Mixed-width aisle configurations for order picking in distribution centers

Space required for the order picking area and labor required to perform the picking activity are two significant costs for a distribution center (DC). Traditionally, DCs employ either entirely wide or entirely narrow aisles in their picking systems. Wide aisles allow pickers to pass each other, which reduces blocking, and requires fewer pickers than their narrow-aisle counterpart for the same throughput. However, the amount of space required for wide-aisle configurations is high. Narrow aisles utilize less space than wide aisles, but are less efficient because of the increased likelihood of congestion experienced by pickers. We propose a variation to the traditional orthogonal aisle designs where both wide and narrow aisles are mixed within the configuration, with a view that mixed-width aisles may provide a compromise between space and labor. To analyze these new mixed-width aisle configurations, we develop analytical models for space and travel time considering randomized storage and traversal routing policies. Through a cost-based optimization model, we identify system parameters for which mixed-width aisle configurations are optimal. Experimental results indicate that annual cost savings of up to $48,000 can be realized over systems with pure wide or narrow aisle configurations.     

A constructive aisle design model for unit-load warehouses with multiple pickup and deposit points

We develop a network-based warehouse model of individual pallet locations and their interactions with appropriate cross aisles in order to evaluate the expected travel distance of a given design. The model is constructive in that it uses Particle Swarm Optimization to determine the best angles of cross aisles and picking aisles for multiple, pre-determined pickup and deposit (P&D) points in a unit-load warehouse. Our results suggest that alternative designs offer reduced expected travel distance, but at the expense of increased storage space. The opportunity for benefit also seems to decline as P&D points increase in number and dispersion.     

Travel time estimation and order batching in a 2-block warehouse

Order batching problem (OBP) is the problem of determining the number of orders to be picked together in one picking tour. Although various objectives may arise in practice, minimizing the average throughput time of a random order is a common concern. In this paper, we consider the OBP for a 2-block rectangular warehouse with the assumptions that orders arrive according to a Poisson process and the method used for routing the order-pickers is the well-known S-shape heuristic. We first elaborate on the first and second moment of the order-picker’s travel time. Then we use these moments to estimate the average throughput time of a random order. This enables us to estimate the optimal picking batch size. Results from simulation show that the method provides a high accuracy level. Furthermore, the method is rather simple and can be easily applied in practice.     

Routing order pickers in a warehouse with a middle aisle

This paper considers a parallel aisle warehouse, where order pickers can change aisles at the ends of every aisle and also at a cross aisle halfway along the aisles. An algorithm is presented that can find shortest order picking tours in this type of warehouses. The algorithm is applicable in warehouse situations with up to three aisle changing possibilities. Average tour length is compared for warehouses with and without a middle aisle. It appears that in many cases the average order picking time can be decreased significantly by adding a middle aisle to the layout.     

A travel time estimation model for a high-level picker-to-part system with class-based storage policies

Most previous related studies on warehouse configurations and operations only investigated single-level storage rack systems where the height of storage racks and the vertical movement of the picking operations are both not considered. However, in order to utilize the space efficiently, high-level storage systems are often used in warehouses in practice. This paper presents a travel time estimation model for a high-level picker-to-part system with the considerations of class-based storage policy and various routing policies. The results indicate that the proposed model appears to be sufficiently accurate for practical purposes. Furthermore, the effects of storage and routing policies on the travel time and the optimal warehouse layout are discussed in the paper.     

基于改进粒子群算法V型非传统布局仓库通道优化设计

V型仓储布局是一种典型的非传统布局方式,针对V型布局主通道设计的问题,将主通道抽象为若干个点连接而成的折线通道,每条拣货通道按物动量大小对仓库进行分区,采用更加符合实际的存取货物作业的概率不相等的非完全随机存储策略,建立最小化平均拣货距离的仓库主通道设计数学优化模型。其次,设计了基于极值扰动算子的改进粒子群优化算法(EDO-PSO)进行算法求解,利用极值扰动算子解决易陷入局部最优问题,采用并行深度搜索策略,提高算法性能,并用Benchmark函数与其他改进PSO算法对比验证算法性能。最后,结合具体实验数据仿真分析,计算结果表明,该方法在相同货位分配策略下,能有效缩短总拣货距离,验证了方法的有效性。     

