A hybrid metaheuristic framework for multi-echelon location routing and last-mile delivery under uncertainty in cold supply chains

Pharmaceutical cold chains face strict temperature limits, time-sensitive deliveries, and uncertain demand and travel times. This study formulates a mixed-integer nonlinear model for a three-echelon stochastic open location-routing problem with time windows in pharmaceutical cold chains. The model integrates home delivery and pickup-point service. It represents demand and travel-time uncertainty through finite scenarios. A hybrid Whale Optimization Algorithm with Adaptive Large Neighbourhood Search (HWOA-ALNS) is developed. Its main features are binary encoding, feasibility repair, adaptive operator selection, problem-specific local search, penalty-based reliability handling, and dual stopping criteria. HWOA-ALNS is compared with Hybrid Genetic Algorithm (HGA), Genetic Algorithm (GA), Simulated Annealing (SA), Artificial Bee Colony (ABC), Gravitational Search Algorithm (GSA), and Imperialist Competitive Algorithm with Variable Neighbourhood Search (ICA-VNS) on 30 self-generated instances containing 80 to 2000 customers. It obtains the lowest expected total cost in 26 of 30 instances. It also records the highest demand-weighted customer-satisfaction value in 27 instances. The remaining exceptions are reported explicitly. Sensitivity and uncertainty analyses show the cost-service effects of time-window flexibility and higher variability.