The multi-agent pickup and delivery (MAPD) problem, in which agents plan paths to carry items between locations while avoiding obstacles and collisions, has recently gained attention. Existing MAPD methods mainly focus on automated warehouses but ignore tasks involving agents transporting shelves to picking stations and returning them. Thus, we introduce the MAPD for multi-item packing(MAPD-MP) problem, in which agents carry designated shelves to picking stations to pack multiple items and return them to home locations. The proposed method prioritized path planning with a carrying state (3PCS)efficiently performs MAPD-MP tasks by assigning priorities based on agents’ carrying states and requesting replanning for lower-priority agents when detecting potential collisions. Experimental results show that 3PCS efficiently generates collision-free paths for MAPD-MP tasks, achieving effective execution with a slight increase in computation time.