AI-Enabled Flexible Design of Resilient Forest-to-Bioenergy Supply Chains Under Wildfire Disruption Risk

Abstract

The forest-to-bioenergy supply chain is significantly vulnerable to natural disruptions, including wildfires, heavy snowfall, and windstorms. The increased occurrence of these disruptive events has caused severe challenges in forest biomass harvesting and transportation processes, which are difficult to manage. With the need to support decision-makers in designing resilient supply chains (SCs), we propose a Decision Support System (DSS) combining a two-stage stochastic programming framework with various flexibility mechanisms, such as dynamic network reconfiguration and operations postponement. The DSS incorporates an AI-based methodology to identify the most appropriate datasets and resilience metrics, capturing different supply chain dimensions (supply, demand, and operations). This integrated framework supports the selection of effective resilience-enhancing strategies to mitigate large-scale disruptions, with a particular focus on wildfires. The proposed approach is applied in a real case study in Portugal, where the most significant risk factor is wildfires. We perform computational studies and sensitivity analysis to evaluate the applicability and performance of the model and to drive managerial insights. The results show that adopting the model solutions can significantly reduce supply chain logistics and operational costs under more severe disruptive scenarios. Moreover, the results indicate up to a 60% increase in the tons of forest residues that can be removed and processed.

1. Introduction

To mitigate global warming and lower carbon emissions, bioenergy has emerged as a promising solution [1]. Indeed, some European regions use forest biomass as an energy source that supplies over 50% of all renewable energies [2].

Biomass production and collection form the core of the upstream forest-to-bioenergy supply chain, setting the foundation for sustainable bioenergy generation [3]. This critical phase begins with managing and harvesting forest resources, including woody biomass such as timber residues, forest thinnings, and dedicated energy crops [4]. After harvesting, the forest residues are processed by a machine (chipper) into chips, making this biomass suitable for conversion into bioenergy [5]. Efficient transportation logistics are necessary to move the biomass from the forest to the bioenergy facilities, minimizing environmental impact and energy loss [6]. The structure of the upstream segment is characterized by a complex interplay of forest practices, biomass processing, and logistic considerations, all of which must be optimized to create a sustainable and efficient supply chain for bioenergy production [3,6,7].

However, the forest-to-bioenergy supply chain is often affected by disruptive risks rooted in natural and man-made causes such as hurricanes, floods, earthquakes, and wildfires. Among these risks, wildfires raise particular concerns. In the European Mediterranean region, approximately 60,000 fires occur annually, causing, on average, half a million hectares of forest burnt areas [8,9]. These disruptions negatively impact supply chain performance and continuity, increasing the importance of resiliency management [10,11,12].

The importance of enhancing the resilience of the forest-to-bioenergy supply chain cannot be overstated. As the world grapples with an increasing number of disasters, the resilience of this supply chain is crucial for several reasons. First and foremost, a resilient supply chain can better withstand the impacts of extreme weather events [13,14], such as wildfires, storms, or droughts, which can disrupt the availability of forest biomass [15]. Furthermore, a resilient supply chain can adapt to changing environmental conditions and emerging threats, ensuring a continuous and stable source of renewable bioenergy [16]. This resilience also extends to economic stability, as it helps mitigate the risks associated with price fluctuations and market volatility in the bioenergy sector [17]. Investing in strategies that bolster the resilience of the forest-to-bioenergy supply chain can promote sustainable energy production and enhance our capacity to address the pressing challenges of a changing climate [18].

In this context, this paper addresses critical research gaps in supply chain resilience, primarily focusing on three key areas.

Firstly, although previous studies demonstrate the role of flexibility in mitigating risk [19,20], there is a gap in implementing flexibility strategies to achieve a more resilient forest-to-bioenergy supply chain. We specifically focus on the synergistic effects of combining dynamic network reconfiguration with operations postponement because of their expedient and easy adoption within the context of the forestry sector [21].

The second identified gap focuses on risk management models that provide a solution for identified disruptions with a certain probability of occurring. However, disruptive events are, by nature, impossible to predict, so by giving a probability of occurrence, we are biasing the solution provided by the model [22]. The presented definition by Tang [23] categorizes supply chain risks into two main types: operational and disruption risks. The operational risks are rooted in recurrent and inherent uncertainties of a supply chain, such as existing uncertainty in demand, supply, market price, and costs. On the other hand, disruption risks caused by disruption events such as external natural disasters or intentional/unintentional human actions may have undesired influences on the supply chain’s functionality, goals, and performance [24]. We propose an approach combining AI with resilience metrics, in which we only include scenarios of uncertainty that are easily quantifiable to create a supply network capable of responding more quickly and adapting to scenarios of uncertainty and severe disruptions.

Finally, we address a gap related to generating instances in which disruptions occur. Contrary to the literature that presents a set of predefined scenarios in which only parameters vary or interrupt some of the supply chain nodes, we developed an AI-methodology for generating test instances, in which we used a fire simulation model with real data to generate different disruptions. Different disruptive events can occur simultaneously depending on the wildfire’s location and severity. Wildfires cause disruptions, such as a rapid increase in raw material to process, deactivation of bioenergy plants, closure of intermediate nodes for processing and storing biomass, and interruption of operations due to high fire risk or re-ignition.

By conducting a set of systematically designed numerical experiments, together with an empirical analysis based on real data from a third-party logistics provider, we illustrate the impact of adopting flexibility strategies when designing a resilient forest-to-bioenergy supply chain. Our approach proposes an adaptive network design and a supply chain productivity and storage capacity capable of dealing with frequent operational uncertainties while simultaneously mitigating severe disruptive events.

The major contributions of this paper can be summarized as follows:

• A novel resilient two-stage stochastic mixed-integer model is proposed for upstream planning of the forest-to-bioenergy supply chain. This incorporates flexibility strategies exploring a multi-objective approach that maximizes profit and resilience.
• A replicable AI-methodology that allows us to generate and select the best set of uncertainty scenarios to consider in the stochastic model and evaluate which resilience metrics best adapt to the characteristic disruptions of this supply chain.
• The proposed approach is implemented in a real-life case study of a company in Portugal. It allows us to reconfigure the network design and indicate investment decisions based on uncertain scenarios, making the supply chain more resilient and responsive to disruptive events that arise from a wildfire simulation model.
• Derived managerial and practical insights support the decision-making process of forest-to-bioenergy supply chain design under uncertainty and disruptions.

The remainder of the paper is structured as follows. Section 2 reviews the literature regarding disruptions and resilience approaches in forest-to-bioenergy supply chains and contextualizes our work. Section 3 presents the mathematical formulation of our two-stage stochastic model, including resilience metrics. Section 4 describes the methodology to implement the model. Section 5 presents the case study and computational experiments performed in different disruptive scenarios with close-to-reality instances from a forest-to-bioenergy supply chain in Portugal. The managerial insights and conclusions are presented in Section 6.

2. Background Literature

2.1. Forest-to-Bioenergy Supply Chain

The bioenergy industry has to deal with challenges related to low energy density, high harvest, and biomass transportation costs to compete with fossil energy [25]. Consequently, the competitiveness of the forest-to-bioenergy supply chain depends mainly on optimizing network design to minimize transport costs and operations costs [26]. The cost associated with the forest-to-bioenergy supply chain is correlated with the complexity and the number of interactions among its diverse processes and internal and external entities or drivers, such as municipal councils, forest conservation institutes, companies involved in the production of wood and wood pulp, forest owners and logistics operators [27]. This supply chain (SC) comprises a set of operations that include land allocation, planting, harvesting, chipping, storage, and transportation to energy generation at bioenergy centres [3,28,29].

Players upstream of the forest-to-bioenergy supply chain have to deal with an additional challenge: managing fuel loads, which increases the complexity of planning operations and all the flows involved, from materials, people, and products to be processed. The correct forest management encompasses the trade-off between environmental concerns and the economic development of those who live in areas influenced by these spaces. Reducing fuel loads while actively removing forest residues can contribute to achieving this objective.

Kauffman et al. [30] report that the continuity of the live vegetation in the unmanaged forest stands and intensive plantation forestry characterized by young forests and spatially homogenized fuels are the most significant drivers of wildfire severity. Controlling fuel loads contributes to minimizing the occurrence of, and area burned by, severe wildfires in many regions across the globe [29,30,31,32]. Minas et al. [33] alert to the importance of planning fuel load activities that become complex decision-making problems with spatial and temporal dimensions.

Forest-to-bioenergy supply chain exhibits distinct characteristics, featuring a network of supply nodes where chippers (the equipment responsible for converting forest residues into biomass) are deployed to carry out their operations. Biomass is then transported to delivery nodes via trucks. Nevertheless, many of these supply nodes pose challenges, including limited accessibility, prolonged setup times, necessity for site preparation, variable and heterogeneous raw material availability, and disparities in productivity among different regions [34]. Additionally, chipping operations are influenced by site-specific factors, weather conditions, and fluctuations in forest harvesting rates throughout the year [6,35].

The spatial and temporal unpredictability regarding raw material availability significantly impacts supply chain design and planning, necessitating the adoption of strategies to mitigate this uncertainty. Supply chain flexibility is a practical mitigation approach to respond to forest-to-bioenergy uncertainty. It is defined by Sánchez and Pérez [36] as the capacity to adapt or respond to diversity and uncertainty with minimal penalties in terms of time, effort, cost, or performance, ultimately enhancing a company’s competitiveness to do so.

Flexibility strategies such as dynamic network reconfiguration [37] and operations postponement [38,39] allow us to adapt the supply chain design and operations in real-time based on the current availability of resources. These flexibility strategies contribute to achieving economies of scale and reduce operational costs. The strategy of dynamic network reconfiguration entails managing temporary intermediate nodes by opening or closing them throughout a specific timeframe (e.g., Sanci and Daskin [40]), with adjustments made to the number and location of these storage nodes based on raw material availability. This primary flexibility strategy can be complemented by postponing operations (e.g., Jabbarzadeh et al. [41]). In the SC of forest-to-bioenergy, chipping operations are important activities that can be delayed from supply nodes to intermediate nodes to address temporal variations in the supply of raw materials. Such strategies play a crucial in creating resilience in the forest-to-bioenergy SC, and so are going to be explored within this work.

