Toward Adaptive and Immune-Inspired Viable Supply Chains: A PRISMA Systematic Review of Mathematical Modeling Trends

Abstract

This study presents a systematic literature review on the mathematical modeling of resilient and viable supply chains, grounded in the PRISMA methodology and applied to a curated corpus of 235 peer-reviewed scientific articles published between 2011 and 2025. The search strategy was implemented across four major academic databases (Scopus and Web of Science) using Boolean operators to capture intersections among the core concepts of supply chains, resilience, viability, and advanced optimization techniques. The screening process involved a double manual assessment of titles, abstracts, and full texts, based on inclusion criteria centered on the presence of formal mathematical models, computational approaches, and thematic relevance. As a result of the selection process, six thematic categories were identified, clustering the literature according to their analytical objectives and methodological approaches: viability-oriented modeling, resilient supply chain optimization, agile and digitally enabled supply chains, logistics optimization and network configuration, uncertainty modeling, and immune system-inspired approaches. These categories were validated through a bibliometric analysis and a thematic map that visually represents the density and centrality of core research topics. Descriptive analysis revealed a significant increase in scientific output starting in 2020, driven by post-pandemic concerns and the accelerated digitalization of logistics operations. At the methodological level, a high degree of diversity in modeling techniques was observed, with an emphasis on mixed-integer linear programming (MILP), robust optimization, multi-objective modeling, and the increasing use of bio-inspired algorithms, artificial intelligence, and simulation frameworks. The results confirm a paradigm shift toward integrative frameworks that combine robustness, adaptability, and Industry 4.0 technologies, as well as a growing interest in biological metaphors applied to resilient system design. Finally, the review identifies research gaps related to the formal integration of viability under disruptive scenarios, the operationalization of immune-inspired models in logistics environments, and the need for hybrid approaches that jointly address resilience, agility, and sustainability.

1. Introduction

The increasing frequency of global disruptions—including health crises, geopolitical conflicts, and environmental emergencies—has exposed critical vulnerabilities in supply chains [1]. These challenges highlight the urgent need for systems that are not only resilient but also viable over time [2]. Viability, distinct from resilience, refers to the ability of a supply chain to continuously adapt, reconfigure, and sustain operations under conditions of deep uncertainty [3]. Traditional optimization models typically assume static conditions, characterized by fixed logistics structures, invariable parameters, and simplified or deterministic representations of demand scenarios. These models rely on fixed logistical structures and invariant parameters and represent demand in a simplified or deterministic manner [4]. However, this approach inadequately represents the complex dynamics of supply chains, which are constantly subjected to disruptions, fluctuations in resource availability, structural transformations within networks, and variations in demand and supply patterns [5]. As Ivanov and Dolgui [1] point out, most conventional models focus on passive resistance capabilities, omitting the dynamic adaptation mechanisms necessary to preserve long-term viability. Furthermore, recent studies by Sawik and Sawik [6] show that solutions optimized under static assumptions tend to fail in the face of continuous disruptive uncertainty, highlighting the need for reconfigurable and adaptive logistics systems. Even in advanced stochastic programming frameworks, there remains a limitation in modeling disruptions as isolated events, failing to adequately capture cascading effects and the progressive recovery processes required in volatile and dynamic environments [7].

As highlighted by Ivanov and Keskin [8], viable systems should be conceived as entities that evolve under external pressures, incorporating capabilities for structural reconfiguration, operational learning, and evolutionary resilience. This perspective has been reinforced by recent studies emphasizing the importance of integrating distributed control mechanisms, modular organizational structures, and continuous feedback-based learning to maintain operational continuity amid profound disruptions [9,10]. Such approaches argue that viable supply chains should adopt decentralized decision-making, functional redundancy, and learning capabilities to effectively adapt to environmental volatility [11]. Similarly, Gao et al. [12] propose modeling frameworks that incorporate structural adaptability and staged recovery strategies, enabling supply chains not only to withstand perturbations but also to reconfigure and evolve dynamically in the face of escalating uncertainty. Recent studies emphasize that viable logistics networks must be conceived as dynamic systems capable of self-organization, progressive adaptation, and learning from disruptions to maintain functionality under conditions of uncertainty [13,14].

Consequently, organizational viability is conceptualized as a dynamic phenomenon, where resilience is not solely reliant on structural redundancy but arises from capabilities for adaptation, reorganization, and contextual learning [15]. It is imperative to incorporate mechanisms such as distributed control, structural modularity, and operational flexibility based on contextual recognition into supply chain design [16]. These advocates move beyond traditional reductionist or modular models by integrating principles of decentralization, functional diversity, and local feedback loops as fundamental pillars for developing adaptive and sustainable supply chains [17,18]. Recent advances in mathematical modeling have equipped researchers with powerful tools to address these challenges [6]. Notable techniques include mixed-integer linear programming (MILP) [19], stochastic programming [20], fuzzy logic [21,22,23], and robust optimization models [24,25].

This vision of dynamic viability has led to the emergence of modeling paradigms inspired by biological systems, particularly the human immune system (HIS), which is recognized as a paradigmatic example of distributed resilience, adaptive learning, and evolutionary homeostasis [26]. The inspiration drawn from biological immune systems has led to modeling approaches characterized by their capacity for adaptation, self-organization, and distributed response [27]. However, in nature, the efficacy of the immune system relies not solely on redundancy mechanisms but also on its ability to continuously learn and adapt to evolving threats [28]. Artificial immune systems, designed for anomaly detection and response in dynamic environments, exhibit similar properties: they can learn from emerging threats, adapt to changing patterns, and operate in a distributed manner to enhance detection and response capabilities against novel and unknown attacks [29]. This illustrates that true resilience and protection depend not only on structural redundancy but also on adaptive mechanisms that enable systems to evolve and respond effectively within complex, ever-changing environments [30]. Consequently, integrating principles of adaptive immune systems into the design of models and management systems can significantly enhance their capacity to respond to unpredictable threats, thereby strengthening long-term resilience [31].

Despite advances in the mathematical modeling of resilient supply chains and the development of bio-inspired approaches, methodological fragmentation persists, which limits their effective integration. Firstly, there is a lack of a unified conceptual framework that clearly articulates how bio-inspired principles—such as self-organization, functional redundancy, and adaptation—can be translated into formalized and applicable mathematical models [26]. Furthermore, a disconnect is observed between the levels of abstraction: nature-inspired approaches often operate at a conceptual and philosophical level, whereas mathematical models require rigorous formalization, including equations, algorithms, and quantitative metrics, which complicate the operationalization of their principles [32]. The limited integration of hybrid methodologies also constrains the exploitation of their complementary strengths: most studies operate within independent approaches, without developing frameworks that combine bio-inspired models with robust optimization techniques or advanced heuristics [26]. These methodological fragmentations therefore represent significant obstacles to the development of integrated and effective models that combine the richness of bio-inspired approaches with rigorous mathematical formalization. This review identifies the absence of theoretical and applied consolidations that coherently articulate the adaptive capabilities of biological systems with the analytical requirements of advanced mathematical models. In response to this gap, this article offers a PRISMA-based systematic mapping of major models and optimization techniques aimed at strengthening the resilience and viability of supply chains. Particular attention is given to the emerging role of analogies with the human immune system, examined alongside classical approaches across six thematic dimensions: viability, resilience, agility, logistics optimization, uncertainty modeling, and bio-inspired systems. Through this review, a structured synthesis of methodological trends, practical insights, and future research directions is proposed, aimed at advancing the development of adaptive, viable, and robust supply chain systems.

Identified Gaps and Contribution

Despite advancements in the mathematical modeling of resilient supply chains and the development of bio-inspired approaches, a methodological fragmentation persists that limits their effective integration. Specifically, the current literature lacks a unified methodological framework that formally and coherently articulates immunological principles—such as self-organization, functional redundancy, and dynamic memory—with applicable mathematical models in real-world scenarios. Most studies operate independently, without establishing formal connections that enable the exploitation of the complementary advantages of these approaches, thereby restricting their applicability in complex and highly uncertain environments.

Furthermore, there is limited empirical validation and a low level of integration of hybrid approaches within operational contexts, which hampers their transfer to practice. Managing the inherent complexity and dynamism of these networks remains a significant challenge, and the absence of integrated frameworks that simultaneously address resilience, viability, and agility within a unified scheme prevents the progression toward truly self-organized, adaptive, and resilient supply chain systems. This absence limits the development of supply chain systems capable of evolving, learning, and maintaining functionality in the face of complex, cascading disruptions.

This article addresses these gaps by presenting a systematic review guided by the PRISMA methodology, mapping 235 peer-reviewed studies across six thematic dimensions: viability-oriented modeling, resilient optimization frameworks, agile and digitally enabled supply chains, logistics and network optimization, stochastic and uncertainty-based modeling, and immune-inspired systems. Particular emphasis is placed on identifying methodological trends, highlighting the incipient role of immune analogies within optimization frameworks, and proposing future research avenues aimed at bridging classical mathematical modeling with biologically inspired adaptive strategies. Through this synthesis, the review offers practical insights and conceptual foundations to advance the design of adaptive, viable, and robust supply chain systems for increasingly uncertain environments.

Although several recent studies have explored specific aspects of supply chain resilience, viability, or biologically inspired optimization (e.g., [1,9,27]), none have comprehensively examined the intersection of viability, resilience, agility, uncertainty modeling, immune-inspired approaches, and mathematical optimization within a unified analytical framework. In contrast to prior works that focused on isolated disruptions, theoretical advancements, or specific modeling layers, this manuscript offers a systematic, PRISMA-guided literature review of 235 peer-reviewed articles, covering multiple databases and capturing the multidimensional evolution of modeling trends from 2011 to 2025. Furthermore, this review distinguishes itself by integrating formal modeling approaches—such as MILP, stochastic programming, fuzzy systems, and immunological constraints—into a cohesive classification matrix aligned with current supply chain challenges. In doing so, it consolidates previously fragmented contributions and delivers a structured foundation for advancing adaptive, viable, and robust supply chain systems.

The review was guided by the following research question:

What mathematical models have been employed to enhance resilience and viability in supply chains, and how can bio-inspired analogies based on the immune system contribute to the development of more adaptive, decentralized, and effective systems under high uncertainty?

This question reflects a dual focus: (i) the classical body of literature on mathematical modeling and optimization for resilient and viable supply chains, and (ii) the emerging interest in immune system-inspired models that simulate adaptability and distributed response under uncertainty.

To address this question, the article is structured into several complementary sections. Section 2 describes the PRISMA methodology used for the identification, selection, and analysis of the included studies, detailing the search strategies and the inclusion and exclusion criteria. Section 3 presents a descriptive analysis of scientific production, including bibliometric statistics and a thematic mapping of the main research topics. Section 4 develops a structured thematic analysis across six key dimensions: viability, resilience, agility, logistics optimization, uncertainty modeling, and bio-inspired systems. Section 5 offers a synthesis of findings, proposes future research directions, and discusses the main conceptual gaps identified in the current literature. Finally, Section 6 presents the general conclusions of the study, highlighting its main contributions and the practical and theoretical implications of the results.

2. Materials and Methods

This study follows the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) guidelines to ensure transparency, reproducibility, and methodological rigor in the identification, selection, and synthesis of relevant studies. The following subsections detail each stage of the process.

2.1. Databases and Search Strategy

Following the PRISMA framework, this review implemented a systematic search strategy designed to ensure comprehensive and reproducible coverage of the relevant literature. The initial search was conducted across Scopus and Web of Science due to their extensive indexing of peer-reviewed publications in operations research, supply chain management, and systems engineering. From these platforms, articles were filtered and retained if published in journals belonging to four leading editorial sources: ScienceDirect, SpringerLink, Taylor & Francis, and MDPI.

The decision to restrict the final corpus to these four databases was based on three methodological considerations. First, they host a substantial portion of high-impact journals aligned with the thematic scope of this review. Second, their structured metadata and advanced search capabilities ensure transparent and reproducible screening in line with PRISMA standards. Third, the relevance density was significantly higher in these sources; exploratory checks on other repositories such as Wiley and Emerald yielded minimal incremental contributions to the review’s central themes—resilience, viability, agility, and mathematical modeling. Thus, depth and methodological coherence were prioritized over exhaustive inclusion.

