Operational harvest planning under forest road maintenance uncertainty

Highlights

• Forest road access problem under stochastic model applied at operational level.

• The Monte Carlo simulation technique to guide the randomness effects.

• A proposed delay index has designed to explain the uncertainty effects.

• Road maintenance uncertainty has a significant effect on the wood supply.

Abstract

We solve two related problems: i) the harvest scheduling problem and ii) the forest road maintenance scheduling problem. The main objective is to evaluate the effect of stochastic delays of forest road maintenance on forest harvesting. We built a control scenario to evaluate a deterministic model without road maintenance delay and measured the impacts of the delay through a stochastic programming model and simulations. The example used has 400 stands of planted Pinus sp. managed for pulp production. The considered road network is approximately 570 km. A deterministic programming model was formulated for the forest regulation problem, maximizing the number of harvested stands. A Monte Carlo simulation was applied to generate a random seed disturbance. In the tested instances, the number of stands that would have been harvested according to the deterministic schedule but were not harvested, due to delays in the maintenance of segments of the roads, varied from 1 to 400. The timber volume harvested over the planning horizon varied considerably, with periods in which the value was even zero. The stochastic model proposed can be useful to assist managers in decision making. In addition, the approach may help with road classification and reducing risks for better management practices.

Introduction

Forest roads are essential structures which are planned, designed, and constructed to keep the forest products flowing in the regional economic network (Akay et al., 2020; de Carmo et al., 2013; Rönnqvist et al., 2015; Stefanović et al., 2016). There is a consensus that an efficient forest system needs an optimal design of its road network (Bont et al., 2018; Gumus et al., 2008). However, the wood extraction system and implementation of the road network must have an environmental-economic balance (Jaafari et al., 2015). This network has several daily applications and serves not only for the flow of wood production, but also on firebreaks (Stefanović et al., 2016), social recreational activities (White et al., 2010), and connecting people. However, its main purpose is to guarantee access to the stands throughout the year, ensuring the expansion of logging in inaccessible areas (Akay et al., 2020; Najafi and Richards, 2013), and therefore it must be properly planned (Hayati et al., 2013; Keramati et al., 2020).

Despite widespread agreement about the forest road network, there are still gaps in using mathematical models and computational techniques for solving this problem (Alonso-Ayuso et al., 2018). Several optimization models have been built for solving operational problems in forest science. A quantitative approach to decision making is often a numerical optimization algorithm that uses a deterministic procedure. Generally, the simplex algorithm is suitable for most cases, depending on the nature of the decision variable. Naderializadeh and Crowe (2018) applied a mixed integer-programming model (MIP) for forest harvest scheduling problem examining the road and log transportation operations. da Silva et al. (2016) also developed an integer linear programming model (ILP) to minimize harvesting and road maintenance activities costs. Simonenkova et al. (2020) created an exact clustering algorithm based on linear programming to solving a forest roads network layout optimization problem.

So far, deterministic models have been widely applied for solving diverse forest planning problems (Roise et al., 2016; dos Santos et al., 2019; Simonenkova et al., 2020). However, there has been an ongoing debate about the effect of random changes on the solution. Unfortunately, the process might be more sensitive than was initially thought. Uncertainty is part of stochastic environments such as the wood market price, stand yield stocks, weather conditions, natural disturbances or environmental disasters, and machinery malfunctioning (Álvarez-Miranda et al., 2019; Robinson et al., 2016; Veliz et al., 2015; Verderame et al., 2010).

While deterministic optimization is related to global optima and the certainty of its solutions (Alonso-Ayuso et al., 2018; Daniel et al., 2017), stochastic programming allows the planner to produce more variations in the solution (Alonso-Ayuso et al., 2020; Shabani et al., 2013). Uncertainty in the process is often addressed by probability distribution functions, which narrow the random variable effect (Rönnqvist et al., 2015). In forest road science, many components follow a probability distribution because they might be influenced by factors that are not completely known, such as climatic conditions, traffic loading, and machinery utilization rate (Akay et al., 2018; Costello et al., 2005; Ng et al., 2011). Therefore, a comprehensive understanding of the process uncertainty is desirable for forest decision-making considering the wood supply chain.

In this study, the stochastic process was approached by using the Monte Carlo (MC) method, creating simulations of scenarios. MC simulation is a method broadly used to explore scenarios and take into account uncertainties in the data. This method produces stochastic predictions, since information about the probability distributions of uncertain variables is known (Afanasyeva et al., 2016; Hildebrandt and Knoke, 2011; Kallio, 2010; Kroese et al., 2014). Eyvindson and Kangas (2016) explored the use of stochastic programming to take into account and manage uncertainties in forest management planning and the associated risks. They used the MC process to generate a set of scenarios incorporating the uncertainties caused by inventory measurements and growth modeling errors. Shabani and Sowlati (2016) studied the uncertainty in the supply chain of a forest biomass power plant combining MC Simulation with an optimization model.

The expectation of a hybrid optimization method associating a deterministic and nondeterministic models to solve complex problems has been generated throughout the years (Bakan et al., 2017; Fan et al., 2013; Prabatha et al., 2020). Babonneau et al. (2012) combined stochastic linear programming with MC process to work with uncertainties in climatic policies. Azadeh et al. (2014) applied stochastic linear programming to the biofuel supply chain. They stated that the uncertainties associated with the biofuel supply chain create a large number of parameters, which could impact the overall profitability and design. Aldea et al. (2014) used goal programming to build a model that allowed the inclusion of timber and non-timber objectives. They applied the model in a deterministic scenario and another with MC analysis and found for several criteria notable variations in the MC analysis. The present study aims to evaluate the effect of delays in road maintenance on forest harvesting. This stochastic event was weighted with precipitation, something that is critical during the rainy season. Finally, we sum up the set of solution into an index to robustly and accurately measure these impacts and their trends.