Order Fulfillment in a Robotic Mobile Fulfillment System of a Business-To-Business Environment

The robotic mobile fulfillment system (RMFS) is a robotized parts-to-picker material handling system used in warehouses to save traveling and searching time, as well as prevent human errors in the order picking processes. This study focuses on the order fulfillment within the RMFS, which plays a crucial role in determining the system’s overall throughput. Although there have been a few works addressing rack and order allocation in the literature, the specific context of a business-to-business (B2B) environment has not received substantial attention. In B2B scenarios, the volume of ordered items and quantities are higher compared to business-to-customer (B2C) environments. Fulfilling an item of an order require multiple racks due to a large quantity. To address this research gap, a mathematical formulation is proposed. The problem is proved to be an NP-hard problem. Several properties are derived and used for identifying infeasible solutions as well as reducing the feasible solution space. Furthermore, we introduce two lower bound estimation methods to enhance computational efficiency. Leveraging these derived properties and lower bound estimation methods, an efficient extended A-star algorithm is developed to efficiently find the optimal order fulfillment. The experimental results reveal the efficiency of the proposed algorithm.