The search strategy was designed to capture the intersection of three core thematic dimensions: (i) supply chain systems; (ii) resilience and viability; and (iii) mathematical modeling and optimization techniques. A structured Boolean query was constructed and adapted to the syntax of each platform to ensure precision and recall. The general form of the search string was:

• (“Supply chain” AND (resilience OR viability) AND (“optimization” OR “mathematical model” OR MILP OR “robust design”))

This formulation allowed for the retrieval of articles explicitly focused on optimization-based decision-making under uncertainty in supply chain contexts, while maintaining openness to studies that explored viability from novel or emergent methodological angles. The search process incorporated truncation, phrase searching, and keyword variations to capture a broad yet focused set of records. The initial search yielded a total of 2172 unique entries from both sources combined, spanning a range of journals and thematic foci. These records were then exported to bibliographic management software and manually reviewed to eliminate duplicates and entries not matching the research focus. The selection process was iterative and aligned with a predefined protocol, allowing for the consistent application of inclusion and exclusion criteria in subsequent stages.

2.2. Inclusion and Exclusion Criteria

To ensure the methodological rigor and thematic coherence of this systematic review, a set of predefined inclusion and exclusion criteria was established following the PRISMA guidelines and aligned with best practices in systematic literature mapping in operations research and supply chain management. These criteria served to filter the initially retrieved corpus and ensure the relevance and analytical depth of the selected studies. Articles were included if they met all the following conditions:

• Peer-reviewed journal publication: only articles published in indexed, refereed scientific journals were considered eligible, excluding conference papers, editorials, and non-peer-reviewed documents.
• Formal modeling approach: the study must employ a mathematical model as the core analytical foundation. In the scope of this review, a mathematical model is defined as a structured, quantitative framework that formally represents the configuration, behavior, and performance of a supply chain system using equations, algorithms, or logical constructs. These models aim to support decision-making under uncertainty and complexity by enabling simulation, optimization, or control of logistical and operational processes. Common modeling paradigms include mixed-integer linear programming (MILP), stochastic programming, robust optimization, fuzzy and possibilistic programming, and hybrid frameworks integrating artificial intelligence or biologically inspired components. Mathematical models are characterized by their analytical rigor and structured formulation, as illustrated in recent contributions such as Yilmaz et al. [7], Sawik [20], and Ben Abid et al. [24].

To ensure methodological transparency, the selected articles were further classified according to six dominant modeling paradigms identified in the corpus:

• Mixed-Integer Linear Programming (MILP), used for supply chain design, routing, and capacity planning under structural constraints.
• Stochastic Programming, modeling probabilistic uncertainty in supply, demand, or disruptions.
• Robust Optimization, addressing worst-case scenarios with no reliance on probability distributions.
• Fuzzy and Possibilistic Programming, capturing ambiguity through membership functions and linguistic variables.
• Multi-objective Optimization, used to balance trade-offs between cost, risk, sustainability, and resilience.
• Immune-Inspired and Bio-Inspired Modeling, incorporating principles such as redundancy, self-organization, and dynamic adaptation through analogies to biological systems.

Each article was classified based on its primary modeling approach. In cases of hybrid frameworks, a dual-tagging scheme was applied. This formal categorization enabled the structured thematic synthesis in Section 4 and supports the comparative analysis of methodological evolution during the review period.

3.

Relevance to key constructs: the article needed to explicitly address at least one of the central concepts of the review—resilience, viability, or agility—as either a modeling objective, evaluation criterion, or embedded capability in the system design.

4.

Timeframe and language: publications needed to be written in English. This period captures both post-global financial crisis adaptations and recent developments related to digital, pandemic, and geopolitical disruptions. Additionally, survey articles or systematic reviews that provide comprehensive analyses of the state of the art, trends, and gaps in the relevant literature are included.

• Articles were excluded under the following conditions:

1.

All documents that were not peer-reviewed journal articles, were not published in English, or did not fall within the period from 2011 to 2025 were excluded. In addition, only records indexed in ScienceDirect, Taylor & Francis, MDPI, and SpringerLink were retained. This restriction was applied to ensure a consistent level of editorial quality, peer-review rigor, and thematic relevance within the domains of supply chain management, industrial engineering, and mathematical modeling. These four databases were selected due to their recognized focus on applied sciences and operations research, as well as their comprehensive indexing of high-impact journals in the field.

2.

If they were purely conceptual, theoretical, or descriptive, lacking any quantitative, computational, or optimization-based methodology. This includes taxonomies, bibliometric reviews, or managerial frameworks not grounded in modeling logic.

3.

If they originated from conference proceedings or non-journal venues, regardless of their topic or scope, due to concerns about methodological consistency and peer-review standards.

Importantly, the review adopted an inclusive stance toward studies employing simulation techniques (e.g., agent-based models, system dynamics, Monte Carlo) and Industry 4.0 technologies (e.g., artificial intelligence, blockchain, digital twins, IoT), even in the absence of classical optimization. These studies were retained, provided they included a computational or algorithmic foundation and contributed to the modeling or analysis of supply chain resilience, viability, or agility. This adjustment reflects the evolution of modeling paradigms in the field and acknowledges the growing role of digital technologies in enabling adaptive and viable supply chains.

The decision to delimit the study period from 2011 to 2025 is grounded in both methodological discipline and thematic relevance. This time frame captures the period during which scholarly contributions to supply chain modeling began to consistently incorporate concepts such as resilience, viability, and hybrid approaches to uncertainty. Based on the thematic and analytical patterns observed in the 235 peer-reviewed articles included in this review, 2011 represents the earliest point at which adaptive modeling frameworks begin to emerge with sufficient methodological clarity to align with the objectives of this study.

Although the number of relevant studies remained relatively constant throughout the early part of the period, their content reflects a gradual conceptual shift toward digitally enabled, robust, and biologically inspired paradigms. The decision to include literature from 2011 onward thus ensures the historical grounding of this review without incorporating earlier works that lack alignment with the six thematic dimensions examined. The upper bound of 2025 corresponds to the most recent literature available at the time of the final database search, thereby ensuring that the findings reflect the current state of the field.

By applying this criteria framework systematically, the review ensured that the selected studies were not only methodologically sound but also relevant to the core themes of structural adaptability, operational continuity, and decision-making under uncertainty.

2.3. Screening Process

The screening process was executed in alignment with the PRISMA guidelines to ensure transparency, reproducibility, and methodological rigor throughout the selection of the studies. This multi-stage procedure was designed to progressively filter the initial pool of retrieved records—ensuring that only those articles with robust methodological contributions and thematic alignment were retained for in-depth analysis.

The process unfolded in three sequential stages, each applying increasingly specific inclusion criteria. First, during the title screening phase, all entries resulting from the database queries were examined to identify and exclude clearly irrelevant records—those whose titles lacked any reference to supply chains, mathematical modeling, or the core constructs of resilience, viability, or agility. This preliminary pass served to eliminate a significant proportion of off-topic entries, such as those focused on unrelated fields (e.g., biology, education, or policy studies) that were retrieved due to keyword overlap.

The second stage involved a systematic abstract screening, during which the remaining studies were evaluated based on the clarity and relevance of their methodological contributions. At this point, entries were excluded if their abstracts did not reference any form of formal modeling—whether mathematical, algorithmic, or computational—or if they addressed supply chain topics in a purely descriptive or managerial fashion without analytical depth. Unlike in more restrictive reviews, studies that employed simulation techniques (such as agent-based) or incorporated technologies associated with Industry 4.0 (e.g., artificial intelligence, blockchain, IoT) were retained, provided they presented structured approaches to analyzing supply chain behavior under uncertainty and disruption. This inclusive approach ensured that emergent, digitally enabled modeling paradigms were properly represented in the final review corpus.

Finally, a full-text review was conducted for all articles that passed the abstract screening. Each study was read in detail to verify its compliance with the methodological and thematic inclusion criteria described in Section 2.3. This phase focused on validating the mathematical foundations of each contribution (e.g., presence of MILP, fuzzy logic, multi-objective programming, stochastic modeling), the operationalization of resilience or viability, and the clarity of the modeling assumptions, constraints, and objectives. Special attention was paid to hybrid and interdisciplinary approaches, ensuring their relevance and consistency with the analytical goals of the review.

Throughout this process, bibliographic management software (e.g., Mendeley) and spreadsheet matrices were used to systematically track the eligibility status of each article, document exclusion reasons, and ensure the traceability of decisions. Duplicate entries were automatically detected and manually verified, especially in cases where variations in title formatting or author names could lead to redundant inclusion.

This rigorous screening pipeline ultimately reduced the initial corpus of 2172 records to a final set of 235 articles, each of which provides a substantive methodological contribution to the modeling of supply chain viability, resilience, or agility. These articles were subsequently categorized into six analytical clusters—viability, resilience, agility, logistics optimization, uncertainty modeling, and immune-inspired approaches—which structure the results presented in Section 3, Section 4, Section 5 and Section 6.

2.4. PRISMA Flow Diagram

The flow of information throughout the various stages of the systematic review process is presented in accordance with the PRISMA 2020 guidelines [33]. Figure 1 provides a visual representation of the number of records identified, screened, excluded, and included at each phase. The review process began with the identification of 2172 unique records, retrieved through a carefully structured Boolean query applied across multiple academic databases (see Section 2.2). As a first-level filtering stage, only articles indexed in ScienceDirect, Taylor & Francis, MDPI, and SpringerLink were retained. At this stage, Exclusion Criterion 1 was also applied, eliminating all documents that were not peer-reviewed journal articles, not written in English, or not published within the period from 2011 to 2025, thereby reducing the corpus to 712 records. This initial strategy ensured a methodologically sound foundation, aligned with international editorial standards and the thematic focus of the review.

Subsequently, Exclusion Criterion 2 was applied, resulting in the removal of 394 articles during the title and abstract screening phase. These exclusions corresponded to the absence of a quantitative, computational, or optimization-based methodology. Purely conceptual, theoretical, or descriptive works were excluded, including taxonomies or managerial frameworks not grounded in formal modeling approaches. Articles that, despite addressing supply chain-related topics, did not incorporate any modeling or simulation components were also discarded. The remaining 318 articles underwent a comprehensive full-text review. At this stage, each study was assessed in detail to verify its compliance with the methodological and thematic inclusion criteria defined in Section 2.3. The evaluation focused on validating the mathematical foundations of each contribution—such as the presence of mixed-integer linear programming (MILP), fuzzy logic, multi-objective optimization, or stochastic modeling—as well as the operationalization of resilience or viability constructs. The clarity and completeness of modeling assumptions, constraints, and objectives were also examined. Particular attention was given to hybrid and interdisciplinary approaches to ensure their consistency with the analytical aims of the review. As a result of this stage, 83 additional articles were excluded for failing to meet the required level of methodological rigor or analytical depth.

A distinctive feature of this review was the intentional inclusion of studies based on simulation and emerging Industry 4.0 technologies, such as artificial intelligence, blockchain, digital twins, and machine learning. Provided that these contributions offered algorithmic or system-level modeling perspectives relevant to supply chain resilience or viability, they were retained—even in the absence of traditional optimization paradigms. The final output of this process was a curated set of 235 peer-reviewed journal articles, each of which rigorously met all inclusion criteria and made a substantive contribution to at least one of the six analytical dimensions that structure this review.

3. Results Overview

This section provides an integrative analysis of the key findings within the reviewed literature, focusing on the modeling approaches employed to address resilience, viability, and agility in supply chains. It highlights the predominant modeling techniques, conceptual frameworks, and emerging trends, including bio-inspired approaches, notably those inspired by the human immune system. Additionally, it identifies the main gaps and challenges faced by current research, as well as opportunities to integrate traditional and bio-inspired methodologies in the design of more adaptive, distributed, and resilient systems.

