000 ha)

Forest harvesting Wood processing Total Forest operation Wood processing Total

Forest harvesting Wood processing Total Forest operation Wood processing Total

Forest harvesting Wood processing Total Forest harvesting Wood processing Total

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Fig. 3. Lumber recovery proportion from harvested flows by 5-year period in three forest management units (FMUs). The numbers refer to timber harvest optimization models 1–4 (§2.4).

Fig. 4. Boxplots showing the distribution of timber harvest volume and net revenue (undiscounted) by period using four harvest planning models for the most flammable forest management unit 026–65 (burn rate 0.48% y−1) based on 50 simulation runs.

3.2. Long-term stabilization of net revenues

the implementation of optimized solutions with the landscape simulation model was not always successful at reducing the differences between planned and realized solutions because of fire occurrence. As a consequence, we were able to define risk zones corresponding to a range of outputs occurring with a chosen range of probability (Fig. 5). These risk zones provide information similar to interquartile ranges, but they can also be used to estimate the value (harvest volume, revenue or number of jobs) that can be sustained at a chosen probability level (this level refers to the sensitivity of a decision maker to risk – Gardiner and Quine, 2000). For example, the maximum realized harvest volume very likely (p > .90) to occur with model 1 was an average of 0.89 m3 ha−1y−1 and varied between 0.79 and 0.96 m3 ha −1 y−1 among the management units (Fig. 5). The maximum undiscounted revenue very likely to occur with model 1 was $ 6.1 ha−1y−1 ($-0.7–13.5 ha−1y−1) (Fig. 5). The negative value of $-0.7 ha−1y−1 was observed for the forest management unit with the highest burn rate (026–65, Fig. 5).

When we maximized the NPV of timber sales (model 2), the NPV from forest operations was increased between 8 and 73%, the planned harvest volume was reduced on average by 15% (1–30%) and median NPV from wood processing was substantially lower than those produced by model 1 (−26% on average - Table 2). Conversely, when we maximized the NPV of processed wood products (model 3), the NPV from wood processing was increased by 4 to 11%, the total NPV was increased by 4 to 9%, and harvest volume was reduced by 3 to 21%. Once again, the lowest increase in the NPV and the lowest decrease in the harvest volume were observed for the forest management unit with the lowest amounts of premature and mature forest (085–51). When, in addition to maximizing the revenue of processed wood products, we considered even-flows of lumber volumes and of distance-weighted lumber volumes (model 4), the realized median NPV values from both forest operation and wood processing were lower than those produced 26

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Fig. 5. Risk analysis. Complementary cumulative density functions (1-CDF) for the realized harvest volume (top), revenue (middle) and the number of jobs (bottom) using four timber harvest optimization models in three forest management units (FMUs) with varying burn rates (BR). Numbers 1 to 4 correspond to timber harvest optimization models. The dotted horizontal lines represent the probability values 0.33, 0.67, and 0.90 associated with not likely, likely and very likely events, respectively (Mastrandrea et al., 2010).

Table 3 Median annual revenue ($ ha−1y−1) obtained from forest harvesting and wood processing (sawmill) over a 150-year planning horizon using four timber harvest policy models in three forest management units (FMUs). The numbers in parentheses are interquartile ranges of an array of 1500 outcomes (30 periods and 50 repeated simulations). FMU Western (085-51)

Central (026-65)

Eastern (094-52)

Forest harvesting Wood processing Total Forest harvesting Wood processing Total Forest harvesting Wood processing Total

Model 1

Model 2

Model 3

Model 4

5.0 (0.5) 11.7 (7.9) 16.9 (8.2) 0.5 (2.2) 4.9 (11.9) 5.0 (11.8) 0.6 (0.3) 8.3 (14.7) 8.6 (14.6)

5.1 (0.6) 11.1 (5.0) 16.0 (5.0) 1.6 (0.1) 2.8 (7.3) 4.4 (7.4) 0.7 (0.2) 6.7 (13.6) 7.4 (13.5)

