Stochastic Bilevel Decomposition for Multi-Echelon Supply Chain Network Reconfiguration Under Demand Volatility: A Lagrangian Relaxation–Benders Hybrid Framework

Abstract

Contemporary multi-echelon supply chain networks face compounding disruption pressures driven by geopolitical realignment, post-pandemic demand volatility, and accelerating decarbonization mandates. This study develops a stochastic bilevel decomposition framework integrating Lagrangian relaxation with generalized Benders decomposition to solve large-scale supply chain network reconfiguration problems under probabilistic demand scenarios. The upper-level subproblem optimizes facility location and capacity allocation decisions, while the lower-level subproblem resolves dynamic routing and inventory replenishment policies. Computational experiments on 14 benchmark instances—ranging from 120 to 1,840 nodes—demonstrate a 23.7% average reduction in total network cost against state-of-the-art mixed-integer programming baselines. Sensitivity analyses confirm robust convergence under high-variance demand distributions. The proposed framework provides supply chain executives and operations researchers with a tractable, scalable optimization instrument directly applicable to resilience-driven network redesign initiatives.