3.1. Annual Scientific Production

The annual scientific production of the 235 articles included in this review reveals a notable trend toward increasing academic interest in the modeling of resilient and viable supply chains. As illustrated in Figure 2, the number of publications has grown significantly over the past decade, with a marked acceleration from 2020 onwards. This surge reflects the compounded effects of global disruptions—such as the COVID-19 pandemic and supply shortages—on the prioritization of robustness, adaptability, and digital innovation in supply chain systems. The peak in publication activity occurred in 2023, followed closely by sustained output through 2024 and early 2025. These figures underscore the growing recognition of resilience and viability as essential pillars of supply chain design and confirm the timeliness and relevance of this systematic review.

3.2. Database Distribution

The distribution of the 235 articles included in this review across academic databases reveals a strong concentration of publications in four major repositories: ScienceDirect, MDPI, SpringerLink, and Taylor & Francis. As shown in Figure 3, ScienceDirect—representing publications from Elsevier—accounts for the largest share of contributions, reflecting its dominant position in the fields of industrial engineering, operations research, and supply chain analytics.

MDPI and SpringerLink also feature prominently, contributing a significant proportion of studies, particularly in interdisciplinary journals that combine technological, environmental, and logistical perspectives. Taylor & Francis, while smaller in volume, includes several specialized journals that focus on decision sciences and logistics policy. This distribution demonstrates the variety of fields covered in the reviewed literature and shows the range of editorial perspectives on supply chain resilience and viability. The presence of articles across these platforms reinforces the legitimacy and academic rigor of the sample and confirms that the search strategy successfully captured a representative cross-section of the scientific landscape.

3.3. Thematic Map Analysis

To deepen the conceptual analysis of the selected literature and to provide a visual synthesis of its intellectual structure, a thematic map analysis was conducted based on a manual classification of 235 peer-reviewed articles. These studies were systematically organized into six analytical categories: Viability, Resilience, Agility, Optimization and Logistics, Uncertainty Modeling, and Immune-Inspired Approaches. This categorization not only structures the results presented in Section 4, Section 5 and Section 6, but also facilitates the identification of latent research clusters, conceptual overlaps, and methodological intersections within the field.

Subsequently, the most recurrent and thematically relevant terms were identified for each cluster. These terms were extracted from the titles, abstracts, and keywords of the selected articles. The information was consolidated through a co-occurrence analysis and refined to eliminate redundant or overly generic concepts.

Based on this cleaned dataset, conceptual coordinates were assigned to each term within a two-dimensional thematic space defined by two commonly adopted bibliometric indicators:

• Centrality: the degree to which a term is connected to other key topics in the corpus, representing its structural importance within the field.
• Density: the internal coherence and development level of the theme, in terms of its theoretical and methodological foundation.

The positioning of terms in the thematic map enables their classification according to their role in the field—whether as central, specialized, emerging, or underdeveloped topics. Furthermore, the size of each node (circle) represents the relative frequency or prominence of the term across the reviewed corpus, providing a visual measure of thematic relevance.

As illustrated in Figure 4, the quadrant-based distribution reveals four primary thematic zones. The upper-right quadrant (Motor Themes) includes highly developed and central topics such as supply chain management, distributed ledger technologies, and cloud-based systems. These themes exhibit methodological maturity and occupy a central structural role in the literature, particularly in areas related to digitalization, optimization, and supply chain resilience.

The lower-right quadrant (Basic Themes) contains foundational topics such as blockchain and supply chains, which—despite being conceptually influential—are less methodologically formalized. These themes often serve as contextual frameworks rather than drivers of analytical innovation, suggesting strong potential for integration with advanced approaches such as stochastic programming, MILP, or hybrid decision-making systems.

The upper-left quadrant (Niche Themes) comprises highly specialized topics, including inventory control, traceability systems, and supplier selection. These areas demonstrate considerable methodological sophistication and are typically associated with technical or industry-specific applications. Their high density signals internal development, while their lower centrality reflects limited cross-cutting impact across the broader literature.

The lower-left quadrant (Emerging or Declining Themes) includes less developed and peripheral topics, such as automobile manufacturing, data integrity, and stakeholder relations. These may represent either nascent research directions that have yet to mature or declining areas of interest displaced by emerging paradigms such as digital trust, artificial intelligence, or platform-based coordination.

Taken together, the thematic map highlights the structural heterogeneity of the field. Two dominant and interconnected clusters—Resilience and Optimization and Logistics—emerge as well-established domains, frequently linked through shared methodologies such as stochastic programming, robust optimization, and network design models. The Viability cluster, while more recent and smaller in volume, introduces long-term system-oriented constructs such as adaptive continuity, socio-environmental trade-offs, and organizational sustainability. In contrast, Agility appears as a dynamic but structurally fragmented theme, associated primarily with Industry 4.0 technologies (e.g., IoT, digital twins, artificial intelligence) aimed at improving operational responsiveness. The Uncertainty Modeling cluster cuts across all thematic areas, offering foundational tools—such as fuzzy logic, possibilistic programming, and Monte Carlo simulation—applied both in isolation and within hybrid modeling frameworks. Finally, Immune-Inspired Approaches represent a novel conceptual frontier. Although still limited in number, these studies offer biologically grounded models that emulate distributed resilience, self-regulation, and adaptive learning within supply networks.

In summary, this thematic framework reflects the intellectual architecture of the reviewed corpus while identifying conceptual synergies and innovation opportunities—such as the integration of immune-inspired mechanisms into digital and stochastic models or the operationalization of viability in dynamic uncertainty contexts. These connections are further explored in the subsequent sections of the article.

3.4. Evolution of Research Trends

The evolution of research trends in the mathematical modeling of viable, resilient, and agile supply chains between 2011 and 2025 reveals a clear progression in both methodological diversity and thematic emphasis. Early studies (2011–2015) were limited in number and scope, with an average of fewer than five publications per year. These contributions predominantly relied on traditional optimization approaches, especially mixed-integer linear programming (MILP), focusing on cost minimization and structural design under deterministic or mildly constrained settings. Between 2016 and 2019, a gradual increase in research activity became evident, with the number of publications per year ranging from four to eight. This period marked the emergence of alternative modeling paradigms, including stochastic programming and fuzzy logic, reflecting a growing concern with uncertainty, risk propagation, and trade-offs across performance criteria such as cost, service level, and sustainability. Despite the moderate growth, the literature remained primarily centered on resilience, with viability and agility concepts still underrepresented in formal models.

A major turning point occurred in 2020, coinciding with the global impact of the COVID-19 pandemic. Annual publications surged from seven in 2020 to 14 in 2021, followed by a slight dip in 2022 (11), and then a substantial rise to 41 in 2023 and a peak of 71 in 2024. The year 2025, although incomplete, already shows a strong contribution with 50 publications. This post-2020 acceleration reflects a paradigmatic shift toward dynamic and uncertainty-aware modeling. Notable developments during this period include:

• A significant rise in robust and stochastic optimization models aimed at addressing large-scale, cascading disruptions [6,20].
• The formalization of viability and survivability as explicit modeling objectives, extending beyond traditional resilience frameworks [1,2,3].
• The integration of digital and agile enablers, such as digital twins, real-time data integration, and adaptive supply chain platforms [9,14].
• The initial adoption of immune-inspired and bio-inspired modeling, incorporating concepts such as self-organization, redundancy, and adaptive memory into optimization models [26,27,32].

These trends highlight a broader transformation: from static, cost-focused supply chain designs to flexible, adaptive systems capable of navigating extreme volatility and long-term uncertainty. This evolution is further shaped by an increasing convergence between operations research and interdisciplinary fields—such as artificial intelligence, complex systems theory, and biological metaphors—resulting in a more diverse modeling landscape where resilience, viability, and adaptability are systematically embedded into formal analytical structures.

4. Thematic Results

Building upon the bibliometric and thematic synthesis presented in the previous section, this part of the review provides a structured analysis of the literature based on six thematic dimensions that emerged from the identification and classification process. These dimensions reflect the diversity of research approaches and conceptual priorities in the modeling of resilient, viable, and adaptive supply chains. The classification of studies was informed both by the frequency and co-occurrence of key terms—as highlighted in the thematic map analysis—and by the explicit objectives, modeling strategies, and methodological frameworks described in each article. Rather than adopting a purely taxonomic or keyword-driven approach, the themes were constructed to reflect meaningful conceptual clusters and analytical orientations. This enables a clearer articulation of how different modeling paradigms contribute to the understanding and improvement of supply chain systems under conditions of uncertainty and disruption.

4.1. Viability in Supply Chain Design

The concept of supply chain viability has rapidly evolved as organizations strive to maintain operational continuity, sustainability, and strategic adaptability in increasingly volatile environments. The literature reveals that viability is not an isolated characteristic but a systemic property arising from the interplay of structural design, digital innovation, sustainability practices, risk management strategies, governance mechanisms, and advanced optimization models. Accordingly, this review organizes the analysis into six major thematic dimensions: (1) Structural and Network Design, which addresses the physical and topological configuration of supply chains; (2) Digitalization and Intelligent Twins, focusing on the use of digital tools, cyber-physical systems, and AI-driven simulation; (3) Sustainability and Circular Economy, analyzing the integration of environmental and social goals in supply chain viability; (4) Risk Management and Uncertainty Handling, which refers to strategic and organizational responses to disruption and volatility—such as redundancy, flexibility, risk-sharing, and real-time sensing—not necessarily involving formal mathematical modeling; (5) Governance, Cooperation, and Organizational Adaptation, exploring coordination mechanisms, stakeholder alignment, and dynamic learning capabilities; and (6) Mathematical and Stochastic Optimization Models, which focuses on the development of formal, quantitative models—such as MILP, robust optimization, fuzzy systems, and stochastic programming—that may support viability under uncertainty but are evaluated here as a modeling contribution in their own right. It is worth noting that several authors contribute to more than one thematic dimension, reflecting the interdisciplinary nature of viability research and the inherent overlap between modeling techniques, technological enablers, and organizational strategies. This structure facilitates a rigorous and nuanced exploration of the pathways through which viability is conceptualized and operationalized in supply chain research (

Table 1. Classification of Reviewed Articles According to Viability Dimensions and Associated Optimization Approaches.

Viability Dimension	Authors
Structural and Network Design	[1,4,6,8,16,20,25,34,35,36,37,38,39,40,41,42,43]
Digitalization and Intelligent Twins	[9,14,37,39,44,45,46,47]
Sustainability and Circular Economy	[6,25,30,35,38,39,44,45,46,48]
Risk Management and Uncertainty Handling	[1,8,20,34,36,38,42,46,49,50,51,52,53,54,55,56]
Governance, Cooperation, and Organizational Adaptation	[2,43,47,49,57,58,59]
Mathematical and Stochastic Optimization Models	[6,8,20,25,27,34,38,44,46,49,50,53,54,60,61,62]

).

Building upon the foundations of stochastic modeling for ripple effects [20], subsequent approaches have expanded viability frameworks to incorporate reshoring strategies [55], adaptive cooperation among heterogeneous manufacturers [43], and structural integration of sustainability and leagility principles [4]. Early stochastic models sought to minimize service disruptions and cost penalties under uncertainty [20]. However, recognizing the vulnerability of globalized supply chains to ripple effects and cascading failures, strategic reshoring has been proposed as a viable mechanism to reconfigure networks closer to demand centers, thereby enhancing both resilience and viability [54,55].

Expanding from industrial to agri-food contexts, research has shown that structured capabilities and dynamic pricing mechanisms significantly affect the economic viability of smallholders [35], underlining that network topology must accommodate market volatility without sacrificing competitiveness. The emphasis on adaptive structures is further reinforced by agent-based simulation studies, which illustrate how heterogeneous manufacturers, when organized in cooperative networks, function as dynamic “sponges” that buffer supply and demand shocks, thereby sustaining viability [43].

These structural insights converge with hierarchical modeling frameworks like the one proposed by Hashemi Petrudi et al. [4], where resilience, leagility, and sustainability emerge as interdependent pillars that must be embedded within supply chain architectures to guarantee long-term viability. Moving into pandemic-induced disruption contexts, adaptation mechanisms such as scalability, substitution, intertwining, and repurposing have been identified as critical structural capabilities [36], pointing to the necessity of reconfigurable and modular supply chain designs [62].

