Benders decomposition for fixed-charge network design problems: An updated review

Fixed-charge network design problems (FNDPs) are among the core optimization challenges in network operations, transportation, telecommunications, power systems, green supply chains, and blockchain networks. Benders decomposition (BD) algorithm addresses FNDPs by splitting the problem into two parts: a master problem for link-selection decisions and a subproblem for network flow optimization, significantly reducing computational demands. Although the BD algorithm performs well in the classical FNDPs, critical gaps remain in emerging applications. Notably, its potential for fixed-cost optimization and resource allocation in blockchain networks remains underexplored. The proposed study further identified three key unaddressed challenges: (1) dynamic models for sector-specific applications such as green supply chains and renewable energy integration; (2) real-time optimization with fluctuating workloads, particularly in blockchain networks; and (3) real-time supply chain resilience strategies, because current methods focus predominantly on static scenarios while lacking probabilistic disruption management metrics. To address these challenges, we performed a scientometric analysis and systematic review of the literature (2006–2024) on the state-of-the-art applications of BD to FNDPs. This analysis highlighted limitations and paved the way for researchers by suggesting future recommendations to advance BD for dynamic, adaptive optimization.