Due to demanding service levels in e-commerce order fulfillment, modeling and analysis of integrated storage and order picking processes in warehouses deserve special attention. The upstream storage system can have a significant impact on the performance of the downstream order picking process. With a particular focus on multiline e-commerce orders, we develop an analytical modeling framework for integrated analysis of upstream (shuttle-based storage and retrieval system) and downstream (pick system) networks. To capture the consolidation delays in fulfilling multiline orders, the downstream pick system is modeled with a closed queuing network that includes synchronization nodes. The configuration of the synchronization station is adapted to model the variety of order profiles handled at the pick station. For the downstream closed queuing network, we propose a decomposition-based solution methodology that results in good solution accuracy. The resulting semi-open queuing network (SOQN) of the integrated system is analyzed using the matrix-geometric method (MGM). To improve the accuracy of analytical estimates of the measures, we propose a hybrid simulation/analytical framework, where the performance measures of complex subnetworks are obtained from simulation. We also develop a detailed simulation model of the physical system for validating the analytical and hybrid estimates of the performance measures. The results from experiments indicate that the hybrid simulation/analytical approach reduces the error in the throughput time estimates to 3% from 18% obtained from the analytical model. Then, we investigate the effect of the upstream network configuration (such as the number of storage aisles) and the downstream network configuration (such as the mixed vs. dedicated picking, CONWIP control for orders, order batching) on the order throughput times. Our analysis provides a threshold on the maximum numbers of allowable orders (CONWIP control) and number of aisles beyond which the improvement in average throughput time of the integrated system is marginal. Numerical experiments with high-order arrivals also highlight that mixed picking in the downstream network can result in significant throughput time reduction in comparison to dedicated picking.

中文翻译：

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储单拣选系统中多行订单的随机建模

由于电子商务订单履行的服务水平要求很高，因此仓库中集成存储和订单拣选流程的建模和分析值得特别关注。上游存储系统会对下游订单拣选流程的性能产生重大影响。特别关注多线电子商务订单，我们开发了一个分析建模框架，用于集成分析上游（基于穿梭的存储和检索系统）和下游（拣货系统）网络。为了捕捉完成多线订单的整合延迟，下游拣货系统使用包含同步节点的封闭排队网络进行建模。同步站的配置适用于对拣选站处理的各种订单配置文件进行建模。对于下游封闭排队网络，我们提出了一种基于分解的解决方案方法，可产生良好的解决方案准确性。使用矩阵几何方法 (MGM) 分析所得集成系统的半开放排队网络 (SOQN)。为了提高度量分析估计的准确性，我们提出了一个混合模拟/分析框架，其中复杂子网络的性能度量是从模拟中获得的。我们还开发了物理系统的详细模拟模型，用于验证性能测量的分析和混合估计。实验结果表明，混合模拟/分析方法将吞吐量时间估计的误差从分析模型的 18% 减少到 3%。然后，我们调查了上游网络配置（例如存储通道的数量）和下游网络配置（例如混合与专用拣货、订单的 CONWIP 控制、订单批处理）对订单吞吐量时间的影响。我们的分析提供了最大允许订单数量（CONWIP 控制）和通道数量的阈值，超过该阈值，集成系统的平均吞吐量时间的改进是微不足道的。高阶到达的数值实验还强调，与专用拣货相比，下游网络中的混合拣货可以显着减少吞吐时间。我们的分析提供了最大允许订单数量（CONWIP 控制）和通道数量的阈值，超过该阈值，集成系统的平均吞吐量时间的改进是微不足道的。高阶到达的数值实验还强调，与专用拣选相比，下游网络中的混合拣选可以显着减少吞吐量时间。我们的分析提供了最大允许订单数量（CONWIP 控制）和通道数量的阈值，超过该阈值，集成系统的平均吞吐量时间的改进是微不足道的。高阶到达的数值实验还强调，与专用拣选相比，下游网络中的混合拣选可以显着减少吞吐量时间。