Optimization models for scheduling operations in robotic mobile fulfillment systems

In robotic mobile fulfillment systems (RMFS), mobile robots carry inventory shelves autonomously from the storage area to picking stations and back. The scheduling of these robots and the order picking activities can be modeled as a collection of interrelated optimization problems. In this paper, we focus on the following optimization problems: the order allocation to picking stations, order sequencing, the inventory pod selection, and the robot scheduling. We present new mixed-integer programming (MIP) models for these decision problems and extended on existing models from the literature. To improve the models further, we include interstation travel which means that inventory racks can be transported from one picking station straight to another station without returning it to the storage area in between, hence reducing the overall travel distance. Moreover, In previous research on RMFS, only some of these decision problems are integrated. Therefore, we developed an integrated model to study the interdependencies between the decision problems. The models are validated through simulations and different performance metrics are analyzed such as the number of pod visits, the total distance travelled, and the system makespan. Moreover, we introduce a cost metric to facilitate the objective evaluation of the system performance. From the computational experiments we conclude that the integration of the decision problems results in significantly better performing systems compared to sequentially optimizing them. However, this comes at the cost of more computational effort. Furthermore, including interstation visits can further improve the overall system performance.