Designing Resilient Biomass Energy Supply Networks under Environmental Disruptions and Market Uncertainty: An Integrated Data-Driven Clustering, MCDM, and Bi-Level
Abstract
Given the growing energy demand, limitations of fossil resources, and the urgent need to mitigate environmental impacts, developing renewable energy supply networks, especially those based on biomass, has gained significant importance. Accordingly, this study proposes a hybrid multi-phase decision-making framework for the optimal design of a resilient biomass energy supply network under environmental and market uncertainties. In the first phase, spatial data from 120 agricultural sites across eight provinces of Iran were clustered into homogeneous groups using four data-driven algorithms, namely Constrained K-Means (CKM), the Gaussian Mixture Model (GMM), Spectral Clustering, and Affinity Propagation (AP). Subsequently, Bayesian Best-Worst and Best-Worst PROMETHEE methods were employed to weight and rank decision criteria, facilitating the identification of optimal hub locations. The resulting clusters and hub scores were then incorporated as input parameters for the network design problem: in the first phase, hub location and cluster-to-hub allocation were determined; in the second phase, a bi-level, multi-period mathematical model was developed to optimize network flows and intra-cluster routing under uncertainty. Numerical results reveal that employing Spectral Clustering led to a 28% reduction in total supply chain costs compared to the uncluttered baseline, with other algorithms achieving reductions between 10% and 19%. This research, grounded in real-world data collected from eight provinces, demonstrates the effectiveness of data-driven and multi-criteria approaches in enhancing the sustainability, cost-efficiency, and resilience of biomass energy supply networks.
Keywords:Biomass supply chainData-driven clusteringMulti-criteria decision-makingNetwork optimizationHub locationUncertainty modeling
1. Introduction
In recent decades, the rapid growth of the global population, increasing energy demand, climate change, and heavy dependence on fossil fuels have posed significant challenges to energy systems and the environment. Among the various renewable energy alternatives, biomass has emerged as a promising renewable energy source, as it can not only reduce dependence on fossil fuels but also contribute to improved waste management, rural employment generation, and mitigation of environmental pollution. However, the design of biomass-based energy supply chain networks has become a complex and multifaceted challenge due to the spatial dispersion of biomass resources, environmental and economic uncertainties, and infrastructural complexities, particularly under crisis conditions.
In this research, an integrated modeling framework is developed for the design of a biomass energy supply chain network, employing a novel approach aimed at mitigating risks and enhancing system resilience. In the first stage, spatial data on agricultural lands are analyzed and partitioned into distinct clusters using Constrained K-Means (CKM), Gaussian Mixture Model (GMM), Affinity Propagation (AP), and Spectral Clustering (SC).
This clustering process not only facilitates the logical aggregation of biomass resources but also provides a foundation for cost reduction, transportation efficiency, and infrastructure optimization. In the next stage, a combination of two Multi-Criteria Decision-Making (MCDM) methods is employed to determine the optimal locations for hub establishment. First, the weights of evaluation criteria are obtained using the Bayesian Best-Worst Method (B-BWM), and subsequently, candidate locations are ranked through the Best-Worst PROMETHEE approach. This methodology enables the incorporation of uncertainty in decision-makers’ preferences while improving the robustness, accuracy, and defensibility of location-selection decisions. The clustering and ranking outcomes are then directly integrated into the mathematical network design model, which is formulated as a bi-level, two-phase, stochastic, and multi-period optimization model. In the first phase, strategic decisions regarding hub location and cluster-to-hub allocation are determined. In the second phase, the complete biomass energy network is designed by considering material and energy flows, storage operations, transportation activities, operational costs, uncertainty scenarios, and intra-cluster routing decisions. The proposed model seeks to provide a reliable and resilient framework for the optimal utilization of biomass resources under global crises and uncertain operating conditions. In addition to ensuring economic viability, the model explicitly incorporates environmental and social sustainability considerations into the design of the energy supply chain network.