配送中心订单分拣系统中的拣货路径选择研究

订单分拣是订单履行流程中一项重要活动,分拣成本是配送中心成本的主要组成部分之一。订单分拣系统的设计需要考虑订单类型、产品特点、分拣策略、分拣区域的布局、分拣路径和储位选择等因素。本文主要评价各种拣货路径方法,作者利用方差分析中的最小显著性差异法.1602640178otmail.com对仿真结果进行多重比较。本文的研究结果显示,当订单规模较小时,单区布局下的最优启发式路径方法是最大间隙法;双区布局下的最优启发式路径是组合方法;而且双区布局下的各种路径方法更能节省分拣行走距离。这些结论有助于配送中心管理人员通过分析订单规模来改变分拣路径和布局,进而提高配送中心分拣效率。     

Travel time analysis for general item location assignment in a rectangular warehouse

A travel time model with general item location assignment in a rectangular warehouse system is presented. We give the exact probability mass functions that characterise the tour of an order picker and derive the first and second moments associated with the tour. We apply the model to analysing order batching and storage allocation strategies in an order picking system. The order picking system is modelled as a queueing system with customer batching. The results are compared and validated via simulation. The effects of batching and batch size on the delay time are discussed with consideration to the picking and sorting times for each batch of orders.     

基于遗传算法的多通道密集式移动货架订单拣选研究

密集式移动货架越来越多地应用到仓储实践中,提高了仓储空间利用率,但增加了订单拣选的时间成本。本文根据密集式移动货架的仓储布局特点,针对多条通道可同时打开的情况,将货架移动时间转换成通道移动距离进行计算,提出了多条通道依次移动的优化规则,以整批订单拣选所耗费的总时间最少为目标,建立了订单拣选顺序优化的数学模型。针对该模型的特点,设计了实数编码且全局寻优的遗传算法,并进行了不同规模的算例模拟。计算结果表明,该算法具有较强的适用性,针对不同规模的问题,均有显著的优化效果;货架数量、订单数量以及移动通道数量的小幅度增减,将会导致总拣选时间较大幅度的波动;多条移动通道初始位置居于中部或均匀分散,总拣选时间略优于其集中于仓储系统一端。     

The impact of order batching and picking area zoning on order picking system performance

This paper proposes an approximation model based on queuing network theory to analyze the impact of order batching and picking area zoning on the mean order throughput time in a pick-and-pass order picking system. The model includes the sorting process needed to sort the batch again by order. Service times at pick zones are assumed to follow general distributions. The first and second moments of service times at zones and the visiting probability of a batch of orders to a pick zone are derived. Based on this information, the mean throughput time of an arbitrary order in the order picking system is obtained. Results from a real application and simulation show that this approximation model provides acceptable accuracy for practical purposes. Furthermore, the proposed method is simple and fast and can be easily applied in the design and selection process of order picking systems.     

Travel time models for automated warehouses with aisle transferring storage and retrieval machine

This paper presents analytical travel time models for the computation of travel time for automated warehouses with the aisle transferring S/R machine (in continuation multi-aisle AS/RS). These models consider the operating characteristics of the storage and retrieval machine such as acceleration and deceleration and the maximum velocity. Assuming uniform distributed storage rack locations and pick aisles and using the probability theory, the expressions of the cumulative distribution functions with which the mean travel time is calculated, have been determined. The computational models enable the calculation of the mean travel time for the single and dual command cycles, from which the performance of multi-aisle AS/RS can be evaluated. A simulation model of multi-aisle AS/RS has been developed to compare the performances of the proposed analytical travel time models. The analyses show that regarding all examined types of multi-aisle AS/RS, the results of proposed analytical travel time models correlate with the results of simulation models of multi-aisle AS/RS.     

A note on the linearity of Ratliff and Rosenthal's algorithm for optimal picker routing

Ratliff and Rosenthal state that their dynamic programming algorithm for optimal picker routing has linear complexity in the number of aisles. Indeed, solving the dynamic program is linear, but computing the cost coefficients of the dynamic program certainly requires the consideration of all picking positions, whose number is independent of the number of aisles. For a given unsorted sequence of picking positions, our algorithm is linear in the sum of the number of aisles and number of picking positions.     

