A Stochastic Time-Dependent Optimization for Sustainable E-Grocery Chain With Cold-Storage Hubs and Perishability Constraints

The rapid growth of e-grocery systems has intensified the need for sustainable and reliable cold-chain logistics capable of handling perishable goods under uncertain demand and dynamic traffic conditions. This study develops a stochastic, time-dependent mixed-integer linear programming (MILP) model that integrates perishability-driven freshness decay, demand uncertainty, and cold-storage hub activation into an environmentally conscious e-grocery delivery framework. The model jointly optimizes economic cost, carbon emissions, and freshness retention while enforcing time windows, routing feasibility, and capacity constraints across multiple time periods. To tackle the problem's combinatorial complexity, a customized Adaptive Large Neighborhood Search (ALNS) metaheuristic is proposed to ensure scalability and near-optimal performance across large-scale instances. Computational experiments based on well-known benchmark scenarios demonstrate that the proposed model achieves global optimality for small- and medium-scale problems, while the ALNS delivers near-optimal solutions within a gap of 1-2% from the optimal and significantly reduces computation time. Ablation studies confirm the essential role of cold-storage hubs in maintaining feasibility and highlight the operational value of time-dependent travel modeling for realistic urban traffic. The proposed model offers decision-makers valuable guidance for achieving sustainable and resilient e-grocery delivery operations in the presence of perishability and stochastic variability.