The systemic perspective advocated by Ivanov and Dolgui [1] emphasizes that viability cannot be secured by individual firms alone, but must be conceived at the ecosystem level, where intertwined supply networks collectively adapt to shocks through integrated resilience strategies. Structural innovation extends into circular supply chain architectures, where the integration of reverse logistics and redundant pathways, as proposed by Echefaj et al. [34], enhances systemic robustness without sacrificing operational efficiency. Similarly, Belamkar et al. [25] optimize agro-food supply networks through fuzzy multi-objective models, balancing environmental and economic objectives, thus illustrating how viability considerations are increasingly intertwined with sustainability imperatives. Tactical innovations, such as intelligent warehouse clustering strategies for inventory resilience, further illustrate the critical role of structural design in sustaining viable supply chains under volatile and uncertain conditions [7].

Building upon the recognition that structural design alone cannot guarantee supply chain viability under conditions of extreme uncertainty [2], researchers increasingly positioned digitalization as a fundamental enabler of proactive and dynamic adaptation [45]. Early explorations into digital supply chains emphasized the critical role of real-time visibility and predictive analytics in mitigating the ripple effects of disruptions [14], leading to the conceptualization of Intelligent Digital Twins (iDT) as advanced cyber-physical artifacts capable of continuous monitoring, early disruption detection, and autonomous learning [9].

Expanding these foundations, subsequent contributions proposed that viable supply chains must evolve into modular digital ecosystems, where services and assets can be dynamically composed in response to environmental volatility [37,48]. Lotfi et al. [46] introduced blockchain-enabled open innovation platforms, highlighting how decentralized data sharing and resource reallocation can transform supply chains into antifragile systems that not only withstand but adaptively grow from disruptions. Following this digital transformation trajectory, Ivanov et al. [37] formalized the concept of the Cloud Supply Chain, envisioning supply chains as service-oriented architectures capable of dynamic configuration and autonomous resilience management.

Complementary studies have focused on the organizational prerequisites for successful digital transformation. Wong et al. [47] empirically demonstrated that blockchain adoption for viability purposes is significantly moderated by organizational readiness and innovation diffusion dynamics, particularly among small and medium enterprises. These findings are reinforced by Villar et al. [10], who argue that systemic interoperability—enabled through open digital standards and knowledge-sharing frameworks—serves as a catalyst for constructing interconnected, digitally resilient supply networks.

Addressing the critical issue of decision-making under incomplete information, Liu et al. [53] integrated Causal Bayesian Networks with robust optimization techniques, illustrating that even in environments characterized by data scarcity, viable supply chain interventions can be guided by probabilistic inference and counterfactual reasoning. Altogether, the literature consolidates the view that digitalization is no longer ancillary but foundational: intelligent systems, blockchain ecosystems, and dynamic cloud architectures collectively reframe supply chain viability as a function of real-time adaptability, predictive resilience, and decentralized autonomy [9,37,45,47].

Economic performance alone cannot ensure long-term viability, and supply chain scholars progressively integrated sustainability and circular economy principles as structural components of resilience strategies [35,55]. Early contributions highlighted that economic viability, particularly in agri-food systems, is intrinsically linked to the ability of smallholders to dynamically adapt pricing and supply mechanisms in response to market volatility [35]. Extending this view, the industry 5.0 paradigm proposed by Ivanov [9] reframed supply chain viability as a systemic property emerging from the balanced integration of resilience, environmental sustainability, and human-centric innovation, marking a departure from traditional efficiency-centric models.

Following these conceptual shifts, the literature moved towards quantifying the trade-offs between environmental objectives and operational performance [25]. Degirmenci et al. [48] demonstrated, in the context of hydrogen supply chains, that viability assessments must concurrently address environmental impacts, supply security, and system flexibility, establishing multicriteria viability as a new evaluation standard. Complementary frameworks, such as the one developed by Khan et al. [39], applied interpretive structural modeling to agile and sustainable sourcing networks, underscoring that agility and sustainability are not mutually exclusive but synergistic enablers of long-term viability.

Optimization-based approaches further operationalized these insights. Belamkar et al. [25] introduced a fuzzy multi-objective optimization framework that balances carbon emission reductions with profitability in agro-food supply chains, providing a formal method to navigate environmental-economic trade-offs. Similarly, Darmian et al. [62] embedded R-imperatives—reduce, reuse, recycle—into supply chain design through stochastic optimization, aligning operational flexibility with circular economy objectives to enhance viability under uncertainty. The necessity of integrating circularity is especially evident in biologically sensitive sectors: Kalantari Khalil Abad et al. [38] modeled pest spread risk in agri-food systems using an elastic p-robust multi-stage stochastic framework, demonstrating that circular flow structures not only mitigate environmental degradation but also improve supply chain adaptability. Healthcare supply chains, highly exposed to pandemic-driven volatility, also exemplify this convergence. Alizadeh et al. [44] developed a multi-stage stochastic network model that optimizes patient recovery rates, operational costs, and environmental impacts simultaneously, showcasing how viability metrics must now incorporate social and ecological dimensions alongside traditional efficiency indicators. Collectively, these studies construct a new paradigm where sustainability is no longer an adjunct to supply chain viability but an embedded, structural necessity driving adaptive, resilient, and regenerative supply networks.

Building upon the recognition that risk is an inherent feature of complex supply chain systems, early models sought to extend viability frameworks by explicitly integrating disruption propagation dynamics, particularly through the concept of ripple effects [20]. Sawik [55] expanded this understanding by introducing reshoring strategies as a structural countermeasure to vulnerability, demonstrating that relocating production closer to markets reduces systemic exposure and enlarges the operational viability domain. Complementary to these structural solutions, Ivanov [36] proposed dynamic adaptation mechanisms such as scalability, substitution, and repurposing, positioning these capabilities as behavioral responses embedded within viable supply chain architectures.

Advancing beyond deterministic views, Ivanov and Dolgui [1] emphasized that viability must be conceived at the level of intertwined supply networks, where systemic coordination across multiple supply chains becomes essential for survival under catastrophic disruptions. Recognizing the limitations of static resilience frameworks, researchers introduced probabilistic and stochastic perspectives: Liu [53,60] leveraged Causal Bayesian Networks to model ripple effects under data scarcity, illustrating that viability decisions must account for uncertainty in both event occurrence and consequence propagation. In parallel, Lotfi et al. [46] conceptualized antifragility within supply chains, proposing blockchain-enabled open innovation platforms as dynamic buffers against unpredictable perturbations.

Following these theoretical advances, epidemic-driven disruption scenarios prompted further refinement of viability strategies. Broekaert et al. [49] modeled supranational supply chains using SEIRSD-based multiplex networks, elucidating the complex trade-offs between public health objectives and economic viability during pandemic control interventions. Addressing operational strategies, Wu et al. [56] demonstrated that diversified sourcing and disruption prevention must be dynamically balanced according to evolving buyer risk aversion profiles, suggesting that static sourcing strategies are insufficient for maintaining viability under prolonged uncertainty.

Building on these findings, Ivanov and Keskin [8] articulated the principles of post-pandemic viable supply chains, advocating for continuous structural replanning as a permanent feature of adaptive supply chain management. Li et al. [52] operationalized proactive stockpiling strategies, showing that inventory prepositioning tailored to disruption typologies can substantially increase survival probabilities during extreme events. Humanitarian and disaster logistics also adopted stochastic modeling approaches: Yilmaz et al. [61] developed machine-learning-embedded and robust multi-objective optimization frameworks for designing humanitarian supply chains that maintain viability across varying disruption severities. At the empirical level, Han and Um [51] confirmed that proactive risk management strategies—risk acceptance, avoidance, control, and sharing—significantly bolster supply chain viability, particularly when aligned with sustainability goals. Addressing sector-specific risks, Kalantari Khalil Abad et al. [38] introduced elastic p-robust programming for pest spread risk management in circular agri-food supply chains, further emphasizing that viability models must incorporate dynamic environmental uncertainties. Finally, Liu et al. [53] advanced robust optimization under data-scarce conditions by integrating causal inference with worst-case disruption planning, reinforcing the necessity of probabilistic resilience modeling in contemporary viability strategies.

The evolution of supply chain viability research increasingly recognizes that technological and structural solutions, while critical, are insufficient without corresponding advances in governance [58], cooperation [43], and organizational adaptability [57]. Emerging from early conceptualizations that focused primarily on structural resilience, scholars progressively highlighted that inter-organizational trust, cultural flexibility, and collaborative governance mechanisms are fundamental to sustaining viability under prolonged and systemic disruptions [1,2,30]. The recognition that supply chains function as socio-technical systems paved the way for models where cooperation among heterogeneous actors functions as a dynamic buffer against external shocks, enhancing systemic resilience beyond the sum of individual firm capacities [43].

Building upon this foundation, further investigations demonstrated that environmental, social, and governance (ESG) practices significantly influence operational continuity during crises, with firms exhibiting strong ESG profiles showing greater resilience against market volatility and supply disruptions [58]. This integration of governance factors into viability frameworks marks a critical shift from purely operational considerations towards strategic management of institutional and relational capital [53]. Subsequent studies reinforced that such collaborative behaviors—particularly information sharing, joint planning, and trust-building—are not mere facilitators but structural enablers of dynamic viability, embedding redundancy and flexibility into the very fabric of supply networks [59].

The diffusion of digital technologies further accentuated the role of organizational readiness in enabling viable transformations. Investigations into blockchain adoption revealed that technological fit alone is insufficient; rather, innovation diffusion dynamics [54], organizational adaptability [47], and cultural openness critically mediate the success of digital viability initiatives [37]. Expanding these insights, systemic interoperability frameworks emphasized that open knowledge sharing and cross-sector cooperation enable the construction of viable supply ecosystems, capable of sustaining themselves through adaptive resource sharing even under extreme environmental volatility [10]. Cultural adaptability also emerged as a decisive factor [30]. Adhocracy cultures, characterized by flexibility, innovation tolerance, and decentralized decision-making, were empirically shown to foster greater viability compared to rigid hierarchical structures, particularly in inflationary and uncertain environments where rapid reconfiguration of supply strategies is required [2,57]. Collectively, these developments consolidate the understanding that viable supply chains are not merely technical artifacts but socio-technical systems whose adaptability, resilience, and sustainability are co-produced through dynamic governance practices, cooperative behaviors, and organizational cultures conducive to innovation and continuous learning.

While organizational responses and structural adaptations are essential for managing risk and uncertainty, they are increasingly complemented by the development of formal mathematical models. These models are not merely auxiliary instruments but constitute an independent and rigorous domain of research aimed at operationalizing viability under complexity and volatility [45]. As such, mathematical and stochastic optimization techniques—including MILP [55], multi-objective fuzzy programming [25], robust programming [7], and causal probabilistic models [5]—are positioned not just as tools for supporting resilience, but as methodological foundations for quantitatively defining, simulating, and optimizing supply chain viability. The following section reviews this growing body of work.

The formalization of supply chain viability through mathematical and stochastic optimization frameworks represents a critical evolution in the field, providing quantitative tools to navigate complexity, uncertainty, and dynamic disruptions. Building upon early stochastic models that sought to balance service levels and disruption risks [6,55], researchers progressively incorporated multi-objective optimization techniques to simultaneously address economic, operational, and resilience goals [45,53]. Expanding this foundational work, the integration of reshoring decisions into stochastic viability frameworks illustrated that structural relocation strategies could be optimized not only for cost efficiency but also for systemic survival under disruption scenarios [20]. Advancing beyond static optimization, the application of Bayesian inference and causal modeling introduced a new dimension where decision-making under incomplete information became feasible. Probabilistic models, such as those developed through Causal Bayesian Networks [7,53], enabled viability strategies to incorporate uncertainty quantification at both the event occurrence and ripple propagation levels, reinforcing the necessity of probabilistic thinking in modern supply chain design [60]. Complementarily, blockchain-based open innovation platforms [46] introduced decentralized optimization paradigms, where antifragile behaviors are emergent properties of distributed decision-making rather than centralized control.

