1. Introduction and Motivation
Forests play essential roles, providing a wide range of resources and functionalities, including protecting watersheds and soil from erosion, as well as mitigating climate change. They are also essential in providing habitats for animals and livelihoods for humans. The importance of forests makes their optimal management crucial. Awareness of sustainable forest management (SFM), and the sustainable utilization and production of forests’ goods and services, are important parts of the sustainable development goals (SDGs), identified in the 2030 Agenda for Sustainable Development, adopted by all United Nations Member States in 2015, specifically as described in the objectives of SDG 15 (
https://sdgs.un.org/topics/forests, accessed on 15 January 2022). The success of SFM towards achieving desired outcomes depends on planning strategies and decisions, supported by appropriate scientifically based methods, such as optimization models, and on a good knowledge of forest growth patterns prediction of stand growth subject to specific management scenarios is usually obtained with growth models or simulators (e.g., [
1,
2,
3,
4]).
The usage of optimization models to support sustainable forest management planning has been intensifying over the years, encompassing diverse problems with different sets of constraints and objectives. One of the most studied problems is maximizing the harvested volume, while considering sustainability, silvicultural, operational and environmental constraints.
Sustainability considerations lead to the identification of the maximum value of harvest that can be imposed on a given forest and sustainably maintained in perpetuity. This level is referred to as the maximum sustainable harvest or maximum sustained yield [
5]. For a given forest, the potential maximum yield depends on site quality and can be modified through silvicultural prescriptions. Earlier studies of forest planning, framed as mathematical programming problems, date back 80 years, and have undergone a marked development with the improvement of computational equipment. Clutter et al. [
5], and the references therein, describe classical approaches for solving forest planning, with linear programming methods. Later, emphasis was additionally placed on environmental constraints.
Environmental constraints are used to prevent a significant reduction in environmental quality, such as wildlife, soil, water, and natural beauty. Within these constraints, there are the clear-cut area constraint and the associated exclusion time. These constraints bound the continuous area of forestland that can be harvested at once, and impose a minimum passage of time before adjacent stands can be harvested (the so-called green-up constraints). This set of constraints has been the topic of study of many operation researchers. There are two formulations for this issue in the literature: the unit restriction model (URM) and the area restriction model (ARM). In the case of the URM model, there are management units (MU), whose area is close to the imposed maximum and no cuts from adjacent MU are allowed during the exclusion period. This approach removes flexibility from the construction of the clearings. Murray [
6] proposes the ARM model, where adjacent harvesting of MUs is allowed in the same planning period, as long as the total size of each continuous final harvested area does not exceed the maximum. The URM is easier to formulate and solve than the ARM approach, but ARM produces better solutions. Three basic ARM formulations are described in the literature: the path formulation [
7,
8,
9,
10], with an exponential number of constraints, the cluster formulation [
7,
8,
11,
12,
13], with an exponential number of variables, and the bucket formulation [
14], with a polynomial number of variables and constraints. It has been theoretically proven that the cluster formulation is stronger than the path formulation [
15], and the bucket formulation [
16], that is, the linear relaxation of the cluster formulation, gives a better bound than the linear relaxations of the other formulations. Furthermore, Goycoolea et al. [
15] implemented the three formulations in a branch-and-bound system and showed no stronger performance between the path and bucket formulations. Borges et al. [
17] present three formulations to establish green-up requirements, based on a dynamic green-up approach, considering: (i) a predefined fixed length for the green-up time, (ii) a predefined variable length for the green-up time and (iii) height information, produced by the growth simulator to define whether management units are in an open state or not. The proposed approach was applied to the Oslo (Norway) municipality forest. The growth simulator GAYA [
18,
19] has been used to generate treatment schedules for other forest areas in Norway.
Reference [
20] addresses the clear-cuts’ patterns to modify fire growth and behavior. León et al. [
21] proposed a landscape-scale optimization model to break the hazardous fuel continuum, while maintaining habitat quality. The model aims to reduce the adjacency of high-fuel load areas.
