Item Storage Assignment Problem in Robotic Mobile Fulfillment Systems With Nonempty Pods

This study examines the item storage assignment problem in robotic mobile fulfillment systems (RMFSs), that determines the assignment of items to pods. Unlike previous studies on this problem that generally considered an empty warehouse, the current study addresses the problem in RMFSs with nonempty pods. The problem is formulated as a mixed-integer program with the goal of maximizing the correlation degree among items. On the basis of the characteristics of the problem, an adaptive large neighborhood search (ALNS) heuristic is designed for the solution. Numerical results show that the gap between the ALNS heuristic and the Gurobi solver is less than 0.32% in small-scale instances. In medium- and large-scale instances, the ALNS heuristic improves the objective value by at least 10% compared with the methods in literature, and it outperforms commonly used storage assignment policies for traditional warehouses (e.g., random, dedicated, and class-based storage) by more than 30%. The ALNS heuristic can also be applied to the special case where the initial state of the warehouse is empty. The computational study of the ALNS heuristic in all instances shows that it can effectively solve this problem by providing high-quality solutions and has good scalability.