4.9 (0.5) 11.8 (7.0) 16.7 (8.2) 0.6 (2.4) 11.2 (7.8) 11.8 (6.5) 0.6 (0.3) 11.3 (13.3) 11.9 (13.3)

4.4 (0.5) 13.6 (1.5) 18.2 (1.0) 0.1 (0.1) 14.2 (1.0) 14.2 (0.9) 0.5 (0.1) 11. 8 (0.8) 12.2 (0.7)

by the first three models (Table 2). However, the lumber recovery proportion remained more stable through time for model 4 (Fig. 3), and consequently, average undiscounted revenues were substantially higher for this model (between 7 and 184%, when compared with model 1 – Table 3). Planned undiscounted revenues using models 1 and 2 were not stable throughout the planning horizon. Rather, they were very high during the early periods, decreased, and then reached low or

negative values as early as the 10th 5-year period. These low or negative values are a result of a progressive decrease in the lumber yield (Fig. 4), which is related to a decrease in harvesting ages from 125 to 150 years to 50–60 years for all three forest management units. In addition, model 4 provided the smallest interquartile ranges for undiscounted revenues ($0.86 ha−1 y−1 compared to $11.53 ha−1 y−1 (8.24–14.55 ha−1 y−1) for model 1 and $8.66 ha−1 y−1 27

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Fig. 6. Boxplots showing the distributions of the number of jobs, lumber and chip flows by period when four harvest planning models were implemented in the most flammable forest (forest management unit 026–65, annual burn rate 0.48% y−1).

($5.04–13.52 ha−1 y−1) for model 2). Model 4 further scheduled smaller harvest volumes (Fig. 4), especially in the earlier periods, which resulted in lower total NPV. As a consequence, and contrary to undiscounted net revenues, the volume harvested decreased when changing the objective to maximizing the net present value of wood products (models 3 and 4), at most between 13 and 39% (models 1 vs 4, Table 2).

reduction in the size of the periodically harvested area implies an increased surplus area available for harvest in successive periods. There were substantial differences in surplus areas among the models (Fig. 8). The proportion of terrestrial area available as a buffer stock was substantially higher using model 4 (4.8%; 1.3–14.4%) compared with models 1 (2.3%; 1.0–14.4%), 2 (1.7%; 0.1–14.4%), or 3 (3.21%; 0.1–14.4%). As a consequence of its higher harvest rate, the harvest plans produced by model 1 scheduled clearcut harvest mostly in young stands (< 75-years-old) from the 7th–10th 5-year period, whereas harvest with model 4 included more mature stands (75- to 100-years-old) and old stands (≥ 100-years-old) throughout the planning horizon (Figs. 3, 8). The age at harvest is related to the proportion of lumber recovery, because the mean lumber recovery increases from 0.47–0.50 for young stands to 0.71–0.76 for old forests in the three FMUs (Fig. 4).

3.3. Total number of jobs and number of jobs per unit of volume harvested The number of forest harvesting jobs remains constant when expressed in terms of harvest volume (28.4 jobs (100,000 m3)−1 y−1) and was therefore related to the volume harvested. As the average harvest volume decreased for models 2 to 4 by 15 to 28%, so did the number of forest operations jobs (Table 2, Fig. 6). The number of wood processing jobs also decreased for models 2 to 4 in all three forest management units, but less (on average between 3 and 15%, Fig. 6, Table 2). Because the number of jobs that must be filled for lumber is higher than for chips or sawdust, the higher lumber recovery factor maintained with models 3 and 4 was associated with more jobs per unit of harvested volume (40 to 47 jobs (100,000 m3)−1 for models 3 and 4 vs 35 to 40 jobs (100,000 m3)−1 for model 1).

