Harvest Scheduling Model Research Articles

Multi-objective forest planning at tree-level combining mixed integer programming and airborne laser scanning

The development of forest planning at tree-level is nowadays feasible due to the advances in laser scanning. Tree-level data remains still not fully utilized in the context of tree selection mechanisms and harvest-scheduling models. Using spatial optimization with tree-level data can shift the situation. The research presented a decision-support model set based on mixed integer programming (MIP) to select trees based on economical and spatial goals. Trees were represented as polygons to conduct spatial optimization and account for perimeter boundary minimization while establishing adjacency constraints. The proposed model framework method was tested in a Stone pine (Pinus pinea L.) stand of almost 4400 trees in Spain where individual tree detection with airborne laser scanning data was conducted. The MIP-based tree selections were presented using different priorities for single and multi-objective optimizations to demonstrate the potential of spatial goals to make forest management planning more efficient when controlling the spatial arrangement of solutions. The results showed the general MIP formulation is feasible and all presented combinatorial problems reached global optimality fast. The use of MIP formulations to schedule tree-level decisions has positive cascading effects towards operational forest planning while expanding the current frontiers of tree-level forest planning based on heuristic optimization.

Solving the integrated forest harvest scheduling model using metaheuristic algorithms

In forestry, the highest operational costs arise from the construction of forest roads and the transportation of harvested wood. Hence, optimization models have been used at the tactical level of planning to reduce these costs by integrating decisions on: (1) the allocation of harvest-blocks, (2) the allocation of access roads to these blocks, and (3) the transportation costs that result from the latter two decisions. The integration of these three decisions, in one optimization model, has been referred to as the integrated model. The integrated model, when binary decision variables are used to represent the cut-blocks and roads, is NP-hard and has been solved using two approaches: exact and metaheuristic algorithms. Unlike exact methods, metaheuristic algorithms have thus far not solved the integrated model, but have solved models which either exclude transportation costs from the objective function, or solve the model sequentially. This is a significant gap in prior research because exact solution methods can only be used on smaller forests and metaheuristic algorithms have therefore been used to solve the tactical forest planning problem, without the integration of transportation costs, on large forests. This failure to integrate transportation costs, on a large scale, is the major economic consequence of this gap. The objective of this paper is to present and evaluate a new solution procedure in which all three elements of the integrated tactical planning model are included in the objective function and solved using metaheuristics. The solution procedure was applied to three forests and the attributes and qualities of the solutions were compared to near-optimal solution values generated using an exact solution approach. The results indicate that this metaheuristic procedure generated good quality solutions. We conclude that this research is a useful first step in representing transportation costs in the integrated tactical planning models to be solved using metaheuristics.

An economic analysis of thinnings and rotation lengths in the presence of natural risks in even-aged forest stands

A harvest scheduling model when the natural risk is not only dependent on the age of the forest stand but also on the stock density is presented in this paper. In addition, damages to human lives, human health and infrastructure caused by natural risks are incorporated. Using a conditional current value approach, the optimal thinning and rotation length conditions are determined and used for the qualitative analysis of the course of the optimal volume path under different risks. Also the impacts of external variables such as stand age, interest rate, timber price and damages to human lives etc. to the optimal harvest schedules are derived. The results and dependencies are discussed in detail and compared to findings presented in the literature.

On the Importance of Integrating Transportation Costs into Tactical Forest Harvest Scheduling Model

In tactical forest management planning, the decisions required to meet the strategic plan are made, and these include: i) scheduling of spatially explicit harvest-blocks; ii) construction of a road-network required to access these blocks; and iii) transportation costs within the tactical forest planning area (hereafter only referred to as transportation costs) that emerge from the first two decisions. These three decisions are interdependent and should therefore be integrated in any optimization model. At present, this integration is not fully made. This is because: i) the integrated model is NP-hard, and exact solutions are not feasible for large and medium-sized forests; and ii) metaheuristic search algorithms, which can be used on larger forests, have not integrated transportation costs realistically.The economic consequences of not integrating transportation costs into tactical planning models has not been quantified and evaluated by researchers; and the objective of this paper is to fill this gap in knowledge. To this end, an exact solution approach is used to solve and compare two integrated models: i) a model in which transportation costs are included in the objective function, and b) a model in which transportation costs are excluded from the objective function. The models were applied to three forests ranging in area from 6628 to 19,677 ha.Results show that: i) the model which included transportation costs yielded solutions with major reductions in both transportation and total costs; and ii) that, as the forests to which the model was applied tripled in area (from 6628 ha to 19,677 ha), the percent reduction in total costs increased disproportionately – more than fivefold (from 3.9% to 21%). These results are important, for they indicate that the integration of transportation costs into a tactical planning model is of major economic consequence.