Regarding environmental sustainability, Álvarez-Miranda et al. [
3] proposed a framework to support strategic decisions when multicriteria decisions are to be made and there is uncertainty in the data due to climate change, based on a combination of Goal Programming and Stochastic Programming. The application was made in forest management of
Eucalytus globulus, involving medium-term (15 years) forest planning. The harvest scheduling model can address, simultaneously, the maximization of the harvest economic value, carbon sequestration, water use efficiency and reduction in runoff water, as a proxy for minimizing potential erosion in the study area. This model is applied to the whole planning horizon, providing a pool of diverse solutions with different trade-offs among the four criteria. The inclusion of uncertainty was achieved through the use of a process-based model, to simulate forest growing profiles for different future climate scenarios. Generalization to other species is currently limited, given the minimal availability and adequacy of calibrated growth models.
In common lands, forest management can also be carried out efficiently through the use of optimization models. Fonseca et al. [
22] developed “easy-to-use” models, supported by optimization techniques, to help the forest managers in the harvest planning of maritime pine stands, in five common lands, within a total area of 4432 ha. The proposed model is easy to apply, providing immediate advantages for short and mid-term planning periods, compared to empirical methods of harvest planning. The thinning and clear-cutting operations were planned to maximize the incomes over five years, with silvicultural, operational, and sustainability constraints, imposing a lower bound in the average ending age. It was shown that individualized management, with a balanced distribution of incomes, is an interesting option. It does not drastically reduce the optimal solution, while assuring revenues at least every two years for each common land, as desired by the local communities. Cerveira et al. [
23] proposed a forest management plan for the same study area, also considering spatial constraints, dictated by a maximum clearings area. This limit depends on the legal rules of the country. For example, the limit is 1 hectare in the Czech Republic [
24], while in Portugal, the recommended value is 10 ha.
In [
25], the optimization model proposed for forest management planning in common lands deals with the maximization of the incomes, while considering non-spatial and spatial constraints. Non-spatial constraints address silviculture, operational, organizational and sustainability concerns. Spatial constraints address environmental values, to prevent a significant reduction in environmental quality, bounding the clearings area and the associated exclusion period. The sustainability constraints, which aim to prevent a compromising removal of timber over the planning horizon, ensure that the volume of standing timber and the annual increase in timber production in the last year are not lower than those to be found at the beginning of the first year. Costa et al. [
4] proposed an optimization model to assay different management alternatives, providing the best and adequately selecting the available information. The study area is a common land of around 450 ha. For each stand, growth simulations were performed, following two possible scenarios. The planning horizon was fifty years and a balanced age class structure at the end of the planning horizon was imposed as a sustainability constraint.
As evidenced in the case studies, optimization has proven to be an important tool to support forest area management planning on state areas, private areas and common lands, involving one owner or management body or a very small group. Despite all the research in the literature, there is a gap in knowledge that can have a tangible impact on forest policies, involving the governance of forest areas. Are linear programming-based optimization models flexible enough to accommodate multiple owners? What effect does the grouping of areas (and their owner bodies) have, compared to independent management, on the total volume removed and on the regularization of the age of the forests at the end of the planning period? To the authors’ best knowledge, this has not yet been explicitly analyzed, i.e., how these optimization models perform in extensive areas with multi-actor situations.
A recent reform on forest policy in Portugal, briefly described, as follows, for background purposes, has motivated us to develop the current research. In 2019, the Portuguese Government financed the creation of groupings of common lands under the Forest Reform program (Council of Ministers Resolution no. 9/2019, of 14 January). The chosen grouping of common lands aims to promote the extension of qualified forest management to all forest spaces in community areas, through the development of the model of joint management of forest areas, with all the added value that comes from associativism and the establishment of a model of economy of scale [
26]. The grouping of common lands is also intended to increase the coordination of structural fire prevention actions, a main threat to the national forests. The setting up of groups of common land areas is being promoted by BALADI—Federação Nacional dos Baldios (
https://www.baladi.pt/, accessed on 4 December 2021) and the association Forestis—Associação Florestal de Portugal (
https://forestis.pt/, accessed on 4 December 2021), with the participation of the state, through the Institute for the Conservation of Nature and Forests (ICNF). Due to the large areas involved and the existence of multiple managing bodies, the management of groups of communitarian areas represents a challenge to forest management.
