Evaluating Performance In A Robotic Mobile Fulfillment System Based On Semi-open Queuing Network

Robotic Mobile Fulfillment System（RMFS）is playing an increasingly improtant role in warehouse due to its easier scalability and higher flexibility and lower operating cost as well as the increasing of labor costs.The normal retrieval process consists of three part:once a robot is matched with a request to retrieval a product,it moves from the storage location and moves to a pod that contains the product.Upon arrival,it lifts the pod and takes it to the workstation.After the retrieval process is finished,it then ta kes the pod to the pod’s original storage location.In recent years,evaluating the performance of the system via queueing network is a research hotspot.In this paper,we put forward a re-retrieval strategy to avoid unsuccessful matching between robots and shelves which is often ignored in previous literature especially regarding whether the shelf is available or not.Then,this paper puts forward the“pod allocation”strategy based on re-retrieval strategy to reduce the moving distance of the robot in the order fulfillment process and reduce the turnover time of the order as well.To be more practical consideration,this paper also considers the case where the order contains multiple SKUs,and analyzes the difference of the queueing model when it contains multiple SKUs.The common way to solve semi-open queueing network mainly consists of Approximate Mean Value Analysis Method,Matrix Geometric Method,etc.In this paper,the synchronize is excluded from CQN which is different from the method that CQN contains synchronize station proposed by Buitenhek^[35].we transform synchronize station to a load-dependent service station,and evaluate the Markov transportation between this station and inner network which is also transform into a load-dependent station,and get the probability of all states.This method can avoid the instability of the system during the iterative process effectively.Finally,this paper builds a simulation platform to verify the effectiveness of the improved Approximate Mean Value Analysis Method and the models.After verifying the validity,the paper then does a series of numerical experiments to design the optimal warehouse system layout.And we find the following regularity:（1）the turnover time of the order is closely related to the layout of the warehouse and the distribution of the workstations;（2）the“pod allocation”strategy can effectively reduce the turnover time of the order,and effect becomes more obvious as the increase of workstation;（3）when the system is stable,the busy period of the workstation is only related to the arrival rate of the order and the total number of servers;（4）under the premise of total number of servers is unchanged,with the increase of the servers in each workstation,which means the number of workstation is decrease,the picking effec tiveness is improved,while its opposite under the“pod allocation”strategy.（5）the lower the proportion of orders containing multiple SKUs,the more significant the“pod alloctation”strategy will increase the efficiency of the retrieval process.