2.2. Sources of Risk and Uncertainty in the Forest

In the context of the forest-to-bioenergy supply chain, challenges arise from seasonal biomass availability, fluctuations in biomass quality, diverse geographical distributions of feedstock, and varying customer demand [42]. The impact of hazardous events, determined by their severity, frequency, and consequences, significantly affects SC performance, leading to potential losses and disruptions [43,44]. Combining these uncertainties with possible disruptions and market dynamics contributes to the heightened complexity of this supply chain [27].

Forests are affected by wildfires, storms, diseases, and other disruptive events. Wildfires are a phenomenon that affects ecosystems, destroys homes and infrastructure, and endangers the lives of populations [45,46,47]. These hazards are enhanced by climate change and tend to become more frequent, more prolonged, and more severe [15,48]. It is imperative to improve how society deals with wildfires, namely its prevention planning by land managers, affected companies and political agents to minimize the long-lasting effects of these occurrences [49,50].

Some studies suggested that climate change can increase the area burned, the length of the fire season, the intensity, and the severity of the fire, and they predicted that the amount of burned area could increase by 74–118% by the end of the century [51].

Although forest wildfires are high-impact events, their occurrence is always uncertain. Therefore, an effective forest-to-bioenergy SC is an essential element in wildfire management since it can have a positive impact as a preventive/proactive and reactive measure. Decreasing the amount of fuel can help prevent a rapid fire progression. On the other hand, after a fire, a large amount of forest residue is available to be transformed into biomass since it is no longer used for the wood or paper pulp industry. The timely removal of residues is of utmost importance to prevent the onset of diseases in burned areas and the accumulation of seeds, which could result in a more dense and disorganized forest with an increased likelihood of future wildfires [29,30]. As “a resilient supply chain should be able to prepare, respond and recover from disturbances and afterward maintain a positive steady-state operation at an acceptable cost and time” [22], investigating and enhancing resilient forest-to-bioenergy supply chains is essential, considering the potential consequences of failure.

2.3. Risk Mitigation Approaches to Achieve a Resilient Biomass-to-Bioenergy Supply Chain

Recent studies have shown that using operations research techniques can improve the resilience of biomass supply chains in the face of unpredictable events [52]. For example, [53] developed a stochastic optimization model to determine biomass processing plants’ optimal location and capacity considering feedstock supply seasonality and facility disruptions. However, this work followed a traditional supply chain risk management approach by associating the disruptions with probabilities.

In line with the previous study, Maheshwari et al. [54] highlight the importance of considering disruptions like floods and equipment failures in the biomass-to-biofuel supply chain design, especially for capital-intensive components like intermediate nodes. The study introduces an optimization model incorporating disruption probabilities, demonstrating that optimizing intermediate node locations can reduce expected disruption costs by up to 38%. The results vary based on disruption intensity and feedstock type, emphasizing the significance of local factors such as yield and biomass price and highlighting the role of flexible network design in enhancing supply chain resiliency.

Ref. [55] also developed an optimization model for a biomass-to-biofuel supply chain integrating flexible network design, focusing on resilience against disruptions. The model incorporates risk-averse optimization, transitional probabilities, and spatial statistics to address uncertainties in demand and raw material availability. The results showed that increasing the conversion rate of biomass to biofuel by 20% led to a substantial rise in biofuel production and a decrease in supply chain costs due to improved biorefinery capacity distribution. However, the study found that the proposed resilient model incurred higher total supply chain costs under random disruptions, although the failure costs decreased significantly.

Also on supply chain design, Soren and Shastri [16] introduce an optimization model for the design of a biomass-to-energy system, taking into account potential disruptions in biomass supply. The supply chain comprises farms, regional biomass re-processing depots, and biorefineries. Disruptions, such as drought, are characterized by varying probabilities and levels of impact across different locations. Penalties are incurred for fuel production shortfalls and short-term feedstock procurement. The model includes mass balance equations as constraints, and decision variables encompass design choices (biorefinery and regional biomass re-processing depots’ locations and capacities) and operational decisions (feedstock flows). The objective function aims to minimize the probability-weighted sum of costs under ideal and disrupted scenarios. In a case study involving 443 farms, 16 potential re-processing depots, and five potential biorefinery locations, the results are compared with a model that neglects disruptions. The proposed model demonstrates a notable reduction of up to 7.6% in actual costs.

In all these studies, flexibility strategies for network design are presented. When coupled with the forest-to-bioenergy supply chain specifications, the network design reconfiguration strategy offers an alternative approach to the conventional biomass processing method at forest sites. This alternative involves introducing intermediate nodes in the supply chain dedicated to storage and biomass processing. This flexibility strategy, known as operations postponement according to Budiman and Rau [38], de Keizer et al. [39], Jabbarzadeh et al. [41], Kisperska-Moron and Swierczek [56], Li et al. [57], Wong et al. [58], Saghiri and Barnes [59], Budiman and Rau [60], Sarkar et al. [61], involves deferring biomass processing, transporting forest residues from the sites to these intermediate nodes, and conducting the processing there. There is a gap in studies that combine flexibility in network design with operations postponement to achieve more resilient supply chains.

In addition to this gap in risk mitigation strategies, in all these studies, the optimization model provides a solution for a set of identified disruptions with a certain probability of occurring. However, disruptive events are, by nature, impossible to predict, so by giving a probability of occurrence, we are biasing the solution provided by the model. We propose to overcome this drawback by developing an approach using resilience metrics, similar to the study by [62], in which we only include scenarios of uncertainty that are easily quantifiable to create a supply chain capable of responding more quickly and adapting not only to scenarios of uncertainty but also to severe disruptions.

In this setting, generating instances involving disruptive events poses a significant challenge when creating models to assess resilience. Salehi et al. [52], Fattahi and Govindan [63], Ahranjani et al. [64], in order to enhance resilience against uncertainties and disruptions that solely occur at a specific node within the supply chain, use a hybrid approach that combines robust stochastic and possibilistic programming methods to achieve a reduction in costs and greenhouse gas emissions when compared to other techniques that do not include resilience. On the other hand, Liu et al. [53], Sharifi et al. [65], Zhao and You [66] quantify resilience by introducing variability in specific stochastic parameters while generating test instances.

The present study uses a methodology to define scenarios that assess the resilience of the forest-to-bioenergy supply chain based on a fire simulation model that generates instances with disruptive events. Disruptions arise from wildfires and can occur in isolation, or we can have several instances of disruptions simultaneously. According to the research developed by Szpakowski et al. [49], depending on the location and severity of the wildfires, we have disruptions such as the sudden increase in biomass to process (supply disruptions), closure of bioenergy plants (demand disruptions), closure of intermediate nodes (disruptions in capacity), and interruption of forest operations due to the high risk of fire or re-ignition (disruptions in operations). These disruptive events will be incorporated into test instances that we present in the computational experiments section.

3. Problem Statement and Mathematical Formulations

3.1. Problem Characterization

The problem studied here involves long-term decisions that impact network design and production and storage capacity. Decisions regarding network architecture hinge on the dynamic reconfiguration strategy, specifically determining which intermediate storage facilities to activate and their respective capacities. Production investment decisions are based on acquiring more machines and are related to the operations postponement strategy. The postponement of chipping operations from several small supply nodes to large intermediate nodes results in a gain in efficiency associated with economies of scale and reduced deployment and set-up costs. This problem combines these long-term decisions with tactical decisions regarding machine allocation, working hours, processes flows, and stocking levels, while considering uncertainty and the occurrence of disruptions.

Key strategic choices within the model focus on acquiring new chipping equipment and establishing fresh intermediate hubs for biomass reception and storage. These decisions are not independent; rather, they interact synergistically to enhance the overall resilience of the supply chain when facing unexpected disruptive events.

In the occurrence of a wildfire that consumes a large forest area, a substantial and sudden influx of biomass becomes available within a short time frame. Under such conditions, increasing both the number of processing units (chippers) and the number of reception intermediate nodes significantly enhances the system’s response capacity. Additional intermediate nodes improve spatial accessibility and reduce transportation bottlenecks, while increased processing capacity allows faster conversion of raw biomass into usable feedstock.

Together, these strategic decisions enable the supply chain to absorb shocks more effectively, reduce congestion and delays, and maintain operational continuity under extreme conditions. Consequently, their combined implementation directly contributes to improving the robustness and resilience of the biomass supply chain in the face of disruptive wildfire events.

Figure 1 illustrates the structure and flows considered, the sources of uncertainty present in the forest-to-bioenergy supply chain and the possible disruptions that affect different nodes of the network design. The uncertainties in this problem are modeled as stochastic parameters and arise from the difficulty in estimating the quantity of raw material available to process, breakdowns affecting machines’ availability and productivity, variability in demand, and short periods without operations due to breakdowns (in yellow). The disruptions under study (in red) are the closure of bioenergy centres, which drastically affects demand; the closure of intermediate nodes, which affects the storage capacity; the interruption of forest operations for several consecutive days, which affects production capacity; and the sharp and sudden increase in raw material. Wildfires trigger all of these disruptions and are not independent events. They can occur in isolation or in a combination of these disruptions simultaneously.

In green, the figure shows the possible machine allocations without and with operations postponement. In orange, it illustrates the decision to open the intermediate nodes, a new echelon that could serve as a stockyard and location for processing when the machines are allocated there. The strategic decisions of the number and productivity of machines to be used and the location, number, and capacity of intermediate nodes to open play a fundamental role in the resilience of this supply chain. The problem in this study can be described as:

Given:

• An existing SC network.
• Possible intermediate nodes to include in the SC.
• Availability of raw material.
• Alternative machines to be used.
• Machines productivity.
• Intermediate nodes storage capacity.
• Demand in bioenergy centres.
• Intermediate nodes’ capacity.
• A cost structure (intermediate nodes, machines, transports, working hours).
• Supply variability.
• Demand prices.
• Representative uncertainty and disruptions.
• A multi-period time frame.