Balancing timber production and habitat conservation of Okinawa Rails (Gallirallus okinawae): Application of a harvest scheduling optimization model in subtropical forest in Okinawa, Japan

Finding the right balance between timber production and the management of forest-dependent wildlife species, present a difficult challenge for forest resource managers and policy makers in Okinawa, Japan. A possible explanation of this can be found in the unique nature of the forest management area which is populated with various kinds of rare and endangered species. This issue has been brought to light as a result of the nomination of northern Okinawa Island in 2018 as a candidate for World Natural Heritage site. The nomination has raised public awareness to the possibility of conflicting management objectives between timber extraction and the conservation of habitat for forest-dependent wildlife species. Managing exclusively for one objective over the other may fail to meet the demand for both forest products and wildlife habitat, ultimately jeopardizing the stability of human and wildlife communities. It is therefore important to achieve a better balance between the objective of timber production and conservation of wildlife habitat. Despite the significance of this subject area, current ongoing discussions on how to effectively manage for forest resources, often lack scientific basis to make sound judgement or evaluate tradeoffs between conflicting objectives. Quantifying the effect of these forest management activities on wildlife habitat provides useful and important information needed to make forest management and policy decisions. In this study we develop a spatial timber harvest scheduling model that incorporates habitat suitability index (HSI) models for the Okinawa Rail (Gallirallus okinawae), an endangered avian species found on Okinawa, Japan. To illustrate how the proposed coupling model assembles spatial information, which ultimately aids the study of forest management effects on wildlife habitat, we apply these models to a forest area in Okinawa and conduct a simple simulation analysis.

A Discussion of Vintage Optimization Models in Forest Economics

Abstract Optimal forest harvesting is a problem that dates back many centuries. Modern forest-management needs models taking into account the relatively long rotation, the multiaged structure, the age-dependent timber content of trees, and the multiple services forests provide. Approaches to characterize the optimal management policy range from models that represent the forest by a unique state variable that can usually be solved analytically (i.e., models that consider forests composed by a unique even-aged stand or allow a uneven aged forest but only consider its total biomass), to much more sophisticated linear and integer programming harvest scheduling models. In this survey, we focus on dynamic optimization problems where the forest is represented with an age-class structure. These models present richer dynamics than one-variable models while preserving their analytic tractability to some extent.

The effective hydrological neighborhood: A new concept to formulate harvest area constraints

Forest managers have struggled to develop several measures to mitigate the impacts of logging operations on soil erosion. Two measures have consisted in considering slope restrictions and limiting the size of clearcut harvest areas in timber harvest scheduling models by means of adjacency constraints. However, these constraints build on an externally predefined limit on harvest area valid to all stands regardless of their topographic features. Thus, we present a methodology to formulate maximum harvest area constraints for each stand on the basis of its topographic features and hydrological connectivity. Using a grid-based digital elevation model, we first introduce the concept of the “Effective Hydrological Neighborhood” and propose a method to compute it through the analyses of water flow directions and the LS topographic factor of the USLE. Then, we develop a recursive procedure to compute for each stand the maximum harvest area in any single period and in consecutive periods of the planning horizon. Finally, we formulate a set of maximum harvest area constraints for each stand. The methodology is applied to a eucalyptus plantation in northwestern Spain. The constraints can then be considered in strategic timber harvest scheduling models along with other constraints. In this way, the harvest plans derived at this planning level can be compatible with later solutions considering hydrological connectivity concerns at the tactical level.

