Abstract:

In the replenishment phase of mobile robot fulfillment systems， constantly changing consumer demand necessitates timely decisions regarding the allocation of replenished items to storage locations and the adjustment of pod positions within the storage area. A well-organized pod layout is crucial to mitigate congestion in the aisles where robots operate， which can significantly impact the efficiency of picking operations. The joint optimization of item and pod storage assignment problems is addressed during the replenishment phase， with a focus on achieving workload balance across picking aisles. The research problem originates from the need to enhance operational efficiency in robotic warehouses， where dynamic consumer demands and spatial constraints present significant challenges. Accurately assigning items to pods and optimally positioning these pods within the warehouse can lead to improved picking efficiency and reduced robot congestion. The problem is formulated to consider both the internal composition of pods and their spatial distribution in the warehouse. A bi-objective mixed-integer programming model is developed to maximize the total product correlation on pods and the matching degree between pods and storage locations. The product correlation objective aims to group items that are frequently ordered together onto the same pod， thereby reducing the number of pod visits required during order fulfillment. The matching degree objective ensures that pods are stored in locations that minimize travel distances. To solve this complex bi-objective optimization problem， an improved non-dominated sorting genetic algorithm II （NSGA-II） is designed. The algorithm is enhanced by incorporating a decentralized pod storage assignment strategy to facilitate balanced aisle workload distribution， ensuring efficiency and reducing congestion. Numerical experiments are conducted using data that reflect typical warehouse scenarios to validate the proposed algorithm. The results demonstrated the accuracy and effectiveness of our approach through comparisons with exact solutions obtained by Gurobi， a state-of-the-art optimization solver. Furthermore， advantages of the joint optimization model over a two-stage heuristic algorithm are highlighted in terms of achieving a better balance between product correlation and pod-storage matching. Sensitivity analysis is performed， and several key insights are obtained： increasing the weight coefficient for aisle congestion is found to alleviate congestion but decrease the matching degree between pods and storage locations. Conversely， higher replenishment rates are shown to enhance product correlation on pods and the matching degree but increase pod transportation distances. Additionally， it is observed that a warehouse length-to-width ratio closer to 1 and lower product correlation favor overall product correlation on pods and matching degree. It contributes to the field by offering a novel approach to managing the joint storage allocation and pod positioning in the replenishment phase. By balancing efficiency and operational constraints while addressing fluctuating consumer demands， the proposed model and algorithm provide valuable insights for optimizing warehouse operations. The findings can significantly aid related research in warehouse management and logistics optimization， offering strategies that enhance the responsiveness and efficiency of fulfillment systems in the face of dynamic market conditions.

Key words: robotic mobile fulfillment system, replenishment phase, aisle congestion, storage assignment problem, multi-objective evolutionary algorithm