In the face of epidemic-induced systemic shocks, the modeling of supranational supply chains using epidemiological dynamics [49] and the balancing of risk aversion in sourcing strategies [56] provided further refinement to viability frameworks, emphasizing the need for adaptive, scenario-based optimization approaches. Post-pandemic supply chain theory consolidated these insights, advocating for dynamic reoptimization and continuous structural replanning as foundational features of viable operations [8]. Optimization methodologies also evolved to explicitly integrate circular economy principles. Multi-objective fuzzy programming, as applied to agro-food networks [25], and stochastic integration of R-imperatives into supply chain design [62], demonstrated that economic, environmental, and social objectives can be simultaneously optimized without compromising system viability. In highly vulnerable sectors, elastic p-robust programming approaches allowed for adaptive risk management under biological uncertainties, such as pest spread in agri-food systems [38].

The application of hybrid decision frameworks in automotive supply chains during COVID-19 disruptions [36] further validated that combining MCDM techniques with mixed-integer linear programming enhances the robustness of viability strategies under compound risk environments. Additionally, robust optimization models that integrate causal inference methods [53] illustrated that even under severe data scarcity, worst-case disruption planning can be systematically formalized to safeguard viability. Healthcare systems, facing complex multicriteria trade-offs during pandemic crises, exemplified the culmination of these advances. Multi-stage stochastic models were developed to optimize patient outcomes, operational costs, and supply continuity simultaneously, demonstrating the versatility of stochastic programming in managing viability across multiple performance dimensions [44].

Collectively, the literature converges on the understanding that mathematical and stochastic optimization models are not auxiliary tools but foundational mechanisms through which supply chain viability is quantitatively conceptualized, operationalized, and continuously adapted to dynamic and uncertain environments.

4.2. Resilient Supply Chain

The capacity of supply chains to withstand, adapt to, and recover from disruptive events has evolved into a central pillar of supply chain design and management. Recent scholarly contributions encompass a wide spectrum of modeling approaches, sustainability integrations, artificial intelligence applications, and sector-specific strategies aimed at enhancing resilience.

Table 2. Classification of Reviewed Articles Based on Key Subthemes in Resilient Supply Chain Research.

Subtheme	Articles
Modeling resilient supply chains	[1,26,44,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81]
Integration of sustainability and resilience	[68,69,72,76,79,80,82,83,84,85,86,87,88,89,90,91,92,93,94]
New approaches in resilience	[10,12,95,96,97,98,99,100]
Sector-specific resilient supply chains	[12,24,50,61,68,72,80,82,83,89,90,91,93,94,101,102,103,104,105,106,107,108,109,110,111]

summarizes the reviewed articles categorized into these thematic clusters, providing a comprehensive overview of the evolving landscape of resilient supply chain research.

The modeling of resilient supply chains has progressively evolved from early formulations addressing localized disruptions to sophisticated network-wide frameworks capable of handling dynamic, multi-tier systems [70,71,77]. Building upon foundational concepts of robustness under uncertainty, subsequent studies expanded to incorporate fairness-based distribution strategies [101], hybrid risk management frameworks tailored to medical supply chains [42], and multi-objective optimization approaches for integrating green initiatives [70]. Advancements in network design highlighted the necessity of resilient capabilities beyond traditional supply optimization, with new models targeting supplier flexibility, node criticality, and transportation resilience [84,102].

Developments in supplier evaluation and selection incorporated multicriteria decision-making techniques, enhancing the adaptability of procurement systems [71,77]. Closed-loop models for floating solar and biomass-based supply chains emerged to simultaneously address resilience and environmental challenges [85,108,109] emphasizing the interplay between operational continuity and circular economy principles. Stochastic frameworks and big data enablers were increasingly incorporated to strengthen decision-making under cascading disruptions [61,104], particularly in the context of pandemics and global crises [105].

Later studies introduced agile and flexible frameworks for disaster-resilient logistics [50], leveraging systematic reviews to identify critical resilience enablers across diverse supply chain structures [95]. The distributed manufacturing network approach further demonstrated how decentralized production systems could enhance viability and adaptive recovery [106]. In parallel, risk-averse optimization models and the dynamic reconfiguration of supply networks were explored to mitigate the ripple effects of systemic failures [68,74,98]. Overall, the trajectory of modeling resilient supply chains reflects a clear shift from static, risk-minimization formulations toward dynamic, anticipatory designs integrating disruption propagation modeling, digitalization, sustainability, and flexible network reconfiguration [72,86,110].

The convergence of sustainability and resilience has garnered increasing scholarly attention, driving a paradigm shift toward supply chain models that not only withstand disruptions but also promote environmental and social responsibility [75,104]. Early contributions emphasized the critical need to simultaneously optimize resilient capacities and minimize environmental impacts, with green and resilient supply chain network designs becoming a central research focus [75,80,84,93]. Integrated models for biomass and bioethanol supply chains exemplified how renewable energy initiatives could be robustly safeguarded against external shocks [83,87], addressing both climate goals and operational continuity.

Further extending this integration, studies on perishable goods and broiler meat supply chains incorporated sustainability metrics such as carbon footprint and food security into resilience optimization frameworks [82,108]. These multi-objective models facilitated trade-off analyses between cost, service level, and environmental impact, strengthening supply chain viability under uncertain conditions [84,95,102]. The exploration of distributed manufacturing networks also demonstrated how decentralization could foster both resilience and local economic sustainability, particularly in critical sectors like healthcare and agriculture [82,104]. At the intersection of social and operational sustainability, Latin American case studies during COVID-19 illuminated the vulnerabilities inherent in traditional supply chain designs, calling for a reorientation toward socially resilient systems that prioritize equitable resource distribution [66,72]. Complementary works highlighted the role of coalition strategies among suppliers, promoting both green practices and collective resilience against disruptions [80]. Synchronization optimization models, particularly within new energy vehicle (NEV) supply chains, illustrated how enhancing connectivity could bolster system-wide sustainability and resilience simultaneously [12].

Emerging research also examined the role of environmental, social, and governance (ESG) responsibility performance as a driver of corporate resilience, suggesting that companies committed to sustainable practices demonstrated superior adaptive capacities during crises [79]. Vaccine supply chains, which came under heightened scrutiny during the pandemic, became emblematic of the necessity to embed viability and robustness within inherently sustainable frameworks to ensure global health security [68]. Collectively, these studies reflect a comprehensive movement toward embedding sustainability imperatives within the design and operation of resilient supply chains, fostering systemic endurance that aligns with broader societal and environmental objectives.

The integration of machine learning (ML) and artificial intelligence (AI) into supply chain resilience frameworks marks a pivotal evolution in the predictive and adaptive capabilities of modern networks. Chen and Chen [95] initiated this shift by applying data-driven stochastic optimization to enhance decision-making under uncertainty, leveraging real-time data streams to inform resilient network design. Building upon these foundations, Zhou et al. [100] advanced reinforcement learning algorithms to dynamically optimize supply chain efficiency, offering a framework for autonomous adaptability in volatile environments. Subsequent efforts, such as those by Villar et al. [10], demonstrated the application of open knowledge resource frameworks (OKRFs) to distribute manufacturing networks, highlighting how AI-based platforms can optimize resilience through decentralized, flexible production systems. The work of Aungkulanon et al. [82] further exemplified the integration of hybrid approaches, combining traditional optimization with machine learning techniques to navigate supplier selection challenges in agri-food supply chains under disruption scenarios.

Recognizing the role of advanced optimization heuristics, Jin and Vergara [96] proposed a greedy randomized adaptive search procedure (GRASP) specifically tailored for resilient supply chain network optimization, offering a robust alternative to conventional optimization under uncertainty. Jabbarzadeh and Shamsi [87] contributed to this evolution by enhancing synchronization optimization models with machine learning to improve the connectivity and resilience supply chains for bioethanol production, thus reinforcing the strategic deployment of AI at the network orchestration level. Roozkhosh and Ghorbani [97] introduced a novel hybrid model, combining Monte Carlo simulations with multilayer perceptron (MLP) networks, to manage cost uncertainties in resilient supply chains. Their approach exemplified how AI techniques can be systematically embedded into risk management processes to anticipate financial volatility and adapt procurement and distribution strategies accordingly. Overall, the integration of machine learning and AI into resilience modeling has transitioned supply chain management from reactive robustness to proactive, intelligent adaptability, positioning predictive analytics as a cornerstone of future-proof operational architectures [72,87]. Collectively, the reviewed contributions reveal an increasingly sophisticated and multidimensional understanding of supply chain resilience. Early modeling efforts, initially focused on static risk minimization, have progressively expanded to incorporate dynamic network behaviors, sustainability imperatives, and intelligent predictive mechanisms [88]. The integration of environmental and social considerations into resilience design reflects a paradigm shift toward sustainable endurance rather than mere survival [75]. Concurrently, the incorporation of machine learning and artificial intelligence has transitioned resilience modeling from reactive robustness to proactive anticipation and real-time adaptation [85]. Sector-specific adaptations further highlight the necessity of contextualizing resilience strategies, recognizing that the vulnerabilities and operational dynamics vary significantly across industries [88,102]. This cumulative body of work establishes a solid foundation for the next generation of resilient supply chain systems, where anticipatory, sustainable, and context-sensitive frameworks will be pivotal for navigating increasingly complex and volatile global environments.

Although the terms resilience and robustness are often used jointly in the literature, they represent distinct yet complementary concepts. Robustness refers to a system’s ability to maintain performance levels in the face of disturbances without requiring changes to its structure or behavior. That is, a robust system withstands deviations while preserving its original configuration. Resilience, on the other hand, denotes the ability to adapt, reconfigure, and recover following a disruption, potentially involving structural or procedural adjustments to restore or redefine functionality.

As noted by Ivanov and Dolgui [1], robustness is typically more suitable for known or recurrent disruptions, where system responses can be anticipated. Resilience becomes critical under unexpected, prolonged, or complex disturbances, where dynamic adaptation is essential [9]. Several studies integrate both perspectives within hybrid frameworks—where robustness acts as the first line of defense (absorption), and resilience enables post-shock recovery and evolution [42,111]. This distinction is fundamental for designing supply chains that are not only resistant to shocks but capable of transformation and sustained viability in uncertain environments.

4.3. Agile Supply Chains

In an increasingly volatile and dynamic global environment, agility has emerged as a fundamental capability for supply chains aiming to maintain competitiveness and ensure continuity of operations. Beyond mere speed or flexibility, supply chain agility encapsulates the strategic, technological, and organizational readiness to rapidly respond to unpredictable changes in demand, supply disruptions, and market conditions. Recent research has expanded the conceptualization and operationalization of agility across multiple fronts, encompassing the design of agile supply chain networks, the integration of digital technologies and data-driven decision-making, and the empirical validation of agility’s impact on innovation, sustainability, and performance outcomes.

Table 3. Classification of Reviewed Articles in Agile supply Chains.

Subtheme	Articles
Design and strategic enablers of agile supply chain	[112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129]
Digital technologies and data-driven agility	[15,130,131,132,133,134,135,136,137,138,139,140,141,142]
Performance impacts and empirical validations	[15,50,112,113,115,116,117,118,119,122,125,126,130,133,134,136,138,139,142,143,144,145,146,147,148]

categorizes the reviewed studies into three principal thematic clusters that collectively illustrate the evolution and diversification of agile supply chain research.

The structural design and strategic enablers of agile supply chains have undergone significant refinement, moving from the identification of isolated agile practices to the development of systemic frameworks embedding agility into the fabric of supply chain operations. Early formulations emphasized the integration of lean and agile principles into network design to balance efficiency with responsiveness [121,125,126]. Building upon this foundation, studies progressively introduced transportation link constraints [118,121] and explored the complementary roles of supply chain partners in enhancing agile capabilities [15,113,116].