3.5. Higher net revenues at a chosen probability level of success The width of the risk zones for the realized harvest volumes was most often larger for models 2 to 4 when compared to model 1 (Fig. 5). The widest risk zones for harvest volume was observed with model 4 in the forest management unit 026–65 (0.52–0.82 m−3 ha−1 y−1). As a consequence, harvest volumes implemented with model 4 with a high probability of occurrence (p = .90) were substantially lower than those of model 1 (0.55–0.75 vs 0.79–0.96 m−3 ha−1 y−1). The width of the risk zones for undiscounted revenues was narrower with model 2, helping avoid negative revenues observed during the planning horizon with model 1 (−$0.1–25.1 ha−1 y−1 for model 2 vs -$10.2 to 37.9 ha−1 y−1 for model 1; Fig. 5). Similar patterns were observed with models 3 and 4 for all three FMUs, which have differing fire regimes. The narrowest risk zones for revenues and the highest revenues likely or very

3.4. Decrease in the harvest rate and increase in buffer stock size The median harvest rates varied between 0.82 and 1.27% y−1 with model 1. Harvest rates decreased with models 2 and 3 on average by 11 to 15% (up to 29%), when compared with model 1. The greatest decreases in the harvest rate were however, observed with model 4 (on average 26%, between 10 and 43%). In the case of model 4, harvest rates were reduced to values between 0.59 and 0.94% y−1 (Fig. 7). A 28

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Fig. 7. Violin plots showing the harvest rate (% of terrestrial area) when models 1 through 4 were simulated in three forest management units (FMUs) with varying burn rates (BR). The plots are produced with the output data for 30 periods and 50 simulation runs.

different discount rate. A higher discount rate will increase the drift with a rolling planning horizon (McQuillan, 1986). A higher discount rate is also related to lower forest rotation ages (Yin, 1997) and will increase the contribution in NPV of short-term harvest. As a consequence, the differences in NPV between models 4 and 1 (Table 2) should decrease and could even change sign with a lower discount rate, since model 4 provides higher amounts of lumber in later periods (Fig. 3). We have assumed regionally constant burn rates, independent of species composition and age structure, as did Reed and Errico (1986), Martell (1994) and Savage et al. (2010). Burn rates are however, selective according to species composition and age structure (Bernier et al., 2016; Boulanger et al., 2017), but our three study areas are largely dominated by fire-adapted conifers with minor hardwood components, and we regionalized the burn rate using homogenous fire regions, which already account for landscape, forest cover and flammability (Chabot et al., 2009). Finally, salvage logging, which we did not consider in our study, could alleviate timber losses caused by fire and therefore reduce the impact of fire on timber supply (Leduc et al., 2015). However, its contribution to timber supply is only marginal in the province of Quebec (Nappi and Drapeau, 2011), where our study is located. Two important factors led to substantially lower harvest rates with revenue maximization compared to a volume maximization strategy when considering fire effects. First, the costs of managing the forest, harvesting and processing of timber were minimized by avoiding unprofitable timber harvests (models 2–4). Second, an increased proportion of high-value lumber was recovered with models 3 and4 (Fig. 4), which did not occur when we used models 1 and 2. Models 3 and 4 therefore required a lower harvest volume to yield substantially higher revenues with a higher probability. At the level of strategic planning, economic objectives are a function of harvestable volume flows over time. Optimal solutions found when maximizing harvest volume tend to decrease harvest age (Reed, 1984) and hence lumber recovery (Zhang and Tong, 2005; Liu et al., 2007). This leads to economically distorted solutions over short and long terms when the objective is to maximize the harvest volume (model 1, Fig. 4). Such distortions can be avoided and one can more accurately relate the modeling framework to the preferences of the decision makers and the economic situation, by maximizing the net present value of primary-processed wood products (models 3 and 4). Lumber resources were also depleted through time with the first three models in the forest management units that still had such resources (026–65 and 094–52). This depletion was controlled in model 4 with a sustained and distance-weighed lumber volume flow but the addition of these constraints on lumber flow induced an abrupt reduction in harvest volume, net revenue and the number of jobs in the early periods of the planning horizon. Assuming model 1 represents business as usual, such a reduction would be difficult to justify to decision makers. One option would be to compare the predicted model