Determine:

• The SC network design.
• Logistic flows.
• Processing and storage levels.
• Investments in capacity upgrades (new machines) and new intermediate nodes.
• Operations postponement.

So as to:

• Maximise the expected Net Present Value.
• Maximise the SC resilience metric.
• Provide insights about the role of flexibility in building a more resilient SC.

In the next section, we present the mathematical model developed that stems from this problem characterization. The model supports decision-making by aligning resilience with investment and logistic costs.

3.2. Model Description

This section outlines the modeling approach to the problem, including all the necessary aspects to obtain a realistic solution to this supply chain’s design. We formulate the problem with two objective functions. The primary objective function focuses on profit maximization via Net Present Value (NPV), calculated as the variance between the present value of cash inflows and outflows over a specific planning horizon. The second objective function maximizes resilience. Additionally, uncertainty is considered, as well as a two-stage stochastic problem with fixed recourse.

We select a set of supply nodes to meet the demand of delivery nodes. We include a new echelon that can store processed material from supply nodes. The model encompasses decision variables such as where to process (supply nodes or intermediate nodes), when to process, for how long, and which machine is allocated to perform these operations (Figure 2). First-stage decisions related to the opening of intermediate nodes and selection of machines are highlighted in gray in Figure 2.

The proposed model generates daily operational schedules, assigning machinery to specific supply points to process sufficient raw material to meet monthly delivery targets. In this supply chain, the delivery nodes are bioenergy centres that burn biomass to generate electricity. These daily plans provide the hours worked by each machine, the flows of processed and unprocessed material, and stock decision variables that guarantee the conservation of flows over time.

In addition, we have parameters related to the availability of the material in supply nodes and the demand in delivery nodes. We adopted two time scales, months and days, to have these two decision levels in the same model. The short-term decisions are integrated into medium-term decisions to ensure model feasibility.

The mathematical formulation of this two-stage stochastic mixed integer programming (MIP) model is presented below. The decision variables, sets, and parameters are presented first, followed by the objective function and the model constraints.

• Sets:

$$\begin{array}{cccc}\hfill & \hfill & \hfill P& \mathrm{set}\mathrm{of}\mathrm{supply}\mathrm{nodes}\hfill \\ \hfill & \hfill & \hfill M& \mathrm{set}\mathrm{of}\mathrm{delivery}\mathrm{nodes}\hfill \\ \hfill & \hfill & \hfill O& \mathrm{set}\mathrm{of}\mathrm{intermediate}\mathrm{nodes}\hfill \\ \hfill & \hfill & \hfill N& \mathrm{set}\mathrm{of}\mathrm{destination}\mathrm{nodes},N=O\cup M\hfill \\ \hfill & \hfill & \hfill S& \mathrm{set}\mathrm{of}\mathrm{processing}\mathrm{nodes},S=P\cup O\hfill \\ \hfill & \hfill & \hfill A& \mathrm{set}\mathrm{of}\mathrm{possible}\mathrm{arcs},A=\{(i,j,l):[i\in P\wedge j\in O\cup M\wedge l\in L^t]\vee [i\in O\wedge \hfill \\ \hfill & \hfill & \hfill & j\in M\wedge l\in L^t\left]\right\}\hfill \\ \hfill & \hfill & \hfill K& \mathrm{set}\mathrm{of}\mathrm{machines}\hfill \\ \hfill & \hfill & \hfill I& \mathrm{set}\mathrm{of}\mathrm{possible}\mathrm{allocations},I=\{(k,i,l):[k\in K\wedge i\in S\wedge l\in L^t]\}\hfill \\ \hfill & \hfill & \hfill T& \mathrm{set}\mathrm{of}\mathrm{time}\mathrm{macro}-\mathrm{periods}\left(\mathrm{months}\right)\hfill \\ \hfill & \hfill & \hfill L^t& \mathrm{set}\mathrm{of}\mathrm{time}\mathrm{micro}-\mathrm{periods}\left(\mathrm{days}\right)\mathrm{of}\mathrm{a}\mathrm{macro}-\mathrm{period}t\in T\hfill \\ \hfill & \hfill & \hfill C& \mathrm{set}\mathrm{of}\mathrm{scenarios}\hfill \end{array}$$

• Parameters (deterministic):

$$\begin{array}{cc}\hfill b_o& \mathrm{storage}\mathrm{capacity}\mathrm{at}\mathrm{intermediate}\mathrm{node}o\in O\left(\mathrm{ton}\right)\hfill \\ \hfill \psi & \mathrm{productivity}\mathrm{conversion}\mathrm{ratio}\hfill \\ \hfill d_{ij}& \mathrm{travel}\mathrm{distance}\mathrm{when}\mathrm{traversing}\mathrm{arc}(i,j)\in A\left(\mathrm{km}\right)\hfill \\ \hfill \gamma & \mathrm{conversion}\mathrm{ratio}\mathrm{of}\mathrm{the}\mathrm{transport}\mathrm{capacity}\mathrm{of}\mathrm{a}\mathrm{truck}\mathrm{with}\mathrm{unprocessed}\mathrm{material}\hfill \\ \hfill q& \mathrm{transport}\mathrm{capacity}\mathrm{of}\mathrm{a}\mathrm{truck}\mathrm{with}\mathrm{processed}\mathrm{material}\left(\mathrm{ton}\right)\hfill \\ \hfill {\alpha }_{ki}& \mathrm{hourly}\mathrm{working}\cos \mathrm{t}\mathrm{for}\mathrm{machine}k\in K(€)\mathrm{at}\mathrm{location}i\in S\hfill \\ \hfill s& \mathrm{truck}\mathrm{distance}\cos \mathrm{t}(€/km)\hfill \\ \hfill \omega & \mathrm{last}\mathrm{time}\mathrm{period}\hfill \\ \hfill c_k& \cos \mathrm{t}\mathrm{of}\mathrm{selecting}\mathrm{machine}k\in K(€)\hfill \\ \hfill {\sigma }_o& \mathrm{monthly}\cos \mathrm{t}\mathrm{of}\mathrm{keeping}\mathrm{an}\mathrm{intermediate}\mathrm{node}\mathrm{open}o\in O(€)\hfill \\ \hfill {\beta }_i& \cos \mathrm{t}\mathrm{of}\mathrm{deploying}\mathrm{to}\mathrm{location}i\in S(€)\hfill \\ \hfill e_m& \mathrm{price}\mathrm{paid}\mathrm{per}\mathrm{ton}\mathrm{of}\mathrm{biomass}\mathrm{delivered}\mathrm{to}\mathrm{the}\mathrm{delivery}\mathrm{node}m\in M(€)\hfill \end{array}$$

• Parameters (stochastic):

$$\begin{array}{cc}\hfill a_{\rho tc}^{\prime }& \mathrm{availability}\mathrm{of}\mathrm{raw}\mathrm{material}\mathrm{in}\mathrm{supply}\mathrm{node}p\in P\left(ton\right)\mathrm{in}\mathrm{macro}-\mathrm{period}t\in T\hfill \\ \hfill & \mathrm{in}\mathrm{scenario}c\in C\hfill \\ \hfill a_{ptc}& ={\displaystyle \sum _{t^{\prime }\in T:t^{\prime }\le t}}{a}_{ptc}^{\prime }\mathrm{cumulative}\mathrm{availability}\mathrm{of}\mathrm{raw}\mathrm{material}\mathrm{in}\mathrm{supply}\mathrm{node}p\in P\left(ton\right)\hfill \\ \hfill & \mathrm{in}\mathrm{macro}-\mathrm{period}t\in T\mathrm{in}\mathrm{scenario}c\in C\hfill \\ \hfill g_{mtc}& \mathrm{demand}\mathrm{of}\mathrm{processed}\mathrm{material}\mathrm{at}\mathrm{delivery}\mathrm{node}m\in M\left(ton\right)\mathrm{in}\mathrm{macro}-\mathrm{period}t\in T\hfill \\ \hfill & \mathrm{in}\mathrm{scenario}c\in C\hfill \\ \hfill {\tau }_{lc}& \mathrm{total}\mathrm{working}\mathrm{time}\mathrm{per}\mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{days}\right)\hfill \\ \hfill r_{kc}& \mathrm{machine}\mathrm{productivity}k\in K\mathrm{in}\mathrm{scenario}c\in C(\mathrm{ton}/\mathrm{h})\hfill \\ \hfill p_c& \mathrm{probability}\mathrm{of}\mathrm{occurrence}\mathrm{of}\mathrm{scenario}c\in C\hfill \end{array}$$

• Decision variables for identifying the strategy (first stage):

$$\begin{array}{cc}\hfill y_o& \left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{intermediate}\mathrm{node}o\in O\mathrm{is}\mathrm{open};\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \\ \hfill q_k& \left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{machine}k\in K\mathrm{is}\mathrm{used};\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \end{array}$$