2. Literature Review
A significant body of literature has addressed the strategic design of biomass supply chain networks. Abandansari et al. [1] proposed a multi-objective optimization model for a global biomass-based electricity supply chain that simultaneously considers economic, environmental, and resilience criteria. Similarly, Nunes et al. [2] developed a multi-stage biomass supply chain design model covering all stages from biomass collection to distribution under uncertainty while accounting for economic and environmental requirements. Murele et al. [3] formulated a mathematical model for facility location, resource allocation, and material flow management across multiple network levels. Furthermore, Petridis et al. [4] employed mixed-integer linear programming to design a sustainable biomass supply chain considering economic, social, and environmental dimensions.
Another stream of research has focused on uncertainty, resilience, and risk management in biomass supply chains. Allegranzi et al. [5] proposed a bi-objective mathematical model to minimize both total costs and environmental emissions under uncertain conditions. Likewise, Fattahi et al. [6] adopted a two-stage stochastic programming framework to plan biomass-based electricity supply chains while accounting for seasonal biomass availability and social impacts. More recently, a resilient agricultural biomass supply chain network design framework was developed using a data-driven robust optimization approach capable of addressing uncertain disruptions and risk-averse decision-making environments [7]. In addition, a multi-objective fuzzy optimization model for biomass-to-electricity supply chain design was introduced to simultaneously minimize system costs and carbon emissions under multiple sources of uncertainty [8]. These studies demonstrate the growing importance of incorporating uncertainty and resilience considerations into biomass network design.
This figure is shown in the PDF version of the article.
3.1 Agricultural Land Clustering
In biomass energy supply chain network design, one of the fundamental steps is the effective aggregation of spatially dispersed agricultural areas to define the network's input nodes. Since farm-related spatial data are typically characterized by high dispersion, irregular geographical boundaries, and heterogeneous production capacities, clustering techniques serve as an essential preprocessing tool for reducing problem complexity and improving network coherence. Accordingly, four clustering algorithms, CKM, GMM, AP, and SC, are employed in this study to identify optimal spatial groupings of farms and to facilitate a comprehensive evaluation in terms of clustering quality, operational feasibility, and transportation efficiency.
The first method, CKM, extends the traditional K-Means algorithm by incorporating additional constraints on cluster size and composition. The algorithm seeks to allocate observations to (K) clusters in such a way that the total within-cluster sum of squared distances is minimized while satisfying predefined constraints. The optimization problem is expressed in Eq. (1).
min∑ ∑ ‖xj − μi‖ subject to constraint on |Ci|, (1)
i=1 xi∈Ci
where xi denotes the input data points, μi represents the centroid of cluster i, and Ci is the set of observations assigned to cluster i. This approach is particularly useful when collection-center capacities are limited and explicit control over cluster sizes is required.
In contrast, the GMM adopts a probabilistic perspective by representing the data as a weighted combination of multivariate Gaussian distributions. The probability density function is defined as
p(x) = ∑ πiΝ(x|μi, ∑ ), (2)
i=1 i
where πi, and ∑i denote the mixture weight, mean vector, and covariance matrix of component i, respectively. Parameter estimation is performed using the Expectation-Maximization (EM) algorithm, which iteratively maximizes the log-likelihood function:
max log ∏ ∑ πiΝ(x|μi, ∑ ). (3)
i=1 i
Compared with K-Means, GMM provides greater flexibility in modeling overlapping clusters and datasets with ambiguous cluster boundaries.
The third technique, AP, differs from conventional clustering methods in that it does not require the number of clusters to be specified a priori. Instead, clusters are formed through an iterative message-passing process between data points. Two types of messages are exchanged: responsibility, which reflects the suitability of one point to serve as the exemplar of another, and availability, which indicates the degree to which a point is willing to act as an exemplar. The clustering objective is to maximize the total similarity between observations and their selected exemplars:
max ∑ s(i, ci), (4)
where s(i, ci) denotes the similarity between point i and its assigned exemplar ci. Through this iterative process, the algorithm is also capable of automatically determining the appropriate number of clusters. The fourth approach, SC, utilizes spectral graph theory to identify complex and nonlinear structures within the data. Initially, a similarity matrix W is constructed among all observations. Subsequently, the normalized graph Laplacian is computed as
Lsym = I − D−2WD−2. (5)
where D is the diagonal degree matrix. After computing the eigenvectors of Lsym, the data are projected into a lower-dimensional space and clustered using K-Means. SC is particularly effective for identifying complex and non-convex cluster structures. In this study, the four clustering algorithms are employed to generate alternative spatial configurations of biomass resources rather than merely compare algorithm performance. The resulting diversity in cluster structures enables a comprehensive evaluation of transportation efficiency and network performance, providing a robust basis for selecting the most suitable configuration for biomass supply chain network design.
