Spruce Budworm

Life Cycle Since this research deals with uncertainty focused on natural disturbances, specifically Spruce Budworm (SBW), it is necessary to understand how this event behaves to understand how SBW transition matrix goes from one phase to another. The SBW, Choristoneura funiferana (Clemens), is the most widely destructive forest defoliator in North America. Their massive outbreaks destroy hundreds of thousands of hectares (ha) of valuable forest stands (e.g. Balsam Fir, White Spruce, and Black Spruce) and other softwood species (SOPFIM) (2011). 10 The SBW life cycle spans a single year, one generation per year (see Figure1.3). Normally there are six instars, sometimes even seven or more and it starts with an egg stage during the larval development (moth) consisting of ten days to hatch them. For the first-stage or instar, the female moth lays its eggs in early July on the underside of needles. Then, the larvae molts to the second-stage (overwintering stage); here, the tiny larvae spin silken covers under buds called “hibernacula” and in bark crevices and they stay in the shelter until the following spring. They come out of hibernation and young caterpillars emerge.

Moreover, instead of feeding, they quickly weave a silk cocoon, spending time in it for the next winter months after the first instar (Ministère des Forêts, 2015). During the second-stage, they emerge in early May, just prior to bud expansion. Larvae mine old needles, unopened buds or, when available, staminate flowers. It is suggested that harvesting process is appropriate during this instar as lethal phases are found in first, second and last instar or phase known as the larval or caterpillar phase (Ministère des Forêts, 2015). Later, third and fourth stage, SBW feed on the expanding buds and as the new shoots grow, spin fine silk threads among the needles and between shoots. In epidemic populations, the SBW has consumed the old foliage. Feeding is completed in about five weeks depending on weather conditions. After that, in fifth instar, adults emerge in early July, mate, and lay their eggs. Finally, for the last instar, in July and August, the female lays up to 200 eggs which it leaves in clusters of ten to fifty on the lower side of host tree´s needles, in the upper part of the canopy. The eggs are imbricated forming masses or clusters in the host´s inner surface needle and another SBW life cycle starts again.

The SBW life cycle spans over a single year´s defoliation that has minor impact on the tree. So that over a period equal to one, the harvesting process occurs over the same time. This is the reason why these decisions are considered as tactical planning due to the planning horizon. Also, because the uncertain parameter must be synchronized with the period for a better approach to reality. However, with each year of defoliation, it causes weakening of the tree making it more susceptible to other pests. Defoliation over a few consecutive years causes tree growth loss. However, if defoliation of current-and-previous-year shoots continues uninterrupted over several years, some trees will die, while others will continue to gradually decline for several years, even after the end of the infestation (e.g. Balsam Fir) (NRCAN, 2015). In this first Chapter, we have introduced and described the research problem. The next Chapter will present current studies or/and existing approaches of research methods that have dealt with forest harvest planning with and without uncertainty to compare the existent practices.

Literature Review on Forest Harvest Planning D’Amours, Rönnqvist et Weintraub (2008) explain that the harvest process starts when trees are cut and branches are removed; then the tree is bucked (or cross-out) into logs of specific dimensions and quality. Trees and logs are transported directly to mills or terminals for intermediate storage. This harvesting operation is part of the procurement process of the wood supply chain at the tactical level, according to the matrix for different hierarchical levels in the pulp and paper industry of Carlsson et al. (2006). Also, Figure 2.2 of Troncoso et al. (2015) shows a structure of a simple forest value chain. Here, we will focus only from Part One to Part Two where the area has several forest stands and this is the part where the harvesting process will occur. Once the forest managers treat them, these logs are shipped to different mills. Therefore, harvest planning is considered as the tactical level due to the number of periods over the planning horizon and the type of decisions needed to be taken for forest management. There are several existing approaches that have dealt with forest management and harvest scheduling in a deterministic context, and only a few have dealt with uncertainties like infestation.

D’Amours, Rönnqvist et Weintraub (2008) suggested that for harvesting in tactical planning, Mixed Integer Linear Programming (MIP or MILP) and Stochastic Programming (SP) methods are better to model in the matter of decision-making about at which location and time we should harvest the timber. In general, Rönnqvist (2003) describes that for harvesting, a base model can easily be expanded or changed to include several log-types, storage between periods, crew capacity, road decisions, time constraints and priorities to direct harvesting of areas to specific periods. Rönnqvist (2003) suggests that there should be robust decision support tools based on optimization models and methods to support the forest planning systems. Basic optimization models for forest harvesting considers decisions about which areas to cut, which forest stands, in which per period, what flows to mills, which equipment or crews to use and assign or any attributes that can be added or applied to different models according to each specific context. Other models consider the bucking process as decision variables like Troncoso et al. (2015) who proposes an integrated planning strategy and a generic MIP model to evaluate integrated strategies in the forest value chain by maximizing the Net Value of the forest including decisions of bucking pattern.

The MIP model is implemented in the modelling language AMPL (2003), and CPLEX 11 is used to solve the model and has been applied in different scenarios in a Chilean case. Another approach as in Epstein et al. (2007) includes the basic operational activities related to harvesting, taking into account several characteristics such as quality, length, diameter and delivery. The bucking process tries to obtain as many high-value logs as possible in descending order. The market value will be higher if diameter logs are significantly higher. This approach discusses the total cutting units that we should harvest in each period, technologies, and transportation. In the case of SBW it is similar; if the infestation is higher, the market value of the product is lower, due to the low quality of logs. Therefore, these types of problems should be formulated as Mixed Integer Programming (MIP) models as Rönnqvist (2003) suggests, and when obtained in deterministic context, the results of deterministic models will likely be suboptimal or even infeasible if applied in real life because they do not consider uncertainty. Studies and contributions like Beaudoin, LeBel et Frayret (2007) for detailed tactical model planning, integrate harvesting decisions with a given log distribution, and mills aggregate production planning by allowing wood exchanges between companies with a proposed MIP for a five-year horizon planning.

It manages the wood flow to extract higher value from the logs processed in the mills, through Monte Carlo sampling and probability distribution function for generating scenarios. Also, a sensitivity analysis was applied to find the stochastic parameters. Another example of using MIP for harvesting plan is presented in Karlsson, Rönnqvist et Bergström (2004), who propose a model for an annual harvesting problem compared to the other levels of harvesting planning (see Figure 2.3), including decisions about harvest areas, allocation of crews and transportation. The model is implemented in AMPL language solved with the CPLEX solver by testing the usefulness and comparing the performance of the heuristic procedure. However, when it comes to solving the harvesting models, sometimes it can be complex depending on the model. For example, Vera et al. (2003) uses a Lagrangian relaxation approach for improving the solution process for machinery location problem between towers and skidders in forest harvesting in an MILP model by determining the total amount of timber volume, timber flow, the roads that are going to be built and the location of machinery. Andalaft et al. (2003) introduce a solution approach based on Lagrangian relaxation and a strengthening of the LP formulation of seventeen forests related by demand constraints at the firm level. Andalaft et al. (2003) solved the problem considering deterministic demand and price conditions for each period for log exports, sawmills and pulp plants, and the roads to build for access and storage of timber. The proposed model integrated planning aims to decrease the total cost of different steps of harvesting in the forest to the delivery of logs at the mills. They describe some uncertainties involved in the model.