• Decision variables to evaluate strategy decisions (second stage):

$$\begin{array}{cc}\hfill x_{kilc}& \left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{machine}k\in K\mathrm{is}\mathrm{present}\mathrm{at}\mathrm{location}i\in S\mathrm{in}\mathrm{micro}-\mathrm{period}l\in L^t\hfill \\ \hfill & \mathrm{in}\mathrm{scenario}c\in C;\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \\ \hfill z_{kilc}& \left\{\begin{array}{cc}1\hfill & \mathrm{if}\mathrm{machine}k\in K\mathrm{was}\mathrm{deployed}\mathrm{at}\mathrm{location}i\in S\mathrm{in}\mathrm{micro}-\mathrm{period}l\in L^t\hfill \\ \hfill & \mathrm{in}\mathrm{scenario}c\in C;\hfill \\ 0\hfill & \mathrm{otherwise}.\hfill \end{array}\right.\hfill \\ \hfill f_{ijlc}& \mathrm{flow}\mathrm{of}\mathrm{processed}\mathrm{material}\mathrm{traversing}\mathrm{arc}(i,j)\in A\mathrm{in}\mathrm{micro}-\mathrm{period}l\in L^t\hfill \\ \hfill & \mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{ton}\right)\hfill \\ \hfill e_{polc}& \mathrm{flow}\mathrm{of}\mathrm{raw}\mathrm{material}\mathrm{from}\mathrm{supply}\mathrm{node}p\in P\mathrm{to}\mathrm{intermediate}\mathrm{node}o\in O\mathrm{in}\hfill \\ \hfill & \mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{ton}\right)\hfill \\ \hfill r_{omlc}& \mathrm{flow}\mathrm{of}\mathrm{processed}\mathrm{material}(\mathrm{in}\mathrm{supply}\mathrm{node}p\in P)\mathrm{from}\mathrm{intermediate}\mathrm{node}\hfill \\ \hfill & o\in O\mathrm{to}\mathrm{delivery}\mathrm{node}m\in M\mathrm{in}\mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{ton}\right)\hfill \\ \hfill h_{kilc}& \mathrm{number}\mathrm{of}\mathrm{hours}\mathrm{worked}\mathrm{by}\mathrm{machine}k\in K\mathrm{at}\mathrm{location}i\in S\mathrm{in}\mathrm{micro}-\mathrm{period}\hfill \\ \hfill & l\in L^t\mathrm{in}\mathrm{scenario}c\in C\hfill \\ \hfill h_{kilc}^{extra}& \mathrm{number}\mathrm{of}\mathrm{extra}\mathrm{hours}\mathrm{worked}\mathrm{by}\mathrm{machine}k\in K\mathrm{at}\mathrm{location}i\in S\mathrm{in}\hfill \\ \hfill & \mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\hfill \\ \hfill s_{olc}& \mathrm{quantity}\mathrm{of}\mathrm{unprocessed}\mathrm{material}\mathrm{at}\mathrm{intermediate}\mathrm{node}o\in O\mathrm{in}\mathrm{the}\mathrm{end}\mathrm{of}\hfill \\ \hfill & \mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{ton}\right)\hfill \\ \hfill v_{olc}& \mathrm{quantity}\mathrm{of}\mathrm{processed}\mathrm{and}\mathrm{stored}\mathrm{material}\mathrm{in}\mathrm{intermediate}\mathrm{node}o\in O\hfill \\ \hfill & \mathrm{in}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{ton}\right)\hfill \\ \hfill w_{olc}& \mathrm{quantity}\mathrm{of}\mathrm{processed}\mathrm{material}\mathrm{in}\mathrm{supply}\mathrm{node}p\in P\mathrm{stored}\mathrm{in}\mathrm{intermediate}\hfill \\ \hfill & \mathrm{node}o\in O\mathrm{in}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{micro}-\mathrm{period}l\in L^t\mathrm{in}\mathrm{scenario}c\in C\left(\mathrm{ton}\right)\hfill \end{array}$$

The model incorporates two first-stage decisions involving strategic decisions that cannot be changed throughout the planning horizon. One of the decisions relates to network design, which is the opening of intermediate nodes, which requires the preparation of a contract and an amount paid annually. The other decision is an investment decision and is linked to the acquisition of more machines to process biomass (the chippers).

In addition to deterministic parameters, this problem is modeled using stochastic parameters directly related to the uncertainty scenarios generated. These stochastic parameters encompass variability in demand, variability in supply, variability in machine productivity, and variability in the maximum limit of working hours per day.

The objective function of this stochastic model comprises a resilience metric with two distinct components: profit maximization and resilience maximization. The first component is formulated by the equations $NP{V}_{ref}$ and $NP{V}_c$. $NP{V}_{ref}$ (the reference net profit value) comprises revenues and costs for a baseline scenario without uncertainty, whereas $NP{V}_c$ varies according to the uncertainty scenario generated. This is decomposed by Equations (1c), (1d), (1e), (2c), (2d), (2e), which corresponds to the costs of transporting processed and unprocessed material between the different nodes. Equations (1f), (2f), (1g) and (2g) correspond to the cost of opening intermediate nodes and the cost of machines used respectively. Equations (1h) and (2h) correspond to the cost of deploying the machine in a given location. Finally, Equations (1i) and (2i) concern the minimization of processing costs, which depends on the working hours of each machine. The revenue without and with uncertainty is given respectively by Equations (1b) and (2b), which correspond to the biomass delivered to the bioenergy plants.

Maximizing resilience is integrated into the second objective function through resilience metrics. These metrics relate profit to a set of uncertainty scenarios with specific objectives for each metric that relate to the uncertainty that is intended to be mitigated. We independently evaluate three different resilience metrics ($R{M}_{supply}$, $R{M}_{demand}$, $R{M}_{operations}$) in the objective function. In the section dedicated to computational experiments, the results of adopting each of these metrics will be presented. The solution given by each of these metrics is dependent on the uncertainty scenarios to be incorporated into the model. On the other hand, these metrics prepare the entire supply chain to respond more quickly to uncertainty and be more responsive to disruptive events.

• Objective Function

$$\begin{array}{}\mathrm{(1a)}& \hfill \left[NP{V}_{ref}\right]& \mathrm{(1b)}& & \sum _{(o,m,l)\in A}{e}_m·(f_{oml}+r_{oml})\hfill \mathrm{(1c)}& & -(\sum _{(i,j,l)\in A}{\displaystyle \frac{d_{ij}·s·f_{ijl}}{q}}\hfill \mathrm{(1d)}& & +\sum _{(p,o,l)\in A:[p\in P\wedge o\in O]}{\displaystyle \frac{d_{po}·s·e_{pol}}{q·\gamma }}\hfill \mathrm{(1e)}& & +\sum _{(o,m,l)\in A:\lceil o\in O\wedge m\in M]}{\displaystyle \frac{d_{om}·s·r_{oml}}{q}}\hfill \mathrm{(1f)}& & +\sum _{o\in O}{\sigma }_o·y_o\hfill \mathrm{(1g)}& & +\sum _{k\in K}{c}_k·q_k\hfill \mathrm{(1h)}& & +\sum _{(k,i,l)\in I}{\beta }_i·z_{kil}\hfill \mathrm{(1i)}& & +\sum _{(k,i,l)\in I}{\alpha }_{ki}·(h_{kil}+hextr{a}_{kil}))\hfill \end{array}$$

$$\begin{array}{}\mathrm{(2a)}& \hfill \left[NP{V}_c\right]& \mathrm{(2b)}& & \sum _{(i,m,l,c)\in A}{p}_c·e_m·(f_{imlc}+r_{imlc})\hfill \mathrm{(2c)}& & -(\sum _{(i,j,l,c)\in A}{p}_c·{\displaystyle \frac{d_{ij}·s·f_{ijlc}}{q}}\hfill \mathrm{(2d)}& & +\sum _{(p,o,l,c)\in A:[p\in P\wedge o\in O]}{p}_c·{\displaystyle \frac{d_{po}·s·e_{polc}}{q·\gamma }}\hfill \mathrm{(2e)}& & +\sum _{(o,m,l,c)\in A:\lceil o\in O\wedge m\in M]}{p}_c·{\displaystyle \frac{d_{om}·s·r_{omlc}}{q}}\hfill \mathrm{(2f)}& & +\sum _{o\in O}{\sigma }_o·y_o\hfill \mathrm{(2g)}& & +\sum _{k\in K}{c}_k·q_k\hfill \mathrm{(2h)}& & +\sum _{(k,i,l,c)\in I}{p}_c·{\beta }_i·z_{kil,c}\hfill \mathrm{(2i)}& & +\sum _{(k,i,l,c)\in I}{p}_c·{\alpha }_{ki}·(h_{kilc}+hextr{a}_{kilc}))\hfill \end{array}$$

$$\begin{array}{}\mathrm{(3a)}& \hfill ResilienceMetri{c}_{supply}& \mathrm{(3b)}& & max\sum _{c\in C}{p}_c{\displaystyle \frac{NP{V}_c}{NP{V}_{ref}}}-{\displaystyle \frac{{\sum }_{(k,o,l,c)\in I}{p}_c·s_{olc}}{{\sum }_{p\in P\wedge t\in T\wedge c\in C}{p}_c·a_{\rho tc}^{\prime }}}\hfill \end{array}$$

$$\begin{array}{}\mathrm{(4a)}& \hfill ResilienceMetri{c}_{demand}& \mathrm{(4b)}& & max\sum _{c\in C}{p}_c{\displaystyle \frac{NP{V}_c}{NP{V}_{ref}}}-{\displaystyle \frac{{\sum }_{(k,o,l,c)\in I}{p}_c·(v_{olc}+w_{olc})}{{\sum }_{m\in M\wedge t\in T\wedge c\in C}{p}_c·g_{mtc}}}\hfill \end{array}$$

$$\begin{array}{}\mathrm{(5a)}& \hfill ResilienceMetri{c}_{operations}\mathrm{(5b)}& & max\sum _{c\in C}{p}_c{\displaystyle \frac{NP{V}_c}{NP{V}_{ref}}}-\sum _{(k,i,l,c)\in I}{p}_c·{\displaystyle \frac{hextr{a}_{kilc}}{h_{kilc}}}\hfill \end{array}$$

$NP{V}_{ref}$ provides the deterministic $NPV$ where no uncertainty is considered. $NP{V}_c$ is the $NPV$ considering the existence of uncertainty, and then 3 resilience metrics are defined. The first resilience metric (Equation (3b)) maximizes $NPV$ and minimizes the quantity of unprocessed material. The second resilient metric is adapted from Ribeiro and Barbosa-Póvoa [62], (Equation (4b)) and maximizes $NPV$ and minimizes the quantity of biomass not delivered to bioenergy plants. We replicated the same approach for the resilience metric focused on minimizing overtime operations (Equation (5b)).

The proposed model considers various constraints related to biomass availability, demand contracts, resource availability, capacity expansion, productivity, and stock limitations and constraints to ensure the domain of the decision variables.