3.2 Hub Location Evaluation Using MCDM
To identify the most suitable locations for biomass hubs, a two-stage MCDM framework is employed. First, criterion weights are determined using the B-BWM, which accounts for uncertainty in decision-makers’ judgments by modeling preferences as probability distributions rather than fixed values. This approach provides more reliable and robust criterion weights while enabling improved sensitivity analysis.
Subsequently, candidate hub locations are evaluated and ranked using the Best-Worst PROMETHEE method. By combining the robust weighting capability of B-BWM with the ranking effectiveness of PROMETHEE, this hybrid approach improves decision transparency, reduces subjective bias, and enhances the reliability of the final ranking results. The obtained hub scores are then incorporated into the optimization model as an input for hub location decisions. Due to space limitations, the detailed computational procedures are omitted, and interested readers are referred to [15], [16].
3.3 Bi-Level Biomass Supply Chain Network Design
In this section, the mathematical model for biomass energy network design is presented within a two-phase framework: the first phase is dedicated to hub location and cluster allocation, while the second phase models the complete network structure by accounting for product and energy flows and uncertainties. The complete list of symbols and indices is provided in Table 1.
Table 1. Notation and Indexing.
This table is shown in the PDF version of the article.
us it Visit the position of land i in period t under scenario s xijt s 1 if route goes from farm i to farm j in period t under scenario s; 0 otherwise.
Phase 1 Parameters πh Score of hub h disηh Distance between cluster η and hub h K Maximum number of hubs to be established.
η Maximum number of clusters that can be connected to one hub.
Phase 1 Decision Variables ωht 1 if hub h is established in period t; 0 otherwise.
Zη t h 1 if cluster η is assigned to hub h in period t; 0 otherwise.
MaxZ1 = ∑ πh × ωht. (6)
MinZ2 = ∑ dis Zt . (7)
ηh ηh η,H,T
t (8)
∑ Zηh = 1, ∀η, T.
t (9)
∑ Zηh ≤ η , ∀H, T.
(10)
∑ ωht ≤ K, ∀T.
Zη t h ≤ ωηt, ∀η, H, T. (11) Zη t h, ωηt ∈ {0,1}. (12)
Eq. (6) maximizes total hub scores across planning periods, while Eq. (7) minimizes total distance between clusters and their assigned hubs. Constraints (8)-(11) ensure each cluster is assigned to exactly one active hub per period, limit cluster-to-hub assignments, and control the number of active hubs. The bi-objective model is solved using the weighted-sum method.