Potential gains from spatially-explicit coordinated planning between two large public ownerships in Minnesota

BackgroundMany forested landscapes throughout the world involve a mix of public forest ownerships. This study explores how coordinated planning between two large public ownerships in Minnesota impact landscape-level trade-offs between timber production and production of core area of older forest (COF) for the region. COF is an important metric for wildlife habitat. Emphasis is on better understanding potential gains from both coordinated planning at the site-level where ownerships share stand boundaries and from coordinated planning at a broader policy level involving assumed values of COF by the public. The study area involves over 300,000 ha, 150,000 analysis units and a 100-year planning horizon.MethodsThe concept of influence zones in modeling spatial interdependencies is described and implemented. The estimated total area of COF is assumed an important landscape metric for forest wildlife habitat condition for each forest planning period. COF has a surrounding buffer protecting it from edge effects. Differences are recognized between COF condition requirements and condition requirements for its surrounding buffer. A spatially-explicit harvest scheduling model is applied in conjunction with moving-windows techniques of GIS to find near-optimal management schedules for the large landscape. Multiple model runs are examined to help better understand both potential gains from coordinated planning and the tradeoffs between timber and COF production.ResultsResults demonstrate the ability to incorporate detailed site-level COF production into management scheduling models for broad, landscape-level planning. For the study area and the assumed COF definitions, substantially larger gains are possible by coordinating COF value assumptions across ownerships, as compared to possible gains from coordinating on-the-ground management activities in areas involving shared stand boundaries. Although a general map of the study area shows a definite intertwining mosaic of ownership by the two large public agencies, a detailed breakdown of influence zone information shows that a low percentage of the land is influenced by both of these ownerships for COF production.ConclusionsThis research helps illuminate potential large gains from coordinated planning at a broad policy level by large public ownerships through coordination of assumed COF values. For the study area, these gains are substantially greater than gains from combined modeling efforts addressing spatial detail and shared stand boundaries or neighborhoods. From a practical standpoint, this is important, as spatial detail adds substantially to model size, making combined analysis a major undertaking. Detailed site-level coordination also presents operational challenges in schedule implementation.

Value-added forest management planning: A new perspective on old-growth forest conservation in the fire-prone boreal landscape of Canada

The maintenance of old-growth stands is important for sustaining natural forest ecosystems, but fire disturbances and commonly-used timber harvest practices exert adverse impacts on the retention of old-growth forests. Forest management planning prescribes harvest levels based on the planning policy and models, but the impact of the management strategies on the retention of old-growth forests has not been well studied. The objectives of this study were to examine: a) the impact of implementing three different harvest policies on the retention of old-growth forest and b) the impact of implementing a policy of maintaining a targeted minimum of 20% old-growth area on the harvest revenue that would be generated over a long planning horizon. To simulate the implementation of these policies, we developed three strategic timber harvest-scheduling models. The first model (Model 1) maximizes harvest timber volume; Model 2 maximizes the net present value (NPV) of the timber harvested; and Model 3 maximizes the NPV of value-added products at the primary processing mills. The value-added products we considered were lumber, chips and sawdust. The models were solved for three forest management units with different fire regimes. Solutions to models that did not include a strict constraint on old-growth forest area retention did not retain the targeted level of old-growth forest over a 150-year planning horizon. When an old-growth constraint was implemented, Model 3 produced the greatest revenue with the least variation by 5-year period over the planning horizon. The probability of finding a feasible solution to our optimization Model 3 with an old-growth forest constraint increased to 0.87–1.0 compared with 0.71–0.83 using Model 1, and 0.78–0.87 using Model 2. We conclude that the value-added policy model increases the probability of sustaining the bioeconomy while preserving forest ecosystems initiated by disturbance.