3.2.1. Constraints of Biomass Supply and Demand

$$\sum _{(j,l):(p,j,l,c)\in A\wedge l\in L^t:L^t\le t}{f}_{pjlc}+\sum _{(o,l):(p,o,l,c)\in A\wedge o\in O\wedge l\in L^t:L^t\le t}{e}_{polc}\le a_{ptc},\forall p\in P,\forall t\in T,\forall c\in C$$

(6)

$$\sum _{(i,l):(i,m,l,c)\in A\wedge i\in S\wedge l\in L^t}{f}_{imlc}+\sum _{(o,l):(p,o,l,c)\in A\wedge o\in O\wedge l\in L^t}{r}_{omlc}\ge g_{mtc},\forall m\in M,\forall t\in T,\forall c\in C$$

(7)

The first set of constraints guarantees that material flows do not exceed demand and that demand is satisfied. Constraints related to allocating machines and linked with the conservation of flows are restricted by storage and production capacities.

Since the supply nodes have limited availability of raw materials, Constraint (6) ensures that the flow leaving the biomass supply node does not exceed its availability. Constraint (7) ensures that the flow from processing nodes in each time period meets the demand of delivery nodes in that time period.

3.2.2. Resource Availability Constraints

$$s_{olc}+v_{olc}+w_{olc}\le b_o,\forall o\in O,\forall l\in L^t,\forall c\in C$$

(8)

$$\sum _{i:(k,i,l,c)\in I}{x}_{kilc}\le 1,\forall k\in K,\forall l\in L^t,\forall c\in C$$

(9)

$$\sum _{k:(k,p,l,c)\in I}{x}_{kplc}\le 1,\forall p\in P,\forall l\in L^t,\forall c\in C$$

(10)

$$f_{pmlc}\le a_{ptc}\sum _{k\in K:(k,p,l,c)\in I}{x}_{kplc},\forall (p,m,l,c)\in A:p\in P,m\in M,l\in L^t\in T,\forall t\in T$$

(11)

$$f_{ojlc}\le b_o\sum _{t\in T\in L^t}{y}_o,\forall (o,j,l,c)\in A:o\in O$$

(12)

Constraint (8) ensures that the storage capacity of the intermediate nodes is not surpassed. To prevent scheduling conflicts, Constraint (9) restricts each chipper to a single location per day (micro period). Additionally, it is impossible to have more than one chipper on the same supply node simultaneously, as imposed by Constraint (10). Constraint (11) imposes a unique flow of processed material from a supply node to another node when the machine is in this supply node. Constraint (12) ensures that there is only a flow of processed material from an intermediate node to a delivery node when a machine is present in this intermediate node.

3.2.3. Constraints for Capacity Expansion

$$f_{polc}\le b_o\sum _{t\in T\in L^t}{y}_o,\forall (p,o,l,c)\in A:p\in P,o\in O$$

(13)

$$r_{ojlc}\le b_o\sum _{t\in T\in L^t}{y}_o,\forall (o,j,l,c)\in A:o\in O$$

(14)

$$M·q_k\ge \sum _{k\in K:\left(k,o,l,c\right)\in I,l\in L^t}{x}_{kolc}\forall k\in K,\forall c\in C$$

(15)

Constraints (13) and (14) account for the possibility of opening an intermediate node. If we have flows from an intermediate node and/or machine allocated there, this intermediate node should be open. If there is no intermediate node open $\left(y_o\right)$, then there will be no flow $\left(r_{omlc}\right)$. Constraint (15) ensures that it is only possible to allocate a machine if that machine was previously selected in the first stage of decision variables related to long-term decisions.

3.2.4. Productivity Limitation Constraints

$$h_{kilc}\le x_{kilc}{\tau }_c\forall (k,i,l,c)\in I$$

(16)

$$hextr{a}_{kilc}\le x_{kilc}{\tau }_c\forall (k,i,l,c)\in I$$

(17)

$$\sum _{k\in K:k,p,l,c\in I}{h}_{kplc}\ge \sum _{m\in M:(p,m,l,c)\in A}{\displaystyle \frac{f_{pmlc}}{r_{kc}·\psi }}\forall p\in P,\forall l\in L^t,\forall c\in C$$

(18)

$$z_{kilc}\ge x_{kilc}-x_{ki(l-1)c}\forall (k,i,l,c)\in I$$

(19)

$$z_{ki0c}\ge x_{ki0c}\forall (k,i,\left(0\right)),c\in I$$

(20)

Constraints (16) and (17) limited processing hours that are bounded by the duration of the micro period (day) working time. Constraint (18) ensures that the processing hours of a specific machine in a supply node are higher or equal to its processing productivity of raw material constraint, conversion ratio $\psi$ results from productivity losses related to slope, the quantity of material, and location access. Constraints (19) and (20) ensure that there is only one deployment in a given micro period when a chipper is moved to a different location where it was allocated in the previous micro period.

3.2.5. Stock Limitation Constraints

$$s_{olc}=s_{o(l-1)c}+\sum _{p\in p:(p,o,l,c)\in A}{e}_{polc}-\sum _{k\in K:(k,o,l,c)\in I}(h_{kolc}+hextr{a}_{kolc})r_{kc}\forall o\in O,\forall l\in L^t,\forall c\in C$$

(21)

$$s_{o\left(0\right)c}=\sum _{p\in P:(p,o,(0),c)\in A}{e}_{po\left(0\right)c}-\sum _{k\in K:(k,o,(0),c)\in I}(h_{ko\left(0\right)c}+hextr{a}_{ko\left(0\right)c})r_{kc}\forall o\in O,\forall c\in C$$

(22)

$$v_{olc}=v_{o(l-1)c}^{\prime }+\sum _{k\in K:(k,o,l,c)\in I}(h_{kolc}+hextr{a}_{kolc})r_{kc}-\sum _{m\in M:(o,m,l,c)\in A}{f}_{omlc}\forall o\in O,\forall l\in L^t,\forall c\in C$$

(23)

$$v_{o\left(0\right)c}=\sum _{k\in K:(k,o,(0),c)\in I)}(h_{ko\left(0\right)c}+hextr{a}_{ko\left(0\right)c})r_{kc}-\sum _{m\in M:(o,m,(0),c)\in A}{f}_{om\left(0\right)c}\forall o\in O$$

(24)

$$w_{olc}=w_{o(l-1)c}+\sum _{p\in P:\left(p,o,l,c\right)\in A}{f}_{polc}-\sum _{m\in M:(o,m,l,c)\in A}{r}_{omlc}\forall o\in O,\forall c\in C$$

(25)

$$w_{o\left(0\right)c}=\sum _{p\in P:(p,o,(0),c)\in A}{f}_{po\left(0\right)c}-\sum _{m\in M:(o,m,(0),c)\in A}{r}_{om\left(0\right)c}\forall o\in O,\forall c\in C$$

(26)

$$\sum _{(j,l):(p,j,l,c)\in A\wedge l\in L^t:L^t\le \omega }{f}_{pjlc}+\sum _{(o,l):(p,o,l,c)\in A\wedge o\in O\wedge l\in L^t:L^t\le \omega }{e}_{polc}\le a_{p\left(\omega \right)c},\forall p\in P,\forall c\in C$$

(27)

Constraints (21) to (26) assure the flow conservation by stock constraints. Constraint (27) ensures that at the end of the planning horizon, all raw material available in a given supply node are removed, that is, transported to a destination node (processed or unprocessed).

3.2.6. Non-Negative Constraints

$$x_{kilc},z_{kilc},y_o,q_k\in \{0,1\}$$

(28)

$$f_{ijlc},e_{polc},r_{omlc},h_{kilc},hextr{a}_{kilc},s_{olc},v_{olc},w_{olc}\ge 0$$

(29)

Finally, Constraints (28) and (29) determine the domain of the decision variables.

The following section presents the methodology for identifying the best supply chain design and planning. The quality of the solution given by the optimization model is strictly related to the quality of the uncertainty scenarios generated. The generated scenarios will introduce variability in the stochastic parameters that the model incorporates.

4. AI-Methodology for Scenarios Generation and Resilience Metrics Assessment

The developed methodology, described in Figure 3, consists of an iterative sequence of processes that combines a machine learning algorithm with different uncertainty datasets and resilience metrics to evaluate the network design and productivity capacity that best fits the problem under study.

AI-enabling is used to describe the integration of heuristic search techniques within a simulation–optimization framework to support resilience-oriented strategic decision-making under uncertainty. The AI component is therefore not a data-driven machine learning model, but rather a heuristic search-based decision-support approach that explores the solution space generated by uncertainty scenarios and resilience objectives.

More specifically, AI is employed to iteratively explore and evaluate combinations of strategic decisions, resilience metrics, and uncertainty scenarios, guiding the search toward network configurations that remain feasible and economically viable under disruptive conditions. This approach does not rely on labeled datasets, feature extraction, or loss functions in the traditional machine learning sense. Instead, the learning objective is implicitly defined through the optimization and evaluation process, where candidate solutions are assessed based on feasibility and Net Present Value (NPV) across multiple scenarios.

This methodology encompasses three main steps: scenarios generation, resilience model, and assessment procedure.

The methodology presented is a tool to optimize the two input parameters of the resilience model, which are the resilience metric and the set of uncertainty scenarios. The selection of the resilience metric in the objective function significantly impacts the solution given by the model. Similarly, the uncertainty scenarios to run the stochastic model affect the final solution.

The first step consists of generating uncertainty scenarios to run the resilience model. The stopping criterion is the “$run\_tlimit$” to limit the running time of the stochastic model. The model is restricted to incorporating only a limited number of scenarios within a set time frame. In the second step, the resilience model runs the set of selected uncertainty scenarios and a resilience metric chosen. The output of the model run is the first stage decision variables. In the third step, the assessment procedure incorporates the optimization model to maximize the NPV for a set of disruptions generated in the scenario generator with the first-stage decision variables fixed by the resilience model. The assessment procedure compares the average NPV to the disruptions generated for each solution given by the resilience model. If the average NPV is better than the previous solution, the assessment procedure suggests generating a new set of uncertainty scenarios for the resilience model. If the average NPV is lower than the previous solution, the assessment procedure selects another resilience metric for the objective function of the resilience model. This procedure stops when the time limit of the procedure is reached ($proc\_tlimit$). The output of this methodology is the solution of the resilience model with the set of uncertainty scenarios and the resilience metric selected in the assessment procedure. The resilience model solution is a first-stage decisions encompassing network design and investments.