s s s
MinZ′ = ∑ PSs ( ∑ Ctphr × Pphrt + ∑ Ctrc × Urct + ∑ Ctcc′ × Ucc′t
S P,H,R,T R,C,T C,C′,T
+ ∑ Ctc′t′ × Uc′t′t + ∑ Ctt′d × ELt′dt + α ( ∑ Fe × yet)
C′,T′,T T′,D,T T,e∈{h,r,c,t′}
s s main main (13)
+ α ( ∑ φrct × Cprc + ∑ φcc′t × Cpcc′) + ∑ hcts × ϕphts
R,C,T C,C′,T P,H,T adj adj w s I s
+ ∑ hcts × ϕphts + ∑ hcts × Wpht + ∑ hcts × Ipht
P,H,T P,H,T P,H,T
+ ∑ xijt s × disijη × times ijηt − ∑ ELs t′dt × priced),
i,j,T,η T′,D,T
η (14)
main adj ′ s
ϕphts + ϕphts = ∑ Zηht × ∑ qpft , ∀H, P, T, S,
η=1 f∈Fη
∑ ϕmain ≤ Cap + M × y , ∀H, T, S, (15)
phts h ht ∑ ϕadj ≤ Cap × y , ∀H, T, S, (16)
phts h ht
∑ ϕadj ≥ ∑ ϕmain − Cap , ∀H, T, S, (17)
phts phts h
I + ϕmain + ϕadj = ∑ PS + I + w , ∀P, H, T, S, (18)
ph(t−1)s phts phts phrt phts phts
Pphrt S ≤ M × φs hrt, ∀H, R, P, T, S, (19) S (20)
∑ Pphrt ≤ capr, ∀R, T, S,
∑ PS (1 − α) ≤ ∑ Us , ∀P, R, T, , S, (21)
phrt rct
∑ Us (1 − α) ≤ ∑ Us ′ , ∀C, T, S, (22)
rct cc t R C′
∑ Us ′ (1 − α) ≤ ∑ Us′ ′ ∀C, T′, T, S, (23)
cc t c t t C′ C′
∑ Us′ ′ (1 − α) ≤ ∑ ELs′ , ∀T′, T, S, (24)
c t t t dt C′ D
Urct s ≤ M × EPrc S × φs rct, ∀R, C, T, S, (25) Uc sc′t ≤ M × yct, ∀C, T′, T, S, (26) Uc sc′t ≤ M × EPcSc′ × φs cc′t, ∀C, T′, T, S, (27) Urct s ≤ M × yrt, ∀R, C, T, S, (28) ELt′dt ≤ M × yt′t, ∀T , D, T, S, (29)
∑ ELs′ ≤ I ˜ × M, ∀D, T, S, (30)
t dt dt
us + us ≥ ∑ q + Q(1 − xs ), ∀(i. j) ∈ F , η, T, S , i ≠ j, (31)
it jt pjts ijt η
∑ xs = ∑ xs , ∀j ∈ F , η, T, S, (32)
ijt jit η i∈Fη i∈Fη
∑ xs = 1, ∀j ∈ F , η, T, S, (33)
ijt η
∑ xs = 1, ∀η, T, S, (34)
1jt j∈Fη
∑ qs ≤ us , ∀η, i ∈ F , T, S, (35)
pit it η
∑ us ≤ Q, ∀η, T, S, (36)
it i∈Fη
Pphrt s , Urct s , Us ′ , Uc′t′t s , ELs t′dt , ϕmain phts , ϕadj , Ipht s , Wpht s ≥ 0, (37)
cc t phts
yet , φs rct, φs cc′t, xijt s , ωht , Zη t h ∈ {0.1}. (38)
Eq. (13) minimizes total supply chain costs, including transportation, facility establishment, inventory holding, and intra-cluster routing, net of electricity revenue. Constraints (14)-(18) govern biomass flow from farms to hubs, warehouse activation priorities, and inventory balance. Constraints (19)-(24) regulate biomass-to-energy conversion flows across reactors, condensers, and transformers. Constraints (25)-(30) ensure transfers occur only through active facilities and links, with electricity supplied only to genuine demand regions. Finally, Constraints (31)-(36) manage intra-cluster vehicle routing by eliminating sub-tours, enforcing farm visits, ensuring vehicle return, and imposing capacity limits. Constraints (37)-(38) define variable domains.
4. Numerical Results
The proposed model was solved under three uncertainty scenarios over a planning horizon of seven time periods. The dataset consisted of spatial information from 120 agricultural lands distributed across eight provinces of Iran, and it was assumed that ten hub facilities would be established for biomass collection and distribution.