Formulating the integrated forest harvest-scheduling model to reduce the cost of the road-networks

The integrated harvest-scheduling model addresses the tactical forest management planning problem of maximizing harvest revenues minus road construction and transportation costs. This paper considers the problem of developing innovations to this model such that it can: (1) be used to generate solutions to problem instances containing a large set of candidate roads, with many circuits; (2) yield improved solutions when compared to prior formulations; and (3) achieve improvements in the solutions by reducing the total construction and transportation costs. To the end, a new formulation of the integrated model was developed using the following strategy: (a) each candidate road was represented in the model by two directed arcs (instead of one undirected edge, as used in prior formulations); and (b) a set of strengthening constraints including clique constraint was developed to exploit the property of the directness of the candidate roads. The new model was tested and compared with prior formulations on eight problem instances, ranging in size from 900 to 4900 stands and containing candidate roads ranging in number from 3424 to 19,184. Results show that the new formulation: (1) entails the use of larger set of constraints than prior formulations; (2) produced tighter root-LP gaps, than prior models, as the problem instances grew in size and complexity; and (3) produced solutions with the tightest relative gap, the highest objective function value, and major reductions in the cost of constructing a road network, as the problem instances grew in size and complexity. Our conclusion is that the strategy of formulating the integrated model, used in this paper, may be useful to future researchers and practitioners working on this problem.

The Impact of Assumed Uncertainty on Long-Term Decisions in Forest Spatial Harvest Scheduling as a Part of Sustainable Development

The paper shows how the aspects of uncertainty in spatial harvest scheduling can be embedded into a harvest optimization model. We introduce an approach based on robust optimization that secures better scheduling schematics of the decision maker while eliminating a significant portion of uncertainty in the decisions. The robust programming approach presented in this paper was applied in a real management area of Central Europe. The basic harvest scheduling model with harvest-flow constraints was created. The uncertainty that is assessed here is due to forest inventory errors and growth prediction errors of stand volume. The modelled results were compared with randomly simulated errors of stand volume. The effects of different levels of robustness and uncertainty on harvest-flow were analyzed. The analysis confirmed that using the robust approach for harvest decisions always ensures significantly better solutions in terms of the harvested volume than the worst-case scenarios created under the same constraints. The construction of a mathematical model as well as the methodology of simulations are described in detail. The observed results confirmed obvious advantages of robust optimization. However, many problems with its application in forest management must still be solved. This study helps to address the need to develop and explore methods for decision-making under different kinds of uncertainty in forest management.

A replanning approach for maximizing woodland caribou habitat alongside timber production

We present a forest harvest scheduling model that meets timber harvest targets while maximizing a proxy measure of woodland caribou (Rangifer tarandus caribou (Gmelin, 1788)) habitat based on the configuration of preferred habitat on the landscape. Woodland caribou within the boreal forest region in Canada tend to prefer mature jack pine forest stands, which tend to be rich in their preferred resource, lichen, and also reduce predation pressure. This can create conflict with industrial wood supply needs. We designed a model that can be used to identify good harvest scheduling plans given these competing objectives. Our approach is to use a series of sequential linear programming models that are solved within a replanning framework. Specifically, each individual linear programming model seeks to produce a solution that will meet timber harvest targets while minimizing the harvest of high-quality woodland caribou habitat stands. Stands are assessed with respect to their suitability as woodland caribou habitat based on their contribution to the overall landscape equivalent connected area (ECA), a combined spatial measure of preferred habitat amount and its connectivity. We used our model for a case study of the Trout Lake Forest in northwestern Ontario, Canada, and found that our model creates approximately 10% more caribou habitat than an earlier heuristic procedure and 30% more caribou habitat than the prevailing woodland caribou habitat forest management plan in the Trout Lake Forest while meeting the same timber harvest targets.

長伐期育成循環型人工林の収穫計画・配分モデルについて( 研究発表会)

長伐期育成循環型人工林の収穫計画・配分モデルについて( 研究発表会)

Finding feasible harvest zones in mountainous areas using integrated spatial multi-criteria decision analysis