The proposed methodology ensures that first-stage decisions with a significant economic impact are taken considering the scenarios that best represent the uncertainties present in the supply chain. Furthermore, this methodology ensures that the output represents the solution that designs a more responsive supply chain capable of mitigating unexpected disruptions. The detailed pseudo-code of this methodology, describing the various steps and data flows between the steps, is presented in Algorithm 1. The code used to implement this methodology is available upon request.

Algorithm 1: Methodology outline.

4.1. Scenario Generator

The scenario generator incorporates two types of simulators: the uncertainty simulator (encompass a discrete-event simulator) that is the input for the resilience model and the disruptions simulator (using a fire simulation model) to generate disruptions for the assessment procedure.

Uncertainty scenarios and disruption scenarios play different and clearly separated roles. The uncertainty scenarios are used exclusively to generate the strategic decisions within the stochastic programming model. These scenarios capture structural uncertainty and are sufficient to derive resilience-oriented strategic solutions without relying on precise predictions of disruptive events.

Once the strategic decisions are defined, disruption scenarios are then used only for post evaluation purposes, to test the performance of the generated solutions. Specifically, these disruption scenarios are applied to assess the resulting network in terms of Net Present Value (NPV) and model feasibility, thereby evaluating both economic performance and structural robustness under disruptive conditions.

Therefore, while the model adopts a stochastic programming formulation for decision generation, it does not attempt to predict disruptive events through probabilistic forecasting. Instead, the separation between uncertainty-driven decision generation and disruption-based solution testing ensures that strategic decisions are not biased by assumed disruption probabilities, while still allowing a rigorous and quantitative assessment of resilience.

4.1.1. Uncertainty Simulator

The uncertainty is modeled through stochastic parameters in the stochastic model, and the uncertainty simulator generates scenarios in which one or more parameters vary in a specific period. The output of this simulator provides the parameter that changed, the period in which it changed, the location, and the parameter’s new value. The generated uncertainty scenarios use data from company databases and are characterized by variability in supply (specific supply nodes have different biomass availability in a given period), variability in demand from one of the bioenergy plants, machine breakdowns, and short periods of interruption of operations.

4.1.2. Disruptions Simulator

The disruptions simulator generates a set of disruptive events to be incorporated into the assessment procedure, where the final step of comparing the resilience metrics is developed. Disruptions are generated using a fire simulation model.

To model wildfire dynamics, we modified the cellular automata approach originally introduced by Alexandridis et al. [67] to simulate the dynamics of a wildfire. This simulation model predicts the evolution characteristics in space and time of wildfires. Its accuracy was tested in the real incident observed in the destroyed forest on the island of Spetses. This model incorporates several parameters, such as the type and density of vegetation, the slope, the wind speed and direction, and the ignition point.

The simulation utilizes matrix-based inputs derived from actual geographical maps, representing various intensity scales. We have a pre-processing step that converts each pixel of the heat maps into a matrix that assigns a value to each map pixel location according to its color saturation (e.g., slope, land occupation, and vegetation maps). To ensure scenario variability, stochastic values were applied to other variables, specifically ignition locations and wind conditions. Lastly, the temporal length of the fire event is determined by the historical average duration of wildfires in the specific area.

Finally, the fire simulation model returns the period when the fire occurred and the burned points for each test instance. Each point corresponds to a biomass pile, an intermediate node, and a burned bioenergy centre. Depending on the severity of the fire, the area burned varies, as well as the period of interruption in forestry operations. For each burned pile, a specific amount of extra raw material is available, given the characteristics of the pile. When intermediate nodes burn, the storage and productivity capacity drop; when bioenergy centres burn, demand drops.

4.2. Resilience Model

The formulation of the resilience model is described in the previous section. This two-stage stochastic programming model incorporates two sets of parameters (the uncertainty scenarios and the resilience metrics) that significantly impact the final model solution. The first parameters are the uncertainty scenarios. The number of scenarios selected in each model run impacts the model’s run time ($run\_tlimit$). For this reason, we have a stopping criterion for selecting the number of scenarios to include in each model run, which is the “$run\_tlimit$”. New scenarios are added as long as the “$run\_tlimit$” is not exceeded.

In each run of the resilience model, we combine a set of uncertainty scenarios with a resilience metric that results in the first-stage fixed decision variables that are the input for the assessment procedure.

Based on uncertainty scenarios, the model generates plans and defines medium–long-term decisions to deal with uncertainty. The developed model can measure resilience based on the uncertainty scenarios provided by the scenario generator.

Reaching the stopping criterion for the presented methodology “$proc\_tlimit$”, the output of this model defines strategic decisions for network design (location, number and capacity of intermediate nodes) and investment decisions (number and productivity of machines). This output results from running the resilience model with the set of uncertainty scenarios and the resilience metric selected in the assessment procedure.

4.3. Assessment Procedure

The assessment procedure uses the output of the resilience model (first-stage decision variables) to run an NPV maximization model with these fixed decisions ($dec\_sol$). This procedure saves the average of the objective functions of this model for a set of disruptions (D) generated in the scenarios generator by the fire simulator. In the NPV maximization model, the stochastic parameters assume the baseline value by default, and only the parameters affected by the disruption acquire new values.

In each iteration of this procedure, a new set of fixed decisions ($dec\_sol$), resulting from a new run of the resilience model with a new combination of a set of uncertainty scenarios and a resilience metric, is compared.

The assessment procedure compares the average of the objective functions for each combination and saves the best combination of uncertainty scenarios with the resilience metric. At the end of the procedure, reaching the “$proc\_tlimit$”, the resilience model runs the output of this procedure, which is the best combination of uncertainty scenarios (C) and resilience metrics ($res\_metric$) that best respond to a set of disruptions (D).

Predicting the severity and probability of occurrence of these disruptive events is challenging. However, the proposed methodology supports decision-making to mitigate these disruptive events only using uncertainty data easily obtained in different industrial contexts.

In the following section, we present the comparative results of the solutions obtained with each resilience metric for different uncertainty scenarios and various disruptions.

5. Computational Experiments

The developed methodology is applied in a case study in the biomass-for-bioenergy supply chain. Although the case study focuses on a specific regional context in Central Portugal, the adopted modelling framework and the developed Decision Support System (DSS) are intentionally model-agnostic. The decision logic does not rely on region-specific assumptions; instead, it is driven by a set of scenarios that can be defined to represent conditions from this region or from any other geographical context worldwide.

Importantly, the DSS is not limited to forest biomass or wildfire-related risks. It is designed to be applicable to any supply chain subject to disruptive events, whether arising from the demand-side, supply-side, or operational disturbances. The parameters related to vegetation type, climate, risk intensity, and operational constraints can be adjusted to reflect different forest systems (e.g., coniferous, mixed forests) as well as varying climatic conditions (humid or dry regions), without altering the underlying structure of the model.

The selected case study was used solely as a validation exercise, with the primary objective of demonstrating and validating the proposed simulation-based approach and the robustness of the DSS under a real-world scenario. The conclusions therefore relate to the performance and applicability of the modelling framework itself, rather than to eucalyptus-dominated systems specifically. Our experiments are divided into two studies.

In the first study, we evaluate the impact of the selection of the resilience metric on the network design and production capacity and how these decisions influence the company’s profit in different scenarios of uncertainty and disruptive events.

In the second study, we conduct experiments to analyze the relationship between computing the deterministic $NPV$ (the $NP{V}_{ref}$) and $NP{V}_c$. This second study aims to provide valuable managerial insight for planners on the impact of flexibility strategies and resilience in different risk instances. These experiments compare the operations currently practiced by the case study (Business-as-Usual), an optimization approach with flexibility strategies, a stochastic programming approach, and the resilience planning obtained through the proposed methodology.

In both studies, we intend to demonstrate that our approach allows for the design of a resilient supply chain.

5.1. Case Study

The data and instances used in this study come from a biomass supply company operating in the biomass-for-bioenergy supply chain in Central Portugal. The company is responsible for the pre-processing of forest residues and the transportation of wood chips to bioenergy plants in order to meet contractual delivery commitments. Annual supply agreements are established with regional bioenergy plants, while sourcing contracts are maintained with forest owners for the collection of forest residues generated during harvesting operations.

Eucalyptus plantations designated for pulpwood production dominate the region, typically following a 12-to-15-year harvest cycle. Harvesting byproducts, specifically bark, branches, and foliage, are typically stacked adjacent to forest roads, segregated from the primary pulpwood logs. Harvesting sites are geographically dispersed, and biomass collection at the same location typically occurs only after several years.

Forest residue volumes can be estimated as a fraction of the total harvested volume. In eucalyptus plantations, residues account for approximately 40% of the harvested volume [68], based on historical regional data. However, deviations between estimated and actual volumes are common due to uncertainties in yield estimation and the proportion of residues intentionally left on-site to maintain soil productivity. Based on expert judgment, it is therefore assumed that residue pile volumes may vary by up to 20% relative to the initial estimates.

Due to the seasonal nature of forestry, the residue piles become accessible only after the main harvesting phase is completed. The organization utilizes its own fleet for transport and chipping, staffed by a team of specialized equipment operators.

Table 1. Machine and intermediate node capacities.

Machine Id	Productivity (ton/h)	Intermediate Node	Capacity (ton)
1	20	1	20,000
2	10	2	20,000
3	20	3	40,000
4	10	4	5000
-	-	5	5000

summarizes the available machinery and intermediate reception nodes, along with their respective capacities. Accordingly, the company performs procurement planning to anticipate and contract residue piles over the forthcoming months, defining expected material flows to meet the annual demand of bioenergy plants. Short-term planning further includes the daily assignment and scheduling of workforce and equipment, with the objective of minimizing operational costs.