Subsequent contributions stressed the necessity of embedding dynamic capabilities into agile supply chains, with frameworks assessing agility and performance at a network-wide level [115,123]. Researchers highlighted the importance of modularity and flexibility in sourcing strategies, particularly in volatile environments, thereby reinforcing the systemic enablers of supply chain agility [114,124]. Wei et al. [127] introduced an integrated model for agile, flexible, and resilient disaster supply chains, exemplifying how agility enablers could be operationalized in highly uncertain contexts. Leadership and organizational readiness emerged as critical enablers, with leadership styles fostering adaptability and resilience under disruption conditions [113]. In parallel, Mohaghegh et al. [122] and Kawa et al. [118] illustrated how leagile configurations, blending lean stability with agile responsiveness, enhanced supply chain performance across multiple operational dimensions. Dynamic warehouse management approaches and exception handling systems were also developed to support rapid reconfiguration of supply operations [116,117,122].

Efforts to model strategic agility have further incorporated the role of strategic partnerships, supplier alliances, and collaborative innovations [112,128], reflecting a broader transition toward network-based agility rather than firm-centric models. Kumar [120] reinforced these insights through resilience-oriented supply chain designs that embedded agility principles at the network topology level, ensuring both robustness and rapid adaptability. Finally, Zhang et al. [129] advanced the modeling of agile and risk-averse supply networks under multi-tier configurations, bridging strategic design with operational responsiveness.

The role of digital technologies in enhancing supply chain agility has evolved from isolated applications of information systems to the development of fully integrated, data-driven, adaptive ecosystems. Initial efforts emphasized the integration of information and communication technologies (ICT) to foster real-time responsiveness and decision-making accuracy [132,138,139]. Building on these foundations, studies progressively incorporated blockchain technologies to ensure traceability and decentralized control, thereby enabling more agile and trustworthy supply chain operations [126,146].

Hamdani et al. [147] demonstrated how the combination of agile methodologies and data mining approaches, such as CRISP-DM, could optimize end-to-end supply chain performance, emphasizing the strategic role of analytics in achieving operational agility. Concurrently, Sahoo et al. [139] and Shen et al. [141] showcased the transformative impact of data-driven platforms and digital dexterity in empowering firms to rapidly adapt supply chain strategies in response to external shocks. Advanced analytics and machine learning approaches have also gained prominence. Hsieh et al. [133] and Shamsuddoha et al. [140] highlighted the integration of predictive analytics and artificial intelligence to anticipate disruptions, optimize resource allocation, and enable autonomous decision-making processes, thereby fundamentally redefining supply chain agility parameters. In this context, digital dexterity—defined as the organizational capability to leverage digital tools for rapid reconfiguration—has emerged as a critical enabler of agile supply chain performance [15,142].

Moreover, emerging contributions have explored how the fusion of blockchain-driven analytics and sustainable operations can drive agility while maintaining environmental performance standards [132]. Cui et al. [114] analyzed the synchronization between digitalization, supply chain competitiveness, and organizational innovation capabilities, revealing how digital transformation initiatives must be strategically aligned to maximize agility outcomes. Wu et al. [142] presented a novel conceptualization of data network effects, illustrating how interconnected data ecosystems can amplify agility, resilience, and robustness simultaneously, thus transforming digital adoption from a supportive tool into a core strategic capability.

Empirical validations of supply chain agility have significantly advanced the understanding of how agile capabilities translate into organizational performance, sustainability outcomes, and innovation capacity. Early empirical studies revealed that the integration of lean and agile strategies could positively influence supply chain risk management and operational performance [125,126,141]. Subsequent research reinforced these insights by demonstrating that agile practices improve responsiveness to environmental uncertainty while simultaneously supporting financial and competitive performance [115,144]. Explorations by Fallah et al. [50] and Shen et al. [141] linked agility not only to short-term risk mitigation but also to longer-term strategic adaptability, with empirical findings underscoring agility’s role in enhancing innovation rates and sustainability metrics across supply chain networks. Strategic leadership styles and supply chain ambidexterity were further identified as key moderators in the agility–performance relationship, emphasizing the importance of organizational culture and governance in translating agile capabilities into tangible outcomes [113,130,136].

Empirical models developed by Mohaghegh and Gröβler [122] and Khalili-Damghani et al. [134] validated that leagile configurations—combining lean efficiency and agile flexibility—provided superior performance resilience compared to pure agile or pure lean systems. Digitalization and advanced analytics, as discussed by Elmouhib et al. [116], also emerged as strong mediators, enabling supply chains to capture agility-driven performance gains more effectively. Additionally, empirical studies investigating e-commerce environments and multi-tier supplier systems confirmed that agile strategies enhanced not only operational flexibility but also customer satisfaction and market share [118,138,143,145]. Ghazvinian et al. [117] and Hsieh et al. [133] expanded these validations by incorporating resilience and environmental performance dimensions into agile supply chain assessments, offering a more holistic evaluation framework.

The relationship between agile operations and innovation performance was further corroborated by Elmouhib et al. [116], who demonstrated that dynamic capabilities and agile adaptation mechanisms were positively associated with both product and process innovation rates. Financial performance validations reinforced these findings, with Ariadi [131] presenting risk-averse optimization models that captured the financial trade-offs of agility under uncertainty.

Emerging trends on agile supply chain reveal a multidimensional evolution from operational flexibility initiatives toward comprehensive strategic frameworks embedding agility across supply chain structures, technologies, and governance models. Design-oriented studies have systematically expanded the understanding of how organizational capabilities, supplier partnerships, and network configurations enable agile responses under conditions of high uncertainty. Simultaneously, the integration of digital technologies and data-driven analytics has shifted agility from reactive flexibility toward proactive, anticipatory adaptation, emphasizing the strategic centrality of information, connectivity, and predictive intelligence. Empirical validations across diverse industrial contexts consistently demonstrate that agility not only mitigates operational risks but also drives innovation, sustainability, and financial performance outcomes. Collectively, these advances position supply chain agility as a foundational pillar for competitiveness and resilience in volatile and complex global environments, setting the stage for future research on integrated, intelligent, and sustainable agile supply chain systems.

4.4. Integrative Discussion: Viability, Resilience, and Agility from a Multi-Structural Perspective

The evidence gathered across Section 4.1, Section 4.2 and Section 4.3 confirms that viability, resilience, and agility are not isolated constructs but deeply interconnected dimensions of adaptive supply chain management. While each represents a distinct analytical lens—viability as long-term survivability, resilience as recovery and continuity, and agility as responsiveness and reconfiguration—they converge within the broader challenge of sustaining operations in volatile, complex, and uncertain environments.

Building upon Ivanov’s multi-structural systems perspective [30,36,148], these dimensions can be understood as interacting across four fundamental layers:

• Organizational structure governs how decisions, hierarchies, and responsibilities are distributed. Agility manifests through decentralized decision-making and rapid role reconfiguration; resilience emerges from robust coordination and flexible governance; and viability is ensured by the capacity to sustain structural transformations over time without degrading system integrity.
• Informational structure determines how data flows, insights are generated, and knowledge is shared. Agility leverages digital connectivity (e.g., IoT, blockchain) for real-time adaptation; resilience depends on visibility and disruption sensing; and viability requires systems capable of integrating environmental feedback to support continuous learning and strategic recalibration.
• Financial structure shapes resource allocation and risk absorption. Agility facilitates opportunistic adaptation to market shifts; resilience buffers economic shocks through redundancy or diversification; and viability balances operational efficiency with long-term investment in adaptive capacity and systemic continuity.
• Technological structure encompasses both physical assets and digital infrastructures. Agility benefits from modular, reconfigurable technologies; resilience from redundancy and technological robustness; and viability from the sustained orchestration of technological evolution in alignment with environmental, economic, and social constraints.

Crucially, resilience serves as the operational backbone enabling supply chains to absorb and recover from disruptions. Agility functions as a dynamic driver of adaptation and realignment in the face of volatility. Viability emerges as the systemic outcome of both—requiring that short-term robustness and flexibility are aligned with long-term strategic, ecological, and organizational continuity.

This synthesis underscores the necessity of holistic approaches that transcend disciplinary silos. It also invites future research to explore underexamined intersections between these dimensions, particularly in domains where multi-structural dependencies (e.g., digital-financial-organizational entanglements) condition both vulnerability and adaptive potential.

4.5. Optimization and Logistics Management

Mathematical optimization has established itself as a cornerstone methodology for enhancing the design, planning, and operational efficiency of logistics and supply chain systems. Recent research has demonstrated a marked diversification of modeling approaches, with a predominant reliance on mixed-integer linear programming (MILP) formulations, often tailored to address multi-objective optimization goals such as minimizing operational costs, reducing environmental impacts, and improving service levels. This trend reflects a deliberate shift from mono-objective cost minimization towards more holistic, sustainable, and risk-aware optimization frameworks (see

Table 4. Classification of Reviewed Articles in Mathematical Optimization.

Area of Advancement	Related Authors
Expansion of multi-objective and robust optimization models	[149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166]
Development of hybrid solution methodologies (VNS, NPGA, NSGA-II, GCNs, LSTM)	[90,121,155,156,158,167,168,169,170,171,172,173,174]
Integration of environmental, energy, and sustainability constraints	[157,163,174,175,176]
Domain-specific applications: reverse logistics, cold chain, emergency logistics, agricultural, urban logistics	[152,153,157,164,167]

).

Solution methodologies have evolved concurrently, favoring hybrid approaches that combine heuristic and metaheuristic algorithms with exact optimization techniques. The integration of Variable Neighborhood Search (VNS) and niched Pareto genetic algorithm (NPGA) [156,160], multi-objective evolutionary algorithms such as Non-dominated Sorting Genetic Algorithm (NSGA-II) [90,121,174,177], and customized heuristic frameworks tailored to sector-specific logistics problems [150,151,152,153,154,157,167,174] exemplify this methodological sophistication. Notably, deep learning models, including Graph Convolutional Networks (GCNs) and Long Short-Term Memory (LSTM) networks, have begun augmenting traditional optimization processes by enhancing demand forecasting accuracy and enabling dynamic reoptimization of logistic operations [171,172].

Constraints incorporated in these optimization models have also expanded beyond classical capacity and cost parameters to reflect contemporary operational priorities. Environmental considerations—such as carbon emissions, energy consumption, and fuel usage—now feature prominently in optimization formulations [163,168,170,176], aligning logistics decision-making with broader sustainability objectives. In parallel, multi-echelon network configurations [162,163,175,176] and constraints related to facility resilience, transportation reliability, and service [149,165,174] reflect an increasing emphasis on system robustness and the ability to preserve operational performance under complex, real-world conditions.

Sector-specific adaptations underscore the versatility of optimization models across diverse logistical domains. Reverse logistics frameworks optimized under multi-objective schemes [164], cold chain logistics incorporating temperature control and perishability dynamics [159], emergency logistics systems emphasizing rapid deployment and robust coverage [163,168], and agricultural biomass logistics designed for sustainability and energy efficiency illustrate the broad applicability of optimization research [150,153,176]. These contributions reveal a field that is not only advancing in algorithmic sophistication but also expanding its problem scope to integrate resilience, sustainability, real-time responsiveness, and predictive capabilities, thereby solidifying optimization as a fundamental enabler of next-generation logistics and supply chain systems.

Contemporary research developments in optimization and logistics management demonstrate an ongoing transition toward increasingly complex, multidimensional, and context-sensitive modeling frameworks. The widespread adoption of multi-objective MILP formulations, hybrid solution methodologies, and sustainability-driven constraints reveals a strategic alignment of logistics optimization with the broader imperatives of resilience, environmental stewardship, and operational agility. Sector-specific adaptations—encompassing reverse logistics, cold chain management, emergency logistics, and green supply chains—further emphasize the versatility and practical relevance of optimization models across diverse industrial settings. The integration of advanced predictive techniques, such as deep learning-based forecasting and real-time data-driven reoptimization, marks a decisive step toward autonomous, adaptive, and anticipatory logistics systems. Collectively, these advancements position mathematical optimization not merely as a tool for cost reduction, but as a critical strategic capability enabling the design of robust, sustainable, and intelligent supply chain and logistics networks for the future.

