Abstract

A case-picking operation with Multiple In-The-Aisle Pick Positions (MIAPP) is modeled as an M/G/1/N queueing system. Cases are picked manually from pallets located on the bottom level of storage racks. An aisle-captive Narrow-Aisle Lift Truck (NALT) travels rectilinearly to replenish the floor level of the rack by retrieving a pallet load from an upper level of the rack. From a queueing perspective, the NALT is the server and the order-picking positions in need of replenishment are customers. In this article, the replenishment requests from order-picking positions are assumed to occur at a Poisson rate (i.e., homogeneous customers). The corresponding probability density functions of service times are derived, and their Laplace–Stieltjes transforms are obtained, leading to steady-state performance measures of the system. In many situations, the replenishment requests from individual pick positions may not follow a homogeneous Poisson process, and the order-picking operation consists of heterogeneous customers. However, a simulation study indicates that an M/G/1/N queueing model yields accurate performance measures in such situations. Interestingly, when the number of pick positions is large enough to justify an MIAPP-NALT operation, the time between consecutive replenishment requests within a storage/retrieval aisle is approximately exponentially distributed. A numerical example is provided to illustrate the use of the developed model and to show the practical values of the analytical results in the performance analysis of such storage/retrieval systems.

摘要

具有多个通道内拣选位置（MIAPP）的案件拣选操作被建模为M / G / 1 / N排队系统。手动从位于存储架底部的货盘中拾取箱子。靠过道的窄道起重卡车（NALT）直线行驶，以通过从机架的上层取下货盘负载来补充机架的地板层。从排队的角度来看，NALT是服务器，需要补货的接订单头寸是客户。在本文中，假设来自拣货订单的补货请求以泊松速率（即，同类客户）发生。推导了相应的服务时间概率密度函数，并获得了它们的Laplace-Stieltjes变换，从而得出了系统的稳态性能指标。在许多情况下 来自各个拣配位置的补货请求可能不会遵循均一的Poisson流程，并且拣选操作由异构客户组成。但是，仿真研究表明，在这种情况下，M / G / 1 / N排队模型可得出准确的性能指标。有趣的是，当拾取位置的数量足以证明MIAPP-NALT操作合理时，存储/检索通道内连续补给请求之间的时间大约呈指数分布。提供了一个数值示例，以说明开发模型的使用并显示此类存储/检索系统的性能分析中分析结果的实用价值。订单拣选操作由异构客户组成。但是，仿真研究表明，在这种情况下，M / G / 1 / N排队模型可得出准确的性能指标。有趣的是，当拾取位置的数量足以证明MIAPP-NALT操作合理时，存储/检索通道内连续补给请求之间的时间大约呈指数分布。提供了一个数值示例，以说明开发模型的使用并显示此类存储/检索系统的性能分析中分析结果的实用价值。订单拣选操作由异构客户组成。但是，仿真研究表明，在这种情况下，M / G / 1 / N排队模型可得出准确的性能指标。有趣的是，当拾取位置的数量足以证明MIAPP-NALT操作合理时，存储/检索通道内连续补给请求之间的时间大约呈指数分布。提供了一个数值示例，以说明开发模型的使用并显示此类存储/检索系统的性能分析中分析结果的实用价值。当拣选位置的数量足够大以证明需要进行MIAPP-NALT操作时，在存储/检索通道内连续补给请求之间的时间大约呈指数分布。提供了一个数值示例，以说明开发模型的使用并显示此类存储/检索系统的性能分析中分析结果的实用价值。当拣选位置的数量足够大以证明需要进行MIAPP-NALT操作时，在存储/检索通道内连续补给请求之间的时间大约呈指数分布。提供了一个数值示例，以说明开发模型的使用并显示此类存储/检索系统的性能分析中分析结果的实用价值。