A comprehensive approach to joint picking and replenishment optimization in robotic mobile fulfillment systems

This paper focuses on optimizing the integrated picking and replenishment operations in a robotic mobile fulfillment system (RMFS) using a forward-reserve warehouse layout. The key contributions include: (1) a new mathematical model integrating picking and replenishment over multiple stations to optimize fulfillment time, (2) inclusion of order sequencing decisions, and (3) a tailored algorithmic approach to solve large problem instances efficiently. A mixed integer programming model is developed that concurrently decides order grouping, sequencing, station assignment, pod selection, and replenishment quantities to minimize average order fulfillment time. Due to the complexity of the model, a solution approach is proposed consisting of a construction phase (three stages for order grouping, station assignment, and wave planning) followed by an improvement phase based on Variable Neighborhood Search (VNS). Numerical experiments demonstrate the capability of the model and solution method to generate high-quality solutions within reasonable computational times. The study provides useful insights into synchronizing picking and replenishment activities to improve the performance of systems like Amazon's robotic warehouses.