# Non-Traditional Layout Design for Robotic Mobile Fulfillment System with Multiple Workstations
## 1 Introduction
These objects mentioned above (i.e., containers, ground trolleys, and quay cranes) can be viewed as inventory pods, robots, and workstations in RMFS, respectively. There remain several essential differences between the two, but the one of most relevance to this work is the workstation location restrictions. Specifically, the quay cranes (i.e., workstations in this work) are required to be deployed on the same side of the yard (i.e., the side close to the vessels) in the yard system due to its structural limitations, whereas such restrictions do not exist in RMFS. As multiple workstations could be employed in medium or large warehouses, whereas according to recent survey papers ([5; 21]) and our knowledge, the only two published literature in which the layout aspects of RMFS were mentioned is [PERSON], [PERSON], and [PERSON], (2017) [10] and [PERSON] et al., (2020) [22]. [PERSON] et al. maintain that the locations of the workstations in warehouses directly affect the system throughput. [PERSON] et al. estimate the warehouse performance under various layout configurations. Unfortunately, these analyses are based on several given workstation layouts (multiple workstations), more specifically, four fundamental layout setups in reference [10] and seven layout scenes in reference [22] are pre-defined respectively, and then served as input settings for their proposed model, and afterwards, the performance of these layouts are further evaluated in a simulation manner. This seems exactly a main drawback of the above research that related to our work, i.e., they do not formulate workstation layout as decision variables explicitly and further improve the performance of RMFS from a warehouse design perspective. In summary, most relevant published literature performs single workstation assumption ([16; 23; 24; 25; 26]), or consider multiple ones but tend to treat the positions of the workstations as pre-defined information ([10; 18; 27; 28; 29; 30; 31]). As we will verify in this paper, optimal workstations are not located symmetrically on the top and bottom edges of the warehouse, which is counter-intuitive to our experiences. In this paper, we apply non-traditional warehouse layout design to optimize the location of multiple workstations. Specifically, the flying-V layout is adopted for a RMFS to minimize the total travel distance of all robots in the system. We are going to address the following research questions:  
1. How to appropriately locate the workstations in traditional and flying-V layouts? 2. Whether there exist any patterns under the optimal layout of workstations? 3. Is flying-V a good substitute of traditional layout? To answer these questions, we first develop the expression of travel distance from any pod to any single workstation, for both traditional and non-traditional layouts; then, we formulate an integer programming model to optimize the location of multiple workstations. We demonstrate the proposed model can be solved by a commercial solver (for example, CPLEX) in a very short time even for very large warehouses in the e-commerce industry. We also carry out comprehensive numerical experiments to compare the performance of different warehouse layout types (traditional and flying-V) and different warehouse configurations. Our study makes the following contributions:  
1. To the best of our knowledge, we might be the first to investigate a non-traditional layout for a robotic mobile fulfillment system. 2. We propose an integer programming model to determine the optimal location of workstations. 3. We propose two general rules that can provide an approximately optimal workstation location solution with a less than 5% gap. The remainder of this paper is organized as follows: Section 2 reviews relevant literature; Section 3 presents the expression of the travel distance from any pod to any workstation; and Section 4 presents the workstation location model.