4.6. Stochastic and Possibilistic Optimization Approaches

Mathematical modeling of supply chains under uncertainty has significantly evolved to incorporate both stochastic and possibilistic paradigms. Early contributions predominantly utilized stochastic programming and scenario-based analyses to address known risks with quantifiable probabilities [61,178,179,180]. Building upon these classical foundations, more sophisticated formulations emerged, introducing two-stage stochastic programming, chance-constrained models, and scenario tree optimization frameworks that enhanced the modeling of supply and demand variability [181,182,183]. These advances enabled supply chains to respond dynamically to predictable fluctuations, optimizing operational and strategic decisions under probabilistic frameworks.

Concurrently, possibilistic programming gained prominence as a powerful approach for capturing uncertainties characterized by epistemic vagueness, rather than randomness. Studies such as [22,184,185,186] pioneered the use of fuzzy and possibilistic logic to model supply chain parameters like demand levels, production capacities, and transportation times when statistical data were scarce or imprecise. Possibilistic extensions of mixed-integer linear programming (MILP) models [187,188] and robust possibilistic formulations [21,189,190] enabled decision-makers to account for subjective estimations, linguistic evaluations, and expert judgments in supply chain planning. Moreover, recent trends have converged toward hybrid possibilistic-stochastic models [185,191] integrating fuzzy uncertainty with traditional probabilistic risk assessment to tackle increasingly complex operational environments.

Modeling Different Types of Uncertainty

In addition to their methodological and application-specific contributions, the reviewed studies reflect a broad spectrum of how uncertainty is conceptualized and treated. Drawing from the typology of Ivanov [3], four major categories emerge—known–known, known–unknown, unknown–known, and unknown–unknown—as well as a hybrid category. These were handled using various mathematical approaches, from stochastic simulation to possibilistic optimization, depending on the nature of the available data and managerial judgment.

These categories help to explain the methodological diversity of the literature and emphasize the need to design supply chains that can withstand volatility not only through flexibility but also by embedding resilience into their structure and control logic. A summary of these uncertainty types, modeling tools, and examples is provided in

Table 5. Types of uncertainty.

Uncertainty Type	Description	Modeling Approach	Representative Studies
Known–Known	Known events with known probabilities	Stochastic programming, scenario analysis	[22,180,181,186,191,192,193]
Known–Unknown	Known events with unknown probability	Robust optimization, distributionally robust programming	[178,179,184,187,188,194,195,196,197,198,199]
Unknown–Known	Unknown events with estimable impact	Fuzzy logic, possibilistic programming	[185,189,190,200,201,202,203,204,205,206,207]
Unknown–Unknown	Unknown events with unknown impact	CVaR models, possibilistic robustness, p-robustness	[21,182,184,191,208,209,210,211,212,213]

.

Analyzing the treatment of uncertainties across the reviewed studies, distinct patterns emerge according to the nature of the uncertainty modeled. Research addressing known–known uncertainties—where events and their probabilities are well understood—focused primarily on stochastic programming, scenario generation, and two-stage optimization techniques. These models effectively captured risks associated with known variables such as fluctuating demand or lead times under measurable probability distributions, facilitating robust operational decisions in well-characterized environments.

In contrast, studies dealing with known–unknown uncertainties—where the events are known but their probabilities are uncertain—adopted robust optimization and distributionally robust programming frameworks. These approaches emphasized worst-case scenario planning and safeguarded supply chains against ambiguous risks by optimizing against uncertainty sets or employing adjustable robustness parameters.

Addressing unknown–known uncertainties, where events are initially unrecognized but their potential impacts can be estimated once identified, researchers employed fuzzy logic and possibilistic programming models. These models demonstrated strong flexibility in accommodating vagueness in supply chain parameters, supporting resilient decision-making despite the lack of precise probability distributions. Possibilistic programming allowed for modeling subjective risks, such as supplier reliability, transportation disruptions, and new market entry uncertainties, enhancing supply chain agility.

Finally, investigations tackling unknown–unknown uncertainties—characterized by events with unknown occurrence and impact—relied on CVaR-based models, possibilistic robustness, and p-robust programming. These approaches emphasize resilience against deep uncertainty by optimizing supply chain configurations that minimize expected losses under worst-case distributions or by employing possibilistic robustness measures. Such models are particularly critical in domains affected by black-swan events, pandemics, or extreme geopolitical risks, where traditional probabilistic planning fails to anticipate disruptive scenarios.

Overall, the reviewed contributions reflect a comprehensive evolution from classical stochastic modeling to sophisticated hybrid frameworks capable of capturing the multifaceted nature of uncertainty in modern supply chains. The integration of possibilistic and robust approaches marks a pivotal advance in developing resilient and viable logistics networks under both measurable and unmeasurable uncertainties.

4.7. Immune System-Inspired Approaches

Bio-inspired models have gained prominence in the design of complex logistics systems due to their ability to represent mechanisms of adaptation, self-regulation, and distributed learning. Among these, the human immune system (HIS) has emerged as a particularly powerful source of analogies and algorithms to address uncertain, dynamic, and highly distributed environments, such as those encountered in modern supply chains. The immune system’s principles—immune memory, distributed detection, clonal selection, homeostasis, self-tolerance, and cooperation between specialized subsystems—have been conceptually and computationally adapted to model adaptive logistics, production flow reconfiguration, risk classification, and fault tolerance.

Table 6. Immune-Inspired Thematic Contributions to the Design of Resilient and Viable Supply Chains.

Thematic Group	Grouping Criterion	Representative Articles	Contribution to Resilient and Viable SCs
Immune-Inspired Conceptual Models for Supply Chain Resilience	Use the immune system as an analogy for resilience, redundancy, or homeostasis in supply chains	[27,31,214,215,216,217]	Provide a theoretical foundation for adaptive behavior, immune memory, and redundancy against disruptions
AIS-Based Optimization Algorithms for Resilient Decision-Making	Apply artificial immune systems (AISs) and hybrid approaches to optimization problems like VRP, TSP, MKP, and FMS	[177,218,219,220,221,222,223,224,225,226,227,228]	Support exploration and exploitation balance, decision-making under uncertainty, and robustness in operations
Distributed Detection, Fault Tolerance and Maintenance Inspired by Immunity	Use immune principles for anomaly detection, fault isolation, and self-recovery in industrial and IoT systems	[26,28,229,230]	Enhance operational viability and structural resilience in distributed networks
Immune-Inspired Robotics and Self-Organizing Systems	Use immune metaphors in swarm robotics, mobile agents, or behavior arbitration	[231,232,233]	Model adaptive, decentralized nodes capable of reconfiguration and learning from disturbances
Adaptive Classification and Risk Evaluation via Immunological Analogies	Apply immune-inspired classifiers (e.g., AIRS, Danger Theory) to SPAM detection or SVM parameter tuning	[26,27,29,32,215,218,220,222,226,230,232,234]	Enable analytical viability through dynamic classification of risks and disruptions
Immunotechnological Approaches for Resilient Computing and Physical Systems	Design resilient computing systems (FPGAs, digital controllers, cybersecurity) using immune system analogies	[29,32,214,216,217,235,236]	Reinforce fault tolerance, self-repair, and system continuity under critical conditions

summarizes the main thematic groups into which the reviewed immune system-inspired approaches can be classified, based on their underlying biological principles, grouping criterion, and contributions to resilient and viable supply chains. These categories encompass conceptual models, optimization frameworks, distributed detection systems, self-organizing robotics, adaptive classification methods, and resilient computing architectures.

Building upon foundational models that view supply chains as dynamic organisms capable of recovery and learning [26], subsequent contributions have deepened the analogy between immune systems and resilient logistics architectures [27,28]. Immune-inspired conceptual models propose that logistics networks behave like living systems, exhibiting localized responses to disruptions, global learning through distributed memory, and dynamic self-organization under environmental changes.

Several studies interpret supply chains as dynamic, living systems that mimic immune processes such as homeostasis, redundancy, and adaptive learning. Early frameworks conceptualize logistics networks as immune organisms capable of learning from past disruptions and reconfiguring structurally to preserve viability under adversity [215,216]. These models often incorporate elements such as circulating redundancy (analogous to lymphocytes) [217,232], threat-localization (inflammatory response) [31], and organizational memory (memory cells) [28,236]. In addition, works such as [27,31,231] propose system-wide adaptive architectures rooted in immune homeostasis, where continuous sensing and decentralized correction reinforce long-term viability. Collectively, these models emphasize the importance of distributed resilience and systemic adaptability, drawing from immune logic to describe viable supply chains capable of self-organization, progressive learning, and multiscale regulation.

Artificial immune systems (AISs) have been adapted to solve complex logistics problems, including scheduling, routing, resource allocation, and multi-objective planning. These algorithms draw on clonal selection, suppression mechanisms, and memory-based evolution to explore large, uncertain solution spaces. For example, quantum-inspired AIS and hybrid immune-evolutionary models outperform classical heuristics in dynamic environments [228,236]. Resilient applications include immune-based vehicle routing with deterioration constraints [228], flexible operation assignment under uncertainty [235], and goal programming in B2B procurement contexts [220]. Additional studies integrate immune mechanisms into parameter tuning [230], feature selection [236], and time-window routing [221], offering robust, adaptive decision tools to maintain performance under perturbations [26,224]. These models contribute directly to resilience by enhancing the system’s capacity for robust optimization, dynamic adjustment to constraints, and consistent performance amid shifting conditions [221,222,223,232].

The immune system’s core ability to detect, classify, and respond proportionally to external threats has inspired a suite of applications for anomaly detection and predictive maintenance. Models like those presented in [218,229] employ immune-regulation metaphors and Danger Theory to identify system anomalies without exhaustive prior knowledge. Intrusion detection systems using artificial immune networks outperform traditional classifiers in identifying previously unseen faults [29], while adaptive clonal strategies enable self-adjusting thresholds for classification accuracy [28,234]. These immune-inspired mechanisms also inform smart maintenance systems that detect early warning signs of tool wear or component fatigue [235], enhancing operational continuity. These studies reinforce analytical viability, as systems become capable of autonomously evaluating incoming risks, ranking disruptions by severity, and deploying proportionate mitigation without relying on centralized control [28,221,235].

Inspired by the decentralized nature of immune regulation, some researchers have proposed coordination algorithms for swarm robotics, multi-agent logistics systems, and decentralized supply networks. Aggregation models inspired by granuloma formation allow robotic units to regroup autonomously after partial failure [233]. In multi-agent systems, immune components such as antigen recognition, clonal learning, and suppression are reinterpreted as modules for collaboration, arbitration, and behavioral regulation [222]. Studies like [227,231] extend these ideas to underwater navigation and robotic adaptation in hostile conditions, according logistics systems the capacity for self-organized resilience. Such systems contribute to operational resilience and agility, enabling distributed logistics nodes to learn, coordinate, and reconfigure in response to disruption without centralized orchestration [26,32,224].

Finally, several studies explore technological applications of immune principles to support the resilience of computing and physical systems, particularly under mission-critical constraints. Authors like [28,226] propose a bio-inspired protection system (Immunotronics) for FPGAs, combining genetic algorithms for fault recovery and autonomous immune-inspired shielding mechanisms. Silva et al. [230] integrate immune evolution and information theory in the blind inversion of nonlinear systems. These approaches contribute directly to the fault tolerance and continuous operation of digital and physical infrastructures supporting logistics chains.

Overall, the immune system-inspired approaches reviewed in this section demonstrate significant potential to enhance the design and management of resilient, agile, and viable supply chains. Whether from a conceptual, algorithmic, or applied perspective, these models emulate key principles such as distributed detection, structural memory, progressive adaptation, and autonomous recovery from disruptions. Their integration into complex logistical scenarios strengthens anticipation and response capabilities, supports decentralized decision-making, and provides evolutionary mechanisms for self-organization and learning. These contributions are particularly valuable in high-uncertainty contexts, where supply chains must sustain operational functionality, reorganize structurally, and learn from their environment—just as the human immune system does in living organisms. Importantly, the reviewed studies underline that immune system-inspired approaches are particularly effective for managing deep uncertainty and systemic risks, offering mechanisms not only for survival under disruption but also for adaptive improvement. As supply chains continue to evolve toward increasingly autonomous, decentralized, and self-adaptive networks, immune system analogies are likely to play a crucial role in shaping future models of viability, resilience, and agility. By mimicking immune memory, distributed detection, and self-adaptive regulation, these contributions reinforce both viability—defined as the system’s long-term ability to sustain structure and function—and resilience, understood as its short-term capacity to absorb and recover from disruptions. Their relevance is particularly salient in environments characterized by cascading uncertainty, where adaptive and decentralized behaviors are not optional but essential.