likely to occur were provided with model 4, independently of the burn rate. 4. Discussion Savage et al. (2010) showed that the incorporation of fire in a timber harvest scheduling model together with periodic replanning, alleviates the variability and reductions in harvest volume caused by fire over the planning horizon. This is what we observed when we used model 1 to manage harvest volume (Figs. 4 and 5). Conversely, our revenue maximization strategies (models 2 to 4) increased revenue and reduced its variability, but slightly increased the variation in harvested timber volume (compared to model 1; Figs. 4 and 5), as has already been noted by Boychuk and Martell (1996). Some variability in realized harvest volumes, revenues or number of jobs occurred across the planning horizon for all four timber supply models (Figs. 4 and 5). It occurred despite the incorporation of fire and even-flow constraints in all four optimization models with replanning. These systematic differences observed between the levels of periodic harvest volume among multiple iterations through the planning horizon are due to planning with a rolling planning horizon framework. Drift size and the direction of harvest volume by period varied from one forest management unit to the next, depending upon the initial forest age structure and rate of depletion of the standing stock (Figs. 4, 8), which may be explained by allowable cut effects (Schweitzer et al., 1972) and an extended planning horizon (McQuillan, 1986). To explain such drift on value-added product supply requires more attributes related to the quality of the harvest flows. As an indicator of quality timber flow, even flow constraints of lumber volume and distanceweighted lumber volumes used in model 4 helped reduce this drift (Figs. 3 and 4). This drift reduction is a result of a lower harvest rate, increasing opportunity to harvest more mature timber and the consequent building of a buffer stock of timber that has more value recovery potential (Fig. 8). We demonstrate here with model 2, that potential harvestable volume gains in successive periods related to a reduced harvest can serve as a contingency for harvest volume only (Boychuk and Martell, 1996). Therefore, we had to embed economic parameters in the planning model to achieve a non-declining supply of value-added products that helped minimize the risk on revenue generated by period over the planning horizon (model 4). We have made a number of simplifying assumptions and here we discuss four sets of them; our use of constant prices and costs, constant discount rate, constant burn rate and not accounting for salvage logging. We use the same financial parameters (harvest and processing costs, selling prices) for all three forest management units to avoid confounding the impact of fire risk with differences in their supply chains (e.g., number and types of processing mills, types of forest products). The results presented in this study might change with a 29

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Fig. 8. The median surplus area (% per period) and realized harvest rate (% per period) in three FMUs with varying burn rates (BR) using four harvest planning models. The surplus area is defined as the percent of the terrestrial area that has standing volume > 50 or equal to m3 ha−1. Light, medium and dark grey shades show the median values of the available area for three age classes (50 to 74 years old; 75 to 99 years old; ≥ 100 years old). The numbers in the shaded areas are the median lumber recovery proportions for the same age class. The dotted lines are the median of realized periodic harvest rates of 50 simulations.

disturbances (Rijal and Lussier, 2017) but, it is also helpful while integrating the potential risk of fire on the sustained supply of high value products. Deferral of the mean age at harvest not only provided an economic opportunity that would counteract the negative effects of fire on timber supplies but also created an opportunity for retaining higher proportions of mature and old-growth stands (Fig. 8). Retaining these stages by volume maximization is difficult when annual burn rate is high (Savage et al., 2011). Reductions in harvest area without lowering revenues may serve as a measure to mitigate the losses of stock due to fire, thereby increasing the likelihood of cumulative natural and anthropogenic disturbances remaining below specified thresholds. Consideration of such disturbance thresholds may also be useful in ecosystem-based forest management (Hunter, 1993).