The authors use, as a case study, the grouping of 22 common lands in the Boticas municipality (ADBaldios do Concelho de Boticas), in the north of Portugal. Most of the trees are maritime pine (
Pinus pinaster Ait.), the dominant species in that region. There are large areas of natural regenerated stands, originated from forest fires. Prediction of stand development was made with the simulator Modis Pinaster [
22,
27]. Based on the detailed data, an optimization model was developed to support forest management in these areas, where maritime pine stands are traditionally managed for their timber production, which is the most valued natural forest resource in this region. The forest management model accounts for the existing diversity of maritime pine forests, in terms of age structure and density of cover, and was designed to try to ensure a set of sustainable management requirements, namely, regularization of age classes, stability of stands to wind effects, vulnerability to forest fire, regularity of income and fulfillment of legal obligations, such as maximum areas of continuous clearings. The problem is formulated as an Integer Linear Programing (ILP) model, following previous successful applications to the species.
The research developed by the authors aims, specifically, to answer two questions: (1) Are there sustainability advantages when considering a joint management plan for extensive areas, resulting from clustering and involving several owners or management bodies? (2) What is the expected difference (if any) in timber harvested, as the objective function, over the planning period? The specific research hypothesis being analysed is that there are no relevant differences, either in volume of timber harvested or in sustainability criteria, if multi-stakeholder forest areas are managed independently or if they are managed as a whole. If there are differences (the alternative statement that is endorsed by the authors), the forestry policy will, necessarily, have to consider trade-off decisions between what is sought and what can be achieved.
This outline of the paper is as follows. In
Section 2, the study area is characterized and the adopted methodology for the optimization of forest management, in large communal areas, is described (
Section 2.1 and
Section 2.2). Information about the stratification of forest cover and forest inventory undertaken is presented in
Section 2.3 and
Section 2.4. refers to the simulations of stand growth, using Modis Pinaster. The optimization model is described in
Section 2.5. In
Section 2.6. is described the statistical analysis. In
Section 3, the computational results are presented and analysed. We discuss the effect of grouping areas and involving multiple management bodies in a global optimization model for the whole area, comparatively, to independent forest management for each common area. Finally, we examine whether the model is replicable and recommendable for other clustering situations. In the last section, conclusions are stated.
4. Discussion
Based on the results presented in
Section 3, in particular in
Table 6,
Table 7,
Table 8,
Table 9,
Table 10 and
Figure 4 and
Figure 5, it can be concluded that the base model corresponds to a greater volume of removed timber, 1,928,699.5 m
3. This corresponds to the expected outcome, due to the lower number of constraints included in this base version (
Table 3). The inclusion of stability constraints, FMPs model, leads to a slight reduction in the amount of timber volume harvested (0.76%). A negligible reduction of 0.04% also occurs when the constraints on the revenues per common land, FMPr, are included. The other set of constraints has a greater impact on the reduction in the removed volume, being 5.1% in the model FMPv, 12.89% in model FMPy and 14.76% in model FMP.
Although the total volume of harvested wood is smaller over the planning horizon with the FMP model (1,643,956.8 m3), this model provides a result that is most consistent with the sustainable management of the forests. In the FMP model, the three pillars of sustainability—environmental, economic and social—are addressed. Examples of environmental issues considered in the model are the forest stability and the assurance of a more balanced age class distribution in the area. The achievement of a balanced volume income during the planning horizon, matching the preferences of local entities with guaranteed revenue per vacant land in each 5-year period, directly relates to economic value and social preferences.
The increase in the average stand age at the end of the planning horizon (a value higher than 22 years with the FMP model, see
Table 9) is an additional element confirming the better adjustment to sustainable management criteria achieved with this model. As shown in
Figure 3, at the beginning of the planning horizon, the distribution of maritime pine stands by age classes is not balanced. The main reason is the occurrence of frequent (and recurrent) forest fires that have affected the studied region. The forest inventory shows that 84% of the stands in the study area are up to 20 years old (corresponding to natural regenerated areas after forest fires) and the remaining 16% corresponds to stands with age values greater than 20 years. This imbalance greatly conditioned the set of
periods, in which balanced distribution by age classes is guaranteed, (15). In order to obtain feasible problems, it was only practicable to include this set of constraints at the end of the planning horizon, that is, only,
, was considered, which will facilitate management in later periods. During the planning horizon, the volume regularity already guarantees revenues throughout the planning period.