In the first stage, eight key criteria were considered for hub location selection. Criterion C1 represents accessibility to the inter-regional transportation network, while C2 reflects the availability of technical infrastructure, including electricity and water supply. Criterion C3 evaluates physical expansion and storage capacity, whereas C4 considers geotechnical stability and site safety. Criterion C5 accounts for land acquisition or leasing costs, and C6 measures proximity to consumption centers and downstream industries. Criterion C7 incorporates local community acceptance, while C8 assesses industrial development status and regional synergy potential. These criteria collectively formed the basis for evaluating candidate hub locations. Subsequently, the performance of the four clustering algorithms CKM, AP, SC, and GMM, was evaluated using four widely adopted clustering quality metrics. As illustrated in Fig. 2, SC achieved the best or near-best performance across all evaluation criteria, obtaining a Silhouette coefficient of 0.78, a Davies–Bouldin index of 0.22, a Dunn index of 0.71, and a Calinski–Harabasz score of 310. These results indicate that SC provides superior cluster cohesion, inter-cluster separation, and overall structural quality compared with the alternative methods. CKM was identified as the second-best clustering approach and also demonstrated satisfactory
This figure is shown in the PDF version of the article.
The results of the mathematical optimization model are presented in Fig. 3. In Phase 1, optimal hub locations were determined by simultaneously minimizing total assignment distances and maximizing hub evaluation scores. The resulting cluster-to-hub allocation structure is illustrated in Fig. 3. To demonstrate the routing capability of the proposed framework, Gilan Province was selected as a representative case study, and the corresponding routing and biomass collection results are also reported. Although the same analysis was conducted for all provinces under consideration, only the results for Gilan Province in the third planning period under the pessimistic scenario are presented for brevity.
Fig. 4 compares the total biomass supply chain costs obtained under five different configurations. The results reveal that the highest total cost is associated with the no-clustering scenario, reaching 21,354,851 monetary units. In contrast, SC produced the lowest total cost of 15,326,458 monetary units, representing a cost reduction of approximately 28% relative to the baseline case. CKM also achieved significant cost savings, reducing total costs by approximately 18.9% compared with the no-clustering scenario. These findings highlight the critical role of data-driven clustering strategies in enhancing the operational efficiency of biomass supply chain networks and reducing overall system costs, particularly under conditions characterized by uncertainty and operational complexity.
This figure is shown in the PDF version of the article.
This figure is shown in the PDF version of the article.
5. Conclusion
This study proposed a multi-stage decision-making framework for the design of a biomass energy supply chain network under uncertainty. The framework simultaneously addresses hub location selection, resource allocation, and product and energy flow design by integrating data-driven clustering techniques, MCDM methods, and a bi-level optimization model. Through the combination of these methodologies, a comprehensive and practical framework was developed to support the design and management of sustainable bioenergy supply chain networks. The computational results demonstrated that the integration of clustering techniques with optimization modeling can significantly enhance both the economic and operational performance of the network. The proposed approach achieved substantial reductions in total supply chain costs, improved resource allocation efficiency, reduced logistical complexity, and enhanced overall network effectiveness. Furthermore, the findings revealed that the selection of an appropriate clustering method constitutes a strategic decision that can considerably influence network design outcomes, particularly in large-scale problems characterized by high-dimensional and spatially dispersed data.
The results also highlight the importance of adopting data-driven and integrated decision-support tools for the development of sustainable and resilient bioenergy supply chains. As environmental disruptions, resource uncertainties, and market fluctuations continue to increase, the need for flexible and adaptive planning frameworks becomes increasingly critical. The proposed framework provides decision-makers with a systematic tool for improving network performance while accounting for operational and strategic uncertainties. Several directions for future research can be identified. First, the proposed model can be extended to dynamic and real-time decision-making environments by incorporating online data updates and adaptive optimization mechanisms. Second, advanced machine learning techniques may be integrated to improve clustering performance, demand forecasting accuracy, and uncertainty estimation. Third, future studies may explicitly incorporate policy-related considerations, environmental regulations, carbon management strategies, and social equity objectives into the network design process. Such extensions would contribute to the development of more efficient, adaptive, and socially responsible bioenergy supply chain systems capable of supporting long-term sustainability and resilience objectives.
Acknowledgments
The authors sincerely thank all those who contributed to this research through their guidance, expertise, and helpful recommendations.
Funding
No funding was received for this research.
Data Availability
Relevant data supporting the conclusions of this study can be obtained from the corresponding author upon reasonable request.
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