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

Andrés Polo, Daniel Morillo-Torres and John Willmer Escobar ()
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Andrés Polo: Departament of Industrial Engineering, Fundación Universitaria Agraria de Colombia, Bogotá 110110, Colombia
Daniel Morillo-Torres: Department of Civil and Industrial Engineering, Pontificia Universidad Javeriana Cali, Cali 760001, Colombia
John Willmer Escobar: Department of Accounting and Finance, Universidad del Valle, Cali 760001, Colombia

Mathematics, 2025, vol. 13, issue 14, 1-44

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.

Keywords: supply chain viability; mathematical modeling; PRISMA methodology; robust optimization; uncertainty modeling; immune system-inspired models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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