Some authors [
4] include restrictions that limit the final average age. In this work, we have chosen not to include such constraints. Although the constraints that limit the average final age, inferiorly, are not included, the values presented in
Table 9 allow us to conclude that constraint (15), in addition to ensuring the most balanced distribution by area classes, leads to satisfactory values of the final age, 19.94 for the model FMPy and 22.28 for FMP. Without constraint (15), the average age at the end is very low, ranging from 10 to 15 years (models FMPb, FMPs, FMPr and FMPv). The value of stand age equal to or lower than 15 years does not fit with the typical rotation values proposed for the species, even when considering a shorter rotation length which, is around 20 years [
4,
41].
In the optimal solution of the base model, FMPb,
Table 8, 89% of the clear-cutting area is cut in the last two 5-year periods. With the FMP model, the total area subjected to clear-cut decreases compared to FMPb. Furthermore, although in the later years the total clear-cut area is larger, the difference is not so substantial, in the last two 5-year periods, clear-cutting corresponds to about 55% of the total clear-cut area.
The results obtained for the group of 22 common lands confirm the usefulness of linear programming-based optimization models to accommodate multiple owners. In terms of flexibility to accommodate changes or to be applied to other areas, the mathematical model presented in
Section 2.5 is generic enough to be easily adaptable to account for stands of various stages of development and stand densities. For the case study, high density values were identified in early stages, which is in accordance with the maximum attainable density trajectory for the species presented by [
46]. Those values were accounted for in the simulations performed with ModisPinaster and considered in the optimization model.
Generalization to other forest systems can be easily accommodated. For example, considering another species with different conditions to perform a final cut should adapt constraints (2) and (3). Further, the wind instability in constraint (7) could be different for other species.
The mixture of several forest species can also be easily contemplated. Constraints (2)–(5) impose conditions for carrying out clear-cutting, and should be adjusted to the species under study. Constraint (6), which prevents the formation of clearings with more than 10 ha, with an exclusion period of two years, should cover all stands, regardless of the forest species. In constraint (7), which ensures the stability of the stands, the threshold value considered for the quotient between average height and diameter must be adjusted for each of the species under study. Constraints (8) and (9), which ensure revenues per each common land, must include all the plots of it. Constraints (10) and (11), which assure balanced volume revenue, must include all the study area, regardless of the species. Constraints (12)–(15), which establish conditions on the age structure of the forest, should be adapted for each species.
The crown fire potential effect, evaluated through the variable canopy bulk density (CBD), can be easily added, in constraint similar to constraint (7), used for tree stability. For the case study, its use was not considered in the models because the majority of the stands had values of CBD higher than the threshold limit of 0.08 (km/ kg/m
3) [
47]. Development should extend the optimization problem to account the broad role and multiple functions of forests, such as the production of resin and carbon sequestration. The effect of disturbances, such as pests and diseases, can also be handled with this optimization approach for forest management planning.
With this research, the authors also aimed to analyse the effect of grouping areas (with different owner bodies), compared to independent management, in terms of sustainability. The criteria used for the assessment are the total volume removed over the planning horizon and the regularization of the age of the forests at the end of the planning period. Examination of the effect of the set of constraints was also performed. Comparing the results obtained in individual management and global management with the base model (FMPb and FMPb-IND, global results provided in
Table 10), the following remarks should be highlighted:
As expected, the volume removed per common land area either coincides or is lower with global management. This is because, in the global management scenario, the clearing constraints consider adjacencies between patches that are distinct vacant areas and, therefore, the clearing constraints become more restrictive. In this case study, the reduction in volume occurred in only four fallow patches, with reduction values between 0.2% and 1.6%.