Moreover, the risk of wildfire occurrence is significantly higher during the summer period, and this seasonal effect is explicitly reflected in the modelling framework. Several real-world parameters incorporated into the wildfire simulation model are season-dependent, including meteorological conditions such as temperature, wind, and dryness, which strongly influence fire ignition and spread. By integrating these meteorological and environmental constraints, the simulator captures the increased wildfire risk and intensity typically observed during summer months, thereby realistically representing seasonal variability.

5.2. Resilience Metrics Analysis

In the first study, in which the three resilience metrics are compared, a set of disruptions “D” is generated. In addition to the disruptions generated in the fire simulator, one of the outputs of the assessment procedure, the set “C” (which represents the set of scenarios used to run the resilience model) is included, as well as the “baseline” scenario, which does not include any source of uncertainty or disruption.

The AI-driven wildfire simulator used in this study is designed to incorporate real-world physical and environmental parameters, including land-use and land-cover data, terrain slope, wind conditions, and other biophysical variables that directly influence wildfire behavior. This allows the simulated fire spread dynamics to remain physically consistent with observed wildfire processes.

It is important to note that the simulator operates without explicitly modelling firefighting or suppression activities. Consequently, a stopping criterion must be defined externally. In the context of this study, this choice was intentional, as it allows the generation of conservative disruption scenarios that reflect the potential maximum impact on the biomass supply chain in the absence of intervention.

Given the availability of detailed and well-documented data on the 2017 wildfire events in the study region, these historical fires were used as a reference to define and calibrate multiple disruption scenarios. Specifically, a set of scenarios with varying levels of severity was considered, ranging from less severe events to scenarios with disruption intensity and spatial extent closely aligned with the impacts observed during the 2017 wildfires. This approach ensures that the simulated scenarios are grounded in empirically observed extremes, rather than being purely synthetic or arbitrary.

Disruptions generated by the fire simulator include events such as the closure of bioenergy plants (e.g., $D\_05$), periods without operations (e.g., $D\_06$, $D\_14$ and $D\_20$), an increase in biomass to process in supply nodes (e.g., $D\_01$, $D\_07$ and $D\_16$), and more severe disruptions that combine in the same scenario the disruptions already described (e.g., $D\_08$, $D\_09$, $D\_17$ and $D\_18$). The other scenarios correspond to the disruptions already presented.

These experiments aim to present and discuss the NPV obtained by each network design of each resilience metric for different uncertainties and disruptions.

Table 2. Number and ID of chippers and intermediate nodes selected in each of the resilience metrics.

Resilience Metric	${\mathit{q}}_{\mathit{k}}$-Machines	${\mathit{y}}_{\mathit{o}}$-Int. Nodes
$resMet\_sup$	1;2;3	1;2;4;5
$resMet\_dem$	1;2	1;2;4
$resMet\_ope$	1;3	1;2;5

demonstrates the variation in the number and capacity of opened intermediate nodes, productivity, and number of machines used. This output results from the solution (first-stage variables) of each resilience metric that obtained the highest average NPV value for the set of disruptions analyzed in the assessment procedure.

Table 3. Comparison of the NPV of network designs obtained with each resilience metric for a set of disruptive events.

Scenarios	resMet_sup	resMet_dem	resMet_ope
baseline	413,579€	435,959€	410,888€
“C”	389,689€	269,727€	355,601€
$D\_01$	35,606€	−262,557€	−97,752€
$D\_02$	−55,455€	−339,782€	−203,988€
$D\_03$	−245,142€	−544,461€	−381,562€
$D\_04$	139,365€	5922€	66,142€
$D\_05$	262,692€	280,567€	260,112€
$D\_06$	161,198€	−81,239€	44,359€
$D\_07$	35,680€	−157,254€	−61,786€
$D\_08$	−298,316€	−480,897€	−376,994€
$D\_09$	−298,322€	−502,355€	−377,594€
$D\_10$	−533,007€	−723,246€	−618,899€
$D\_11$	285,910€	−502,355€	76,868€
$D\_12$	−253,923€	−500,587€	−382,719€
$D\_13$	−118,676€	−355,318€	−237,459€
$D\_14$	116,019€	76,781€	112,409€
$D\_15$	−92,949€	−222,340€	−166,484€
$D\_16$	17,356€	−115,863€	−1620€
$D\_17$	−383,406€	−638,349€	−488,632€
$D\_18$	−549,120€	−794,486€	−684,670€
$D\_19$	141,033€	−15,759€	66,744€
$D\_20$	294,223€	154,860€	277,216€
Average	4692€	−187,359€	−74,850€
SD	292,567€	356,755 €	320,141€

presents the objective function of the plan generated with a specific resilience metric tested in a set of disruptive events “D” provided by the fire simulation model. All presented objective functions resulted from model runs with optimal solutions. The objective functions’ average and standard deviation are calculated to help interpret the results.

Extreme scenarios, even when associated with a negative Net Present Value (NPV), play an important role in shaping the model’s strategic decisions. Such scenarios typically correspond to highly disruptive wildfire events that generate a substantially larger volume of biomass within a short period. Under these conditions, the model is forced to activate or invest in additional chipping machines and intermediate biomass reception nodes in order to handle the excess biomass and avoid severe operational bottlenecks. As a result, these extreme scenarios directly influence the selection and intensity of strategic decisions, even if they are not economically optimal when evaluated in isolation through NPV. In this sense, negative-NPV extreme scenarios act as stress tests for the system, revealing the infrastructure and capacity expansions required to ensure operational feasibility and resilience under worst-case conditions.

We compare the different network designs resulting from resilience metrics under study: resMet_sup, resMet_dem and resMet_ope. The decisions to open intermediate nodes and use new machines affect each plan’s productivity and storage capacity. Specifically, these metrics guide the selection of strategic investments (e.g., capacity expansion, infrastructure placement) under disruptive scenarios.

The evaluation of the resulting network design is then performed using Net Present Value (NPV) and model feasibility. NPV is used to assess the economic performance of the selected strategy, while feasibility acts as a proxy for structural robustness. An infeasible solution indicates insufficient capacity or structural limitations in the network, meaning that the designed supply chain is unable to absorb disruptions and therefore cannot be considered resilient. In this sense, feasibility directly reflects a fundamental resilience property: the ability of the system to continue operating under stress.

The resilience metric “resMet_sup”, which maximizes the amount of biomass processed, achieved the best objective function value in 20 of the 22 instances tested (reaching the best result in 90.9% of the scenarios). In the average of the instances, it was the only metric that still managed to make a profit and had the lowest standard deviation value. This value is significant, as it shows the ability of this metric to minimize the impact of the most extreme disruptive events.

“resMet_sup” has proven to be the best response to disruptive events, having reached the best objective function value in 19 of the 20 instances with disruptions. Only “$D\_05$” has a lower NPV than “resMet_dem” because this disruption corresponds to a closure of a bioenergy plant. This responsiveness can be related to the increase in production and storage capacity, as seen in Table 2.

The results presented in Table 3 show a very marked variation in the values of the objective function, which are explained by the set of disruptive events that include the cessation of operations for periods of one week to approximately one month, closure of one of the delivery nodes and an increase of raw material to process, which can triple the amount initially existing. In the disruptions related to the increase of biomass to process ($D\_01$, $D\_07$ and $D\_16$), the “resMet_sup” maintained profits while the remaining metrics showed losses.

The increase in biomass to be processed can be overcome by opening intermediate nodes that allow storing a higher quantity of raw material and continuously processing more biomass with higher productivity. Observing the model’s behavior with the resilience metric “resMet_sup” in a period in which disruptive events do not occur “baseline”, it is possible to conclude from Figure 4 that even in this optimal scenario, three intermediate nodes are being used to allocate machines. This increase in capacity makes the entire supply chain more resilient and brings productivity gains due to the economies of scale that intermediate nodes enable. A more significant number of intermediate nodes provides more storage capacity, facilitates logistical operations and allows machines to work continuously with shorter set times when compared to supply nodes.

Figure 4 highlights the network design and the flow of raw material and processed biomass between the different supply chain nodes of the case study under study. It is also possible to observe the allocation and deployment of machines for the selected period. In this figure, the intermediate nodes ($y_1;y_2;y_4$), the bioenergy centre ($M_1;M_3$), and the machines ($q_1;q_3$) are represented. In the $period\_05$, it is visible in Figure 4 that one of the machines ($q_3$) remains constantly processing in the same intermediate node ($y_4$). In contrast, the other machine ($q_1$) deploys the intermediate node ($y_2$) to the ($y_1$). All intermediate nodes receive and process raw material from the supply nodes. The bioenergy centre ($M_1$) receives processed biomass from the intermediate nodes ($y_2;y_4$) while the ($M_3$) receives biomass from the intermediate node ($y_4$).

The plan generated by the model minimizes the distance traveled with raw material, allocating the flow of raw material to the closest intermediate nodes since raw material transport occupies three times more volume than already-processed biomass. The flows of one month of work, which correspond to the $period\_05$, are shown in Figure 4.

5.3. Global Analysis

The second set of experiments is designed to provide critical managerial insights for forest-to-bioenergy supply chain decision-makers by comparing different approaches, including flexibility, stochasticity, resilience, and Business-as-Usual (BAU).

This second study incorporates three frequent disruptions that arise after a wildfire in a forested area: sudden increase in biomass to process, long periods without operations being allowed in the forest, and the closure of intermediate nodes. The amount of extra biomass, the intermediate nodes closed, and the periods of interruption of operations are disruptions all generated by the fire simulator.

Table 4. Wildfire scenarios.

Wildfire Severity	Number of Piles	Amount of Extra Biomass (Tons)
none	0	0
low	8	9875
medium	18	24,330
high	29	38,665

presents the number of piles burnt and the impact on biomass availability for processing depending on the severity of the wildfire. These instances were selected from a set of instances resulting from one run of the fire simulation model with real data. The selected instances present different fire intensities, facilitating the analysis of the results.