Terrain conditions, stand structure attributes, and environmental factors are important elements that determine the success of timber harvests. Planning designs for timber harvesting projects must also be physically feasible, environmentally acceptable, and economically viable and address potentially competing objectives upfront in a multi-purpose planning effort. Under mountainous conditions involving highly variable and steep terrain, harvest planning is a particularly complex decision-making process. Here, quantitative (objective) information (e.g., stand volume) is jointly considered with qualitative (subjective) information (e.g., expert judgment of slope failure event and preference value of a certain stand) to arrive at a compromise plan that considers conflicting management objectives. The objective of this paper was to evaluate the existing terrain conditions of a large management area to find zones in which harvest operations can be conducted, assess which portions of the terrain can be harvested by different equipment that is available in the region, and locate landing sites for ground-based skidding operations. The criteria used in this study included quantitative and qualitative elements that were measured/evaluated across different scales. To address this complex decision-making process, we used an integrative approach that combined spatial analyses with multiple-criteria decision analysis (SMCDA). Existing geospatial data were combined with information obtained through pairwise evaluations of environmental, topographic, and stand structure elements to create maps in which the terrain was divided into zones of different suitability classes for timber harvests, placement of landing sites, and deployment of different harvesting systems. The results and assessment of this case study indicate that the methodology has great potential for a more integrated policy, in particular, where multiple spatial objectives explicitly need to be taken into consideration when solving complex forest-management problems in mountainous conditions. One key finding from this work that needs to be further explored involves efficient ways of incorporating this methodology into traditional harvest scheduling models to better support the operational and tactical phases of the timber harvesting.

Spatial considerations of an area restriction model for identifying harvest blocks at commercial forest plantations

Abstract In the past few decades, ecological and environmental issues have dominated the forest industry worldwide, but economic aspects have been much less studied in this dynamic period. However, a sustainable and efficient forest biomass supply is critical for socio-economic development in many regions, particularly in rural areas. Nature protection efforts have contributed to reduced harvesting quotas, which have resulted in an imbalance of the environmental functions of the forests and forest management, particularly wood supply. Considering the size and distribution of forest production management units and the forest stands that compose those units, there is a clear need for improved decision-making tools that help forest managers in planning harvest sequences. The optimization of harvest scheduling should consider economic and spatial factors, which may reduce production costs by increasing the logistic efficiency. Moreover, incorporating maximum harvesting opening size constraints into planning can help preserve biodiversity. This article presents a new spatial harvest scheduling model based on the integer programming method; it was developed using real data from a forest production unit located in the northern part of the southeast region of Brazil. The goal of the proposed scheduling approach is to maximize the net present value and concentrate the harvesting locations in each period. In spite of the fact that the object of the study is plantation forest under management different to common conditions in Europe or North America, the model is flexible and can be used in management of forest in Central Europe.

A model for managing edge effects in harvest scheduling using spatial optimization

ABSTRACTActively managed forest stands can create new forest edges. If left unchecked over time and across space, forest operations such as clear-cuts can create complex networks of forest edges. Newly created edges alter the landscape and can affect many environmental factors. These altered environmental factors have a variety of impacts on forest growth and structure and can alter harvest yields and habitat for wildlife. For example, chances of windthrow and regeneration shading can increase, which in turn can reduce the expected yield of merchantable timber. Additionally, forest edges can compromise interior forest habitat for wildlife and expose sensitive species to harmful processes such as nest predation or parasitism. We introduce a harvest-scheduling model that can keep track of and control the spatiotemporal development of forest edges. This allows the forest resource analyst to put constraints on edge production in an attempt to meet a variety of production and sustainability objectives. To demonstrate the model’s functionality and tractability, we apply it to a case study in the Pacific Northwest region of the United States.

Combining spatiotemporal corridor design for reindeer migration with harvest scheduling in Northern Sweden

ABSTRACTReindeer husbandry and commercial forestry seek to co-exist in the forests of Northern Sweden. As interwoven as the two industries are, conflicts have arisen. Forest practices have reduced the distribution of lichen, the main winter diet for reindeer. Forest practices have also increased forest density, compromising the animals’ ability to pass through forested areas on their migration routes. In an attempt to reduce impacts on reindeer husbandry, we present a spatially explicit harvest scheduling model that includes reindeer corridors with user-defined spatial characteristics. We illustrate the model in a case study and explore the relationship between timber revenues and the selection and maintenance of reindeer corridors. The corridors are not only to include sufficient lichen habitat, but they are also supposed to ensure access for reindeer by connecting lichen areas with linkages that allow unobstructed travel. Since harvest scheduling occurs over a planning horizon, the spatial configuration of corridors can change from one time period to the next in order to accommodate harvesting activities. Our results suggest that maintaining reindeer corridors in harvest scheduling can be done at minimal cost. Also, we conclude that including corridor constraints in the harvest scheduling model is critical to guarantee connectivity of reindeer pastures.