The total removed volume with global management, in the 18 common lands, was reduced by about 0.2%, corresponding to 4242 m3 during the 30 years of the planning horizon.
The average final age of the common land varies in both individual and global management scenarios, between 0.9 and 26.2 years (data per common land not shown), presenting a minor positive difference, when considering all of the common lands (
around 10 years,
Table 10).
It should be noted that the authors do not advocate the use of the base model, FMPb, for forest managers to follow. The FMPb model is a reference point, where the constraints that must be considered (silvicultural and green-up) are considered, highlighting the importance of guaranteeing sustainability and operational constraints. The average final age achieved with the optimal solution is particularly low, which compromises the future management of the study area.
The comparison of the results obtained by individual and global management with the complete model must be done with caution (FMP and FMB-INV, global results provided in
Table 10), but does not prevent the highlighting of important patterns accounted for by the management mode. As mentioned before, it was necessary to make adjustments to the individual management model to obtain feasible solutions. In the global management model, FMP, constraints on the area by classes of age ensure reasonable values for the average final age of the whole study area, 22.28 years, as well as a better balance of area per age class (
Figure 6). When analysing the final average age per common land, it varies between 15.6 and 38.2 years. For individual management, because of the constraints bounding average final age to at least 20 years, common land’s average final age varies between 20 and 26.2 years. As far as volume is concerned, the results achieved with the global management optimal solution show a reduction in total wood harvested over the 30-year planning horizon, in the order of 140,000 m
3, 8.6% in a relative basis (
Table 10). This difference has proved to be statistically significant (
p = 0.000). The analysis made per common land shows a variation from −20% to +2.9%, regarding the results obtained with the FMP model, compared to the FMP-IND model.
The option for global management is more interesting than individual management, in terms of guaranteeing the sustainability of resources, even though a compromise is implicit between the reduction in the amount of wood that is cut and what is gained in the medium term, in terms of resource sustainability.
The proposed model is replicable and recommendable for other clustering situations, either of communal areas or of areas belonging to multiple private owners, under a private governance model. Examples of the latter occur in Eastern European countries, where private forest ownership is often highly fragmented, with properties of small size, after the restitution of landownership [
48]. As stated in the FAO study, forest owners’ organizations, such as forest owners’ associations and forest owners’ cooperatives, are an instrument for supporting the sustainable management of private forests. The use of optimization models, such as the FMP developed in this study, can easily help with this aim.
5. Conclusions
This work considers a relatively long planning horizon, 30 years, in a large group of communal areas, involving diverse management bodies, where the decision of the period in which clear-cutting and thinning takes place is provided by the optimal solution of the optimization model. The proposed optimization model takes into account the specific silvicultural constraints of maritime pine species and is consistent with the specification of the problem that was intended to be studied: it ensures sustainable management with a balanced age classes structure at the end of the planning horizon; it includes constraints on the maximum area of clearings; it ensures balanced revenues of volume over all the study area and regular revenues per common land that meet the interests of the communities; it considers the stability factor that allows the management plan to be adjusted, taking into account susceptibility to wind damage, associated with climate change and beyond that, it can be used or adapted to other regions, regardless of species, and to other groups of areas with multiple managing bodies, such as the ones occurring with implementation of associativism. To the best knowledge of the authors, assessment of the impact of changing governance policies in the management of forest areas has never been accomplished for real cases of study, involving common lands in Europe.
When comparing the type of management, individual or global, the global joint management approach, supported by the FMP optimization model, presented a noticeable reduction of around 8.6% in removed volume and a higher value of age for the existing stands at the end of the planning horizon, compared to the model that considers individual management (FMP-IND model). It should be noted that individual management does not guarantee environmental restrictions of the stands, assured with global management, because at the spatial level, there are patches with continuity between the commons, jeopardizing the landscape structure, and translating into possible impacts on the ecosystem.
It can be concluded that global management, when compared to individualized management, implies a trade-off between the wood harvested, which is reduced in the former, and what is gained, in the medium term, in resource sustainability, as proven by the increase in the average age of the remaining stands at the end of the planning period in the latter.