A bi-level optimization approach for joint rack sequencing and storage assignment in robotic mobile fulfillment systems

This paper studies a novel rack scheduling problem with multiple types of multiple storage locations (RS-MTMS), which can decide the retrieval sequence of racks and assign each rack a storage location after visiting a picking station. A major challenge in RS-MTMS is that the storage assignment problem and the retrieval sequence decision are closely coupled. If the RS-MTMS is solved directly, the storage assignment scheme and the retrieval sequence of racks are generally generated separately, thus resulting in poor performance. To overcome this difficulty, we propose a bi-level optimization approach for jointly optimizing the storage assignment and retrieval sequence (BiJSR). In BiJSR, the storage assignment problem is solved by variable neighborhood search (VNS) in the upper-level optimization. Effective candidate modes are incorporated into VNS to improve solution quality and computational efficiency. The sequencing optimization is obtained in the lower-level according to the given storage location set. A transformation strategy with sufficient problem-specific knowledge is developed to identify the lower-level optimization as the traveling salesman problem and its variants. Then these identified problems are solved using the loop-based strategy. Experimental results show that the proposed BiJSR is more effective and efficient than the representative algorithms in solving the RS-MTMS problem.