Time Efficiency of Selected Types of Adjacency Constraints in Solving Unit Restriction Models

Spatial restrictions of harvesting have been extensively studied due to a number of environmental, social and legal regulations. Many spatial restrictions are defined by adjacency constraints, for which a number of algorithms have been developed. Research into the unit restriction model (URM) using a branch and bound algorithm focused on decreasing the number of adjacency constraints in harvest scheduling models, since the early solvers have been limited by the number of constraints and integer decision variables. However, this approach can lead to a loss of efficiency in solving mixed integer models. Recent improvements in commercial solvers and personal computers have made the reduction of constraints less relevant, since many solvers now accept an unlimited number of constraints and decision variables. The aim of this paper was to compare the time efficiency of solving unit restriction harvest scheduling models with different types of adjacency constraints using a commercial solver. The presented results indicate that the type of adjacency constraints can have a significant effect on the solving time and therefore could be a crucial factor of the time required for developing forest plans. We note that pairwise adjacency constraints may be sufficient today for addressing unit restriction forest harvest scheduling problems.

Simulating Harvest Schedule for Timber Management and Multipurpose Management in Teak Plantations

Sustainable management of teak plantations in Java requires an improvement of the existing yield regulation method to optimize multiple benefits of the plantations at risk of stand destruction. This study was therefore aimed to formulate an alternative harvest scheduling model that integrates risk of stand destruction for supporting multipurpose management of teak plantations. The proposed model used a state-space planning model to simulate the dynamic of plantations due to timber harvesting and stand destruction, and then sought optimal solutions for two management scenarios, i.e. timber management that optimized total harvest volume and multipurpose management that optimized net present value (NPV) while increasing carbon stocks. Using a case study on a typical teak plantation, this study confirmed that increasing destruction rates reduced harvest volumes, NPV, carbon stocks, and resulted in imbalanced ending age-class structures. Reducing cutting-age limit increased harvest volumes and NPV, but it also reduced carbon stocks of the plantations. Although the multipurpose management generated lower financial benefit, it maintained carbon stocks and produced better ending age-class structures compared to timber management. The proposed harvest scheduling model provides a useful planning tool for managing teak plantations.

Evaluating management tradeoffs between economic fiber production and other ecosystem services in a Chinese-fir dominated forest plantation in Fujian Province

Chinese fir (Cunninghamia lanceolata) is not only a valuable timber species, but also plays an important role in the provision of ecosystem services. Forest management decisions to increase the production of fiber for economic gain may have negative impacts on the long-term flow of ecosystem services from forest resources. Such tradeoffs should be taken into account to fulfill the requirements of sustainable forest management. Here we employed an established, ecosystem-based, stand-level model (FORECAST) in combination with a simplified harvest-scheduling model to evaluate the potential tradeoffs among indicators of provisional, regulating and supporting ecosystem services in a Chinese-fir-dominated landscape located in Fujian Province as a case study. Indicators included: merchantable volume harvested, biomass harvested, ecosystem carbon storage, CO2 fixation, O2 released, biomass nitrogen content, pollutant absorption, and soil fertility. A series of alternative management scenarios, representing different combinations of rotation length and harvest intensity, were simulated to facilitate the analysis. Results from the analysis were summarized in the form of a decision matrix designed to provide a method for forest managers to evaluate management alternatives and tradeoffs in the context of key indicators of ecosystem services. The scenario analysis suggests that there are considerable tradeoffs in terms of ecosystem services associated with stand and landscape-level management decisions. Longer rotations and increased retention tended to favor regulating and supporting services while the opposite was true for provisional services.