机器人移动履行系统（RMFS）即“货到人”拣选系统，由于其较好的可扩展性和较低的运转成本，随着人力成本的提升，其在仓库升级中也扮演着越来越重要的角色。在正常的拣选过程中，机器人的移动过程包括三部分：接受订单后从暂存点移动到目标货架，抬着目标货架从其存储点移动到工作台，在工作台完成拣选后抬着货架返回存储点。近些年，构建排队网络模型对RMFS的性能进行评估也是一大研究热点。本文针对前人在构建模型中没有考虑货架状态而可能造成的订单异常匹配的现象提出了“二次拣选”策略，并构建相应的排队网络模型。紧接着，本文提出了“货架指定”策略来减少机器人在订单履行过程的移动距离从而减少订单的周转时间，并在“二次拣选”策略的基础上构建了相应的排队网络模型。为了使得模型更接近实际情况，本文同样考虑了订单包含多个SKU的情况，并分析上述策略在是否包含多个SKU的时候模型上的差别。在求解半开排队网络模型（SOQN）时，常用的解决办法包括近似平均值估计算法（AMVA）、矩阵几何（MGM）等，本文针对AMVA算法在求解SOQN的迭代过程中可能会出现系统不稳定的问题对算法进行了改进。通过改进后的算法得到系统各个状态下的概率，进而得到工作台队长、订单周转时间、机器人忙期、工作台忙期等指标的表达式。最后本文通过构建仿真平台来验证改进后的近似平均值估计算法求得的各个模型的解析解的有效性，在验证了有效性后，本文接着做一系列数值实验来设计最优的仓库系统的布局。发现如下规律：①订单的周转时间与仓库布局以及工作台的分布关系密切；②“货架指定”策略能够有效降低订单的周转时间，且随着工作台数量的增加降低效果越明显；③在系统稳定的前提下，工作台的忙期只与订单的到达速率以及拣选人员的数量有关；④在拣选人员总数不变的前提下，增加工作台的拣选人数（减少工作台数），可以提高拣选效率，但对于货架指定策略不增反降；⑤包含多SKU订单的比例越低，货架指定策略对拣选效率的提升越显著。
Robotic Mobile Fulfillment System(RMFS) is playing an increasingly important 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 takes 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:①the turnover time of the order is closely related to the layout of the warehouse and the distribution of the workstations;②the “pod allocation” strategy can effectively reduce the turnover time of the order, and effect becomes more obvious as the increase of workstation; ③when 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; ④under 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 effectiveness is improved, while its opposite under the “pod allocation” strategy. ⑤the lower the proportion of orders containing multiple SKUs, the more significant the “pod alloctation” strategy will increase the efficiency of the retrieval process.
