Two-echelon multi-depot location-routing problem with time windows and dynamic customer demands

The rise of the Internet of Things and online shopping platforms has intensified fluctuations in consumer demand, particularly during promotional events, leading to increased rates of order cancellations and new order placements. When not addressed by optimized logistics facility deployment, these fluctuations exacerbate network inefficiencies, raising operational costs and extending delivery times. This study proposes a two-echelon multi-depot location-routing problem with time windows and dynamic customer demands (2E-MDLRPTWD). An autoregressive Poisson model is first applied to predict potential dynamic customer demands in the current period based on historical data. The problem is then formulated as a bi-objective mathematical programming model that integrates demand forecasting, aiming to minimize total operating costs and vehicle usage. To solve this model, a hybrid algorithm is developed that combines a 3D statistical information grid (STING) clustering and an improved multi-objective grey wolf optimizer (IMOGWO). The 3D STING algorithm reassigns customers as new demands arise, thereby simplifying the structure of the two-echelon logistics network. IMOGWO incorporates elite wolf selection and a double-archive update mechanism to improve solution quality and convergence performance. A dynamic adjustment strategy (DAS) and a vehicle sharing strategy (VSS) are further integrated into IMOGWO to support vehicle configuration in the location-routing process. The proposed algorithm is benchmarked against the CPLEX solver, self-learning non-dominated sorting genetic algorithm, multi-objective genetic algorithm with simulated annealing, multi-objective adaptive large neighborhood search, and hybrid multi-objective particle swarm algorithm, demonstrating superior solution quality and computational efficiency. A case study conducted in Chongqing City, China, evaluates different levels of forecasting accuracy, six DAS and VSS combinations, and varying scales of dynamic demands. Furthermore, incorporating artificial intelligence-driven demand forecasting can enhance the adaptability and robustness of the location-routing strategy under uncertainty. These findings provide theoretical support for intelligent logistics system development and the promotion of sustainable urban growth.