results with recent harvest volumes rather than those produced by model 1, as recent harvest volumes are related to the actual processing capacity of the mills and not to the more theoretical maximum harvest level prescribed by model 1. This comparison could be further enriched by an analysis of the impact of the forest-products value chain of each forest management unit on regional economic activity, since the economic health of wood-processing mills can serve as an indicator of regional activity as well (Patriquin et al., 2008; Dahal et al., 2015; Johansen et al., 2017). The transition between models 3 and 4 could also be made smoother by finding external wood procurement sources, as a substitution of the cost of short-term shortfall, to maintain a sustained lumber flow at the mill entrance (e.g., Patriquin et al., 2008). Increasing the number of silvicultural options (Moore et al., 2011; Gautam et al., 2014) may also help increase the sustained lumber yield. Increased value recovery was also associated with an increase in the mean age at harvest from 70 to 100 years. Deferring the harvest age increases the probability of a stand being burned before it reaches maturity (Reed, 1984; Gauthier et al., 2015). In our case, the probability of that happening increased between 31 and 50% (model 1 vs model 4), depending upon the forest management unit and its associated burn rate. The deferred harvesting also decreased its land expectation value (Davis et al., 2001). In our case, these negative impacts of harvest deferral at the stand level seemed to be largely offset at the scale of forest management units with a revenue maximization strategy by 2 to 7%, with a discount rate of 4% y−1 (Table 2). Increasing the proportion of mature stands will also increase the proportion of stands that can be salvaged (Leduc et al., 2015), but such practices are beyond the scope of this study. The build-up of a buffer stock of timber (Fig. 8) results in less frequent harvest flow shortfalls (Leduc et al., 2015), more resilience to risk (Boychuk and Martell, 1996) and less impact due to fire (van Wagner, 1983; Savage et al., 2010). Hence, value-added supply policy is not only efficient when we do not consider forest

5. Conclusion Maximizing net present value from the sale of processed wood products helped create forest management strategies that reduce the fire impact on timber production. It also decreased the timber volume flow since many costs (harvest, transportation, processing) were expressed per unit of harvested volume. As a consequence, harvest rates and volumes harvested were reduced, which helped maintain a buffer stock of timber with a higher potential of lumber recovery proportion over time. This high value potential buffer stock also served as a risk mitigation measure against fire. Harvest age was also deferred because log size is related to a greater lumber recovery per unit of merchantable volume. Decrease of harvest volume and harvest age deferral also helped maintain a greater proportion of old forest. Our study therefore provided an indication that a tighter link between strategic forest management planning and the supply chain between timber harvesting and selling of processed wood products, helped increase the 30

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opportunity of finding better compromises between harvesting activities, revenues and the number of jobs, despite the occurrence of natural disturbances.