A set of experiments is conducted to compare the solution proposed by our methodology with other approaches found in the literature and BAU network designs. These results are significant for understanding each network design’s impact on responsiveness to disruptive events. Four cases with different network design plans were tested and compared in a set of disruptive events:

• Case (A): Business-as-Usual (BAU). In this case, there is no possibility to open intermediate nodes. Consequently, all operations are performed on supply nodes, and the uncertainty is not considered. So the objective function is maximizing $NP{V}_{ref}$ with no uncertainty.
• Case (B): This is the network design plan made by an optimization model considering flexibility (operations can be done on both nodes and intermediate nodes that have a storage and/or a processing function). In this case, the uncertainty is also not being considered. The objective is to maximize $NP{V}_{ref}$ with no uncertainty as well.
• Case (C): This represents the output of the two-stage stochastic model incorporating flexibility. These planning decisions include the occurrence of uncertainty scenarios. However, this model is risk-neutral. The objective is to maximize $NP{V}_c$
• Case (D): This presents the output of the framework developed: the two-stage stochastic model with the resilience metric “resMet_sup” for uncertainty scenarios. This case also includes flexibility strategies.

The disruptive events used to test these cases combine a set of disruptions triggered by wildfires. The disruptions generated by a fire simulator are operations stopped, intermediate nodes closed, and the increase in biomass to process resulting from the severity of the wildfire. Table 4 shows the piles burning and the amount of extra biomass to process depending on wildfire severity to facilitate the analysis of results by the stakeholders of the forest-to-bioenergy supply chain.

Table 5. Network design and the fixed decision variables for each case under study.

Supply Chain Cases	${\mathit{q}}_{\mathit{k}}$-Machines	${\mathit{y}}_{\mathit{o}}$-Int. Nodes
Case (A)	1;2	-
Case (B)	1;2	1;2;4
Case (C)	1;3	1;2;5
Case (D)	1;2;3	1;2;4;5

presents the network design and the fixed decision variables for each case analyzed. It is possible to see from the figure that in the case of an optimal plan without considering uncertainty, “Case (B)”, three intermediate nodes are opened to make the supply chain more efficient. Considering the uncertainty, “Case (C)” changes the intermediate nodes opened and selects the two chippers with the higher productivity. Furthermore, “Case (D)” represents the resilient plan, opens four intermediate nodes, and sets three chippers with sufficient production capacity to respond to possible disruptions.

The results are presented in

Table 6. NPV after disruptions for each of the cases under study.

Fire Severity	Other Disruptions	Network Design Cases
		A (€)	B (€)	C (€)	D (€)
Baseline		354,212	435,252	410,688	413,566
“C”		175,698	286,750	394,765	389,689
none	OS	326,761	407,801	411,011	413,112
	INC	354,212	401,939	361,712	409,257
	BD	326,761	381,377	363,849	409,289
low	N	213,634	346,623	399,677	394,049
	OS	136,729	269,718	355,556	389,624
	INC	213,634	300,168	336,198	389,950
	BD	136,729	223,130	302,056	386,109
medium	N	−299,885	−81,250	44,352	161,186
	OS	−375,862	−157,227	−61,779	35,686
	INC	−299,885	−165,708	−31,470	143,890
	BD	−375,862	−242,813	−138,002	18,111
high	N	infeasible	−262,581	−97,801	35,677
	OS	infeasible	−339,699	−203,887	−55,455
	INC	infeasible	infeasible	infeasible	−6167
	BD	infeasible	infeasible	infeasible	−97,509

Legend: N (none), OS (operations stopped), INC (intermediate nodes closed), BD (both disruptions—operations stopped + intermediate nodes closed).

. The variation in the NPV of each of these cases results from the medium–long-term decision variables given by different network design models.

From the analysis of the results, we can observe that Case (D) does not present the highest profit value in only three instances. In the baseline instance, in which there is no uncertainty, Case (B) presents the highest profit because it optimizes the entire supply chain for a scenario without uncertainty, leading to lower initial investment in intermediate nodes and chippers than in Case (D). Case (C) has a more significant profit in two instances due to the initial investment, which is lower than in Case (D). The instance “C” comprises a set of uncertainty scenarios used to run the stochastic models of Cases (C) and (D). Case (C) presents a higher profit because the model optimized the supply chain for the average of the scenarios of the instance “C”, while Case (D) incorporates a resilience metric that prepares the supply chain not only for the uncertainty scenarios of the instance “C”, but also for possible disruptions that may arise, which leads to a higher investment. Case (D) presents the highest profit value in the remaining instances. In four instances of medium–high severity, Case (D) presents profit, while the remaining cases present losses.

Our approach proves to be more efficient in all instances of severe and very severe disruption, and even in instances with less severe disruptive events, it is more efficient and profitable on average. Regarding the ability to process all biomass and comply with established contracts, Case (D) can process all biomass even in instances affected by severe disruptions, which does not happen in other cases.

From the results shown in Table 6, we can easily compare the relationship between increased investment at an early stage and a greater capacity to respond to disruptions that result from that initial investment. The storage and processing capacity increase resulting from the network design of Case (D), which is the resilient model, leads to a cost increase of just over €20,000 in the baseline instance, where there is no disruption. However, when a severe disruption occurs, as with wildfires, this initial investment can reduce total costs by more than €300,000.

Figure 5 shows each case’s storage and productivity capacity. This figure complements the information in Table 5. It is easier to understand that the impact on storage and production capacity depends on the network design, the number of intermediate nodes opened, and the chippers selected per case analyzed.

Finally, making a rough estimate of these results, we can consider that we are increasing the capacity of processed biomass. Case (D) can still profitably process more than 38,665 tons of biomass. Converting this amount of processed biomass into the forest area, primarily eucalyptus, according to [69,70], corresponds to approximately 2522 ha. Decreasing the fuel volume in the forest decreases the probability of fire occurrence and its severity [31,33,46,71].

The objective of maximizing resilience is not antagonistic to maximizing profit. It has been proven that a resilient supply chain achieves the highest profits in most instances where uncertainty and disruption are present. Considering this industry’s high probability of disruptions, a more resilient supply chain is also more economically, socially, and environmentally sustainable.

6. Conclusions and Managerial Insights

This study introduces a holistic framework designed to assist stakeholders in navigating strategic decisions within the complex forest-to-bioenergy sector. We employ a two-stage stochastic framework to determine optimal flexibility measures and select the most appropriate resilience metric to evaluate network design under disruption to provide insight into the impacts of supply chain network design in different disruptive scenarios, which enable managers to make robust and adaptive decisions.

We first developed an AI-methodology to generate uncertainty in supply, demand, and operations. In addition, disruption events are generated based on a fire simulator. Second, these scenarios are integrated into the stochastic model, providing decisions that fit a more comprehensive range of possible scenarios. Finally, we have an assessment module that compares the responsiveness of network design generated by different resilience metrics under the occurrence of uncertainty scenarios and disruptive events. The output of this methodology gives us the best resilience metric to adopt and the best set of uncertainty scenarios to run the stochastic model. Moreover, it provides a set of fixed strategic decision variables that give us the network design of our supply chain that best mitigates any disruptive events that may arise.

We conducted experiments to evaluate the trade-off between decisions to increase processing capacity and the costs associated with this investment. We also assess the behaviour of the model and its costs when different uncertainty scenarios are considered and when the resilience metric in the objective function is varied. Finally, in disruptive events that arise from a wildfire simulation model, we compare the value of the objective function of a Business-as-Usual model, an optimization model, a stochastic model, and a stochastic model with the resilience metric. Findings indicate that integrating resilience metrics into the stochastic model yields superior profitability across every wildfire scenario tested. The models that do not consider uncertainty can not process all biomass generated in most wildfire severity scenarios. Results show that this approach makes the supply chain capable of cleaning and processing more than 60% of forest residues compared with the current process, corresponding to a forest area of 2522 ha. Adopting the resilient network design, we can reduce supply chain costs by €300,000 for more severe disruptive scenarios.

The results also demonstrated that the cost of increasing processing capacity through the purchase of chippers and increasing storage capacity achieved by opening intermediate nodes ends up being offset by productivity gains, economies of scale, and optimization of the logistics network, which means that in scenarios without uncertainty and disruption, it does not have a significant cost. With high uncertainty in biomass availability and disruptions, planning a resilient supply chain makes it capable of being more responsive when subject to various disruptions. We prove that resilience and cost minimization are not antagonistic objectives and that a resilient supply chain is very competitive even in scenarios with lower uncertainty. Planners and stakeholders can use the developed framework in the forest-to-bioenergy industry to support their decision-making process, especially strategic decisions involving significant company investments.

Our paper provides compelling evidence that resilience and cost minimization are not mutually exclusive. A resilient supply chain can be cost-competitive, even in situations with lower uncertainty. The implication of this finding is profound: managers can confidently prioritize resilience without undue concerns about escalating costs, aligning strategic decisions with the long-term stability of the supply chain. This research also represents a pioneering effort in developing an AI-methodology that exclusively relies on operational uncertainty scenarios to inform strategic decisions. By focusing on these scenarios, the study provides unique insights into crafting network designs that enhance the supply chain’s responsiveness in the face of disruptions. This innovative approach marks a significant advancement in the field, offering a practical and targeted method for bolstering supply chain resilience. Furthermore, the findings of this research not only contribute valuable knowledge to the existing literature but pave the way for further explorations in refining supply chain strategies across various industries.

While our research offers significant insights, it is essential to acknowledge its limitations. The need for more advanced models incorporating nonlinear cost structures, alternative transportation technologies, and a broader spectrum of uncertainty sources is evident. Moreover, comparing the resilience metric with risk measures, such as conditional value at risk, holds promise for future exploration. Conditional Value at Risk (CVaR) is an alternative risk evaluation metric that, if incorporated into a modelling framework of this type, would directly influence strategic decision-making by explicitly accounting for tail-risk and extreme loss scenarios. Its integration would allow decision-makers to assess trade-offs between expected performance and downside risk, in a manner comparable to the resilience-oriented metrics adopted in this study.

Our findings underscore the practicality and viability of enhancing supply chain resilience. By embracing the methodologies and insights presented in this research, decision-makers in the forest-to-bioenergy industry and beyond can navigate uncertainties effectively. In doing so, they ensure the resilience and competitiveness of their supply chains, thereby fostering sustainable growth and adaptability in an ever-changing global landscape.