Investigation of the joint Automated mobile loading systems Two-Stage vehicle routing problem under the consideration of Supply-Demand Imbalance, fair Efficiency, and demand uncertainty

In supply chain management and emergency contexts, efficient and equitable material distribution is critical. Existing research remains underdeveloped in tackling issues like material shortages and demand uncertainty. This paper presents a novel two-stage vehicle routing method to address the imbalance between supply and demand of relief materials, such as food, and demand uncertainty during emergencies like wars and public health crises. By integrating an Automatic Mobile Loading (AML) system with vehicle collaborations in a two-stage routing problem, and using a Mixed Integer Linear Programming (MILP) model, this study optimizes the fairness and efficiency of material distribution. The study innovatively incorporates distance factors and demand uncertainty, proposing a fair and efficient distribution strategy. An improved Adaptive Large Neighborhood Search (ALNS) algorithm, hybridized with Tabu Search (TS) and incorporating Partial Sequence Dominance (PSD) and Exchange Strategy (ES), termed the ALNS/TPE algorithm, is designed to effectively solve the model problem through enhanced destruction and repair operators, greedy selection, and path segment exchange strategies. The improved algorithm demonstrates efficiency in small-scale test cases and superior performance in large-scale cases, generating low-cost solutions rapidly. In experiments conducted in Pudong, Shanghai, the enhanced algorithm reduced total costs by 11.2% compared to the traditional ALNS algorithm. Moreover, the AML-vehicle combination achieved a 37% reduction in total costs and a 42% saving in delivery time compared to single-vehicle distribution, significantly improving resource utilization and service quality.