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Acknowledgements We thank the Ministry of Forests, Wildlife and Parks of Quebec for providing access to the data from their Forest Inventory Program (20022004) and the 1971-2014 fire history map. We also thank Sylvie Gauthier, Luc LeBel and Jean-Martin Lussier for having reviewed earlier versions of this manuscript, Julien Beguin for providing us a map of mill locations and William F.J. Parsons for editing the English of the manuscript. This study was supported by the NSERC Value Chain Optimization (VCO) Network under its research theme 1 “Integrated Forest and Industry Strategies for the Modern Bio-economy.” Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.forpol.2018.09.002. References Armstrong, G.W., 2004. Sustainability of timber supply considering the risk of wildfire. For. Sci. 50 (5), 626–639. Barros, O., Weintraub, A., 1982. Planning for a vertically integrated forest industry. Oper. Res. 30 (6), 1168–1182. https://doi.org/10.1287/opre.30.6.1168. Baskent, E.Z., Keles, S., 2005. Spatial forest planning: a review. Ecol. Model. 188 (2), 145–173. https://doi.org/10.1016/j.ecolmodel.2005.01.059. Bernier, P.Y., Gauthier, S., Jean, P.O., Manka, F., Boulanger, Y., Beaudoin, A., Guindon, L., 2016. Mapping local effects of forest properties on fire risk across Canada. Forests 7 (8), 157. https://doi.org/10.3390/f7080157. Bettinger, P., Boston, K., Siry, J.P., Grebner, D.L., 2009. Forest Management and Planning. Academic Press, New York, pp. 331. Bogdanski, B.E.C., 2008. Canada's Boreal Forest Economy: Economic and Socioeconomic Issues and Research Opportunities. Natural Resources Canada, Canadian Forest Service, Pacific Forestry Centre, Victoria, BC, pp. 59. Information Report BC-X-414, Available from. http://publications.gc.ca/collection_2008/nrcan/Fo143-2-414E.pdf (accessed 17 May 2015). Bouchard, M., Pothier, D., Gauthier, S., 2008. Fire return intervals and tree species succession in the North Shore region of eastern Quebec. Can. J. For. Res. 38 (6), 1621–1633. https://doi.org/10.1139/X07-201. Boulanger, Y., Gauthier, S., Burton, P.J., Vaillancourt, M.A., 2012. An alternative fire regime zonation for Canada. Int. J. Wildland Fire 21 (8), 1052–1064. https://doi.org/ 10.1071/WF11073. Boulanger, Y., Gauthier, S., Gray, D.R., Le Goff, H., Lefort, P., Morissette, J., 2013. Fire regime zonation under current and future climate over eastern Canada. Ecol. Appl. 23 (4), 904–923. https://doi.org/10.1890/12-0698.1. Boulanger, Y., Girardin, M., Bernier, P.Y., Gauthier, S., Beaudoin, A., Guindon, L., 2017. Changes in mean forest age in Canada's forests could limit future increases in area burned but compromise potential harvestable conifer volumes. Can. J. For. Res. 47 (6), 755–764. https://doi.org/10.1139/cjfr-2016-0445. Boychuk, D., Martell, D.L., 1996. A multistage stochastic programming model for sustainable forest-level timber supply under risk of fire. For. Sci. 42 (1), 10–26. Boyland, M., Nelson, J., Bunnell, F.L., Robert, G.D., 2006. An application of fuzzy set theory for seral-class constraints in forest planning models. For. Ecol. Manag. 223 (1), 395–402. https://doi.org/10.1016/j.foreco.2005.12.001. Brandt, J.P., Flannigan, M.D., Maynard, D.G., Thompson, I.D., Volney, W.J.A., 2013. An introduction to Canada's boreal zone: ecosystem processes, health, sustainability, and environmental issues. Environ. Rev. 21 (4), 207–226. https://doi.org/10.1139/er2013-0040. Bureau du forestier en chef (BFEC), 2013. Manuel de détermination des possibilités forestières 2013–2018. Gouvernement du Québec, Roberval, QC, pp. 247. Available from. http://forestierenchef.gouv.qc.ca/wp-content/uploads/2013/01/MDPF_VF. pdf, Accessed date: 8 August 2014. Canadian Pacific Consulting Services (CPCS), 2013. Transportation Costs and Competitiveness of Eastern Canada Lumber in Gcc Markets. Available from. http:// canadawood.org/pdf/report_transportation_costs_competitiveness.pdf, Accessed date: 12 February 2015. Chabot, M., Blanchet, P., Drapeau, P., Fortin, F., Gauthier, S., Imbeau, L., Lacasse, G., Lemaire, G., Nappi, A., Quenneville, R., Thiffault, E., 2009. Le feu en milieu forestier. In: Ordre des ingénieurs forestiers du Québec. Manuel de foresterie, 2e édition. ouvrage collectif, Québec, pp. 1037–1090. Cissel, J.H., Frederick, J.S., Peter, J.W., 1999. Landscape management using historical fire regimes: Blue River, Oregon. Ecol. Appl. 9 (4), 1217–1231. Dahal, R.P., Henderson, J.E., Munn, I.A., 2015. Forest products industry size and economic multipliers in the US South. For. For. Prod. J. 65 (7–8), 372–380. https://doi. org/10.13073/FPJ-D-14-00083. D’Amours, S., Rönnqvist, M., Weintraub, A., 2008. Using operational research for supply

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