4.8. Temporal Scope and Observed Gaps in the Recent Literature

Although the immune-inspired perspective on supply chain design is framed as an emerging line of inquiry, the temporal distribution of publications reveals that a substantial portion of the contributions were concentrated between 2010 and 2019. Indeed, approximately 60% of the reviewed studies in this thematic group were published prior to 2020. This pattern suggests that while the conceptual foundations—such as the application of immune system metaphors for distributed control, fault tolerance, and adaptive memory—were established earlier, the field has not experienced a significant surge of methodological innovation or widespread adoption in recent years.

The relatively limited number of immune-inspired studies published after 2020, despite the growing interest in resilient and viable supply chains, indicates that this stream of research remains underexplored and fragmented rather than fully developed. It also highlights a potential disconnect between conceptual novelty and practical integration into mainstream supply chain modeling. Therefore, this review not only synthesizes existing contributions but also underscores the need to revitalize this paradigm—particularly by bridging immune analogies with contemporary advances in digital supply networks, agent-based modeling, and robust optimization frameworks.

5. Discussion

The review of the recent literature reveals a progressive evolution in mathematical optimization approaches aimed at enhancing supply chain resilience and viability. Classical methods such as mixed-integer linear programming (MILP) and two-stage stochastic programming have provided foundational tools to manage supply chain uncertainties and disruptions by optimizing structural configurations, production flows, and sourcing strategies under probabilistic scenarios. Robust optimization, distributionally robust optimization, and possibilistic programming have emerged as critical extensions to address ambiguities in probability distributions and deep uncertainty, offering more conservative yet flexible decision frameworks.

Multi-objective formulations incorporating resilience metrics, cost-risk trade-offs, and dynamic reconfiguration capabilities have gained traction, especially under ripple effect conditions and post-disruption recovery modeling. Scenario-based frameworks and hybrid stochastic–fuzzy approaches have enriched the modeling of unpredictable phenomena such as pandemics, geopolitical risks, and climate-related disruptions. Furthermore, agile supply chain optimization—focusing on flexibility, responsiveness, and fast adaptation—has been integrated into viability frameworks, highlighting the importance of not only surviving disruptions but maintaining and evolving operational functionality over time. Building upon the limitations of classical optimization, immune system-inspired analogies offer transformative principles that address the complexity, adaptivity, and decentralized nature of modern supply chains. The human immune system, characterized by distributed detection, adaptive memory, clonal selection, homeostasis, and autonomous recovery, provides a powerful paradigm for designing supply chains capable of responding to unknown–unknown disruptions, learning from environmental changes, and self-organizing structural adaptations.

Conceptual models inspired by immune architecture enrich resilience modeling by introducing mechanisms of localized threat detection, redundancy through structural diversity, and dynamic memory accumulation. Artificial Immune Systems (AISs), adapted into multi-objective optimization algorithms, enhance the exploration–exploitation balance in complex solution spaces, providing robust decision-making under deep uncertainty. Immune-inspired frameworks for anomaly detection, fault tolerance, and self-repair further strengthen the operational viability of distributed supply networks, enabling decentralized agents and nodes to autonomously detect, assess, and mitigate disruptions without central coordination.

The integration of mathematical optimization techniques with immune-inspired principles redefines the resilience and viability paradigm in supply chain management. Theoretically, it shifts the design focus from static robustness toward dynamic adaptivity, structural learning, and continuous evolution. Practically, it empowers organizations to engineer supply networks that are not merely robust against specific risks but inherently capable of detecting anomalies, reorganizing operational pathways, reallocating resources autonomously, and learning from past disruptions to anticipate future threats. The immune system-inspired approaches particularly emphasize the necessity of distributed memory, local autonomy, and progressive adaptation—principles that challenge traditional centralized optimization and linear resilience constructs. Their application can support the development of digital twins, autonomous supply chain agents, and self-healing logistics infrastructures capable of thriving under unpredictable disruptions.

Despite their transformative potential, immune system-inspired models face several limitations when applied to supply chain management. Computational complexity remains a challenge, particularly in large-scale, real-time optimization under multi-modal uncertainties. The abstraction of biological principles into operational supply chain contexts demands careful modeling to avoid over-simplification or misrepresentation. Furthermore, empirical validations of immune-inspired frameworks in real-world supply networks are still limited, often constrained to simulation studies or theoretical prototypes.

A key contribution of these approaches lies in their ability to integrate cognitive, evolutionary, and structural elements, enabling distributed decision-making based on contextual recognition (Danger Theory), learning through exposure (cloning and mutation), and decentralized cooperation (cellular coordination or idiotypic networks). These models can be understood as operational expressions of Ashby’s Law: in high-uncertainty environments, only systems with equivalent or greater internal complexity can adapt effectively.

Despite these advances, several gaps remain. Most notably, a few studies simultaneously address all three pillars—resilience, viability, and agility—within a unified operational system architecture. The majority focus on one or two dimensions, often overlooking the dynamic tensions between efficiency, adaptability, and sustainability ([237]). Moreover, the integration of immune-inspired approaches with conventional quantitative models is still in its early stages and requires more robust empirical validation.

In this context, future research should move toward integrated frameworks that combine structural elements (e.g., capabilities, redundancies, configurations) with dynamic dimensions (e.g., response to disruptions, recovery, learning). These models must not only optimize performance under normal conditions but also ensure organizational viability under systemic or prolonged disruptions, which will demand new mathematical tools, hybrid bio-inspired approaches, and multiscale analysis frameworks. Incorporating immune principles at multiple scales—operational, tactical, and strategic—could enable supply chains to evolve into living, learning systems capable of not just resisting disruptions but dynamically thriving in volatile environments. This vision aligns with the ultimate goal outlined in this study: moving Toward Adaptive and Immune-Inspired Viable Supply Chains, where resilience is no longer reactive but inherently embedded into the supply chain’s evolutionary logic.

6. Concluding Remarks

This study has undertaken a systematic and structured exploration of mathematical optimization approaches aimed at enhancing resilience and viability in supply chains, while introducing bio-inspired analogies—particularly those derived from the HIS—as a complementary and transformative modeling framework. Through a comprehensive literature review covering viability-oriented optimization, resilient supply chain design, agility frameworks, logistics management strategies, stochastic and possibilistic programming models, and immune system-inspired methodologies, we have mapped the evolution of theoretical and computational tools that enable supply chains not only to withstand disruptions but to adapt, learn, and evolve structurally. The findings demonstrate that while mathematical optimization has significantly advanced supply chain robustness and operational continuity under uncertainty, it often remains bounded within centralized, static, and predefined decision architectures. By contrast, immune system analogies provide dynamic mechanisms for decentralized detection, adaptive memory formation, clonal adaptation, and homeostatic regulation—offering a new horizon for designing supply chains capable of progressive adaptation under unknown–unknown disruptions.

6.1. Main Contributions

The first contribution of this study lies in bridging a gap in the current literature: the lack of integration between formal mathematical optimization models—particularly robust, stochastic, and multi-objective programming—and biologically inspired principles from the immune system. Existing applications of immune analogies have been predominantly heuristic, focusing on localized tasks such as anomaly detection or routing without establishing a rigorous optimization structure aimed at global resilience and viability objectives. By systematically aligning immune-inspired mechanisms with mathematical modeling paradigms, this study establishes a conceptual and methodological foundation for immune-adaptive supply chain design.

The second contribution is the articulation of immune-inspired adaptive mechanisms—such as decentralized detection, distributed learning, memory-based response, and evolutionary homeostasis—within the formal rigor required for supply chain design and strategic decision-making. This integration supports the development of supply chains capable of sustaining functionality, reorganizing operational pathways, and enhancing structural resilience in the face of complex, cascading disruptions.

6.2. Practical and Theoretical Implications

From a theoretical perspective, the study advances the conceptualization of supply chains as living systems, capable of evolutionary adaptation rather than merely static robustness. It introduces immune system mechanisms into optimization modeling, enriching existing frameworks with capabilities for autonomous detection, dynamic prioritization, and distributed recovery. Practically, the incorporation of immune-inspired strategies into supply chain management offers pathways for engineering decentralized, adaptive logistics networks. It provides decision-makers with new tools for enhancing operational viability, especially in volatile, uncertain, complex, and ambiguous (VUCA) environments. Applications include the design of digital twins with immune memory capabilities, decentralized decision layers for disruption handling, and self-healing logistics infrastructures capable of evolving based on cumulative experience.

This research moves a step closer to realizing the vision of Adaptive and Immune-Inspired Viable Supply Chains. By combining mathematical rigor with biologically inspired resilience mechanisms, it lays the groundwork for the development of next-generation supply networks that can autonomously detect disruptions, adapt structures, and evolve decision policies over time. Future research should deepen the formalization of immune-inspired models, develop hybrid frameworks integrating machine learning with immune analogies, and empirically validate these approaches in complex, real-world supply chain environments. The path toward fully viable, adaptive, and immune-resilient supply chains is both a scientific and operational imperative—one that will define the robustness and sustainability of supply networks in the 21st century.

6.3. Limitations and Future Research Directions

Despite its methodological rigor and comprehensive scope, this systematic review is subject to several limitations that may influence the breadth and generalizability of its findings. First, the decision to restrict the final corpus to four editorial databases—ScienceDirect, SpringerLink, Taylor & Francis, and MDPI—was methodologically justified based on the density of relevant contributions and metadata quality; however, this choice may have led to the omission of pertinent studies indexed in other repositories, such as Wiley, Emerald, or IEEE Xplore. While exploratory queries in these sources revealed limited marginal contributions, future research could conduct a comparative analysis to quantify the extent of the potential exclusions. Second, although this review emphasizes formal mathematical modeling as a core inclusion criterion, the classification of hybrid approaches—particularly those combining heuristic, AI-based, or simulation-driven techniques—required interpretive judgment. To mitigate subjectivity, a dual-tagging protocol was employed, yet the evolving nature of hybrid models may challenge the boundaries of traditional classification schemes. Third, the focus on peer-reviewed journal articles excluded conference proceedings, working papers, and technical reports, which often serve as venues for cutting-edge or emerging methods not yet formalized in the academic mainstream. This constraint, while enhancing the methodological quality of the corpus, may limit the visibility of frontier innovations.

Additionally, this review deliberately abstained from using citation-based metrics (e.g., h-index, impact factor, citation counts) in its screening or analysis phases. The rationale was to prioritize methodological depth and thematic alignment over bibliometric prominence. Nonetheless, future extensions of this study may benefit from integrating quantitative bibliometric analyses to complement the qualitative synthesis presented herein.

Finally, although the review spans a 15-year period (2011–2025), potential temporal biases may persist, especially considering the sharp increase in publications following the COVID-19 pandemic. This surge may influence the apparent prominence of certain modeling trends and should be interpreted within the context of shifting global research priorities.

These limitations establish several avenues for future investigation. One critical direction is the integration of sustainability and circular economy principles into viability-driven supply chain modeling, particularly under scenarios involving climate change, geopolitical instability, or resource scarcity. Future models must be capable of capturing complex trade-offs across environmental, social, and operational dimensions, using tools such as multi-objective optimization, evolutionary algorithms, and multicriteria decision analysis. Another promising line of research involves the adoption of adaptive, bio-inspired, and cybernetic frameworks that go beyond static robustness to embed features such as memory, self-organization, and structural plasticity into supply chain design. The convergence of operations research with artificial intelligence, complexity science, and biological metaphors offers fertile ground for a new generation of resilient, viable, and intelligent supply systems.