基于物料周转率与需求相关性的储位分配优化策略与算法

优化储位分配策略是加快订单拣选速度和提高仓储效率的重要前提。在实际出入库操作中,物料可能具有一定的需求相关性,如螺钉与螺母。若这些需求相关度较高的物料被安排于距离较远的货位,将大大影响其拣选出库的效率。因此,本研究考虑不同储位分配方案的影响,提出将基于物料周转率的存储策略(COI)与物料需求相关度相结合的存储策略,使得周转频率高和相关度大的物料在仓库中的位置接近,且存储于更近仓库出入口的巷道货位。由于模型的计算规模随着参数增长呈指数式增长,本研究开发出一种近似算法,并通过实验证明,相较于商业软件,本算法可更为有效得获取问题的最优或近似解。最后通过实例分析,给出不同COI系数与物料需求度偏好下该仓库的可行储位分配方案     

分类存储返回型与S型拣选路径随机模型的比较研究

物流配送中心中,减小订单拣选行走距离进而优化人工拣选作业系统可有效提高客户满意度,降低成本.货位指派和拣选方式是影响拣选行走距离的两个重要因素.作者在分类存储的货位指派策略下、分别对返回型和S型拣选方式,建立了拣选距离随机模型.仿真结果表明,模型结果能在误差允许条件下较好地与仿真逼近.通过在4种物品订购频率和货位分配情况下对返回型和S型拣选方式的比较,得出两种拣选方式各自适用的情况.     

Space allocation and aisle positioning for an industrial pick-to-belt system

Distribution centres (DCs) are a key component in supply chains. In order to respond quickly to customer demands, most DCs use a fast-pick area where order picking can be executed efficiently. In these areas, the amount of space allocated to each product is of great importance, as it determines the number of replenishments required to guarantee product availability, thus avoiding interruptions in the order picking. The obvious assumption is that the performance of DCs could be improved by using simple strategies such as assigning more space to products having the highest demand. However, as this paper shows, the practical constraints related to the need for aisles granting safe and easy access to storage locations make designing fast-pick areas difficult. A parameter-free, two-phase algorithm based on product-adding heuristics combined with a space-reduction heuristic is proposed to solve this design problem. When applied to real data provided by our industrial partner, this heuristic generated considerable time savings.     

考虑商品数量和商品拣选成本的AGV智能仓库订单分批问题研究

AGV(Automated Guided Vehicle,自动导引车)智能仓库是一种基于“货到人”拣选模式的自动化仓库。本文考虑了订单中商品的需求量和货架上商品的存储量,以极小化货架搬运成本和商品拣选成本为目标,建立了AGV智能仓库订单分批问题的整数规划模型。本文针对订单分批问题的特点,提出了一种基于订单和货架交替选择的贪婪求解算法。对比CPLEX求解器的精确最优解,本文提出的贪婪算法的误差百分比不超过10%,平均误差百分比为5.38%;对比基于相似性的分批算法的求解结果,本文提出的贪婪算法不仅运算时间更短,解的质量也更好。进一步地,对比不考虑商品拣选成本的订单分批模型,本文提出的模型在不明显增加货架搬运成本的前提下,可以大幅度降低商品拣选成本。因此,在订单分批模型中考虑商品拣选成本是非常必要的。     

Performance of miniload systems with two-class storage

To increase throughput, the higher turnover items are often stored near the input/output point of a miniload system. We analyze the performance of such a miniload with a square-in-time rack containing two storage zones: high turnover and low turnover. First, we derive the distribution of the dual command travel time. System performance measures such as the throughput depend upon the distribution of the dual command travel time and the distribution of pick times. We work out the details and obtain closed-form expressions for throughput for two important families of pick time distributions: deterministic and exponential. Finally, we investigate how the size of the high turnover region affects throughput.     

“货到人”拣选系统中电商订单分批优化研究

本文在电商行业迅速发展及人工智能日趋成熟的背景下,研究以自动导引车(AGV)为搬运工具的“货到人”拣选系统订单分批问题。首先以最小化AGV搬运货架次数为目标建立订单分批模型,然后提出了基于货架相似度的两阶段订单分批算法,在第一阶段分为新批次创建及订单加入批次两个步骤得到初始解;在第二阶段采用局部搜索改进初始解。在算法中构造订单选取货架规则,定义货架相似度函数并设计两种方法创建新批次,同时考虑周转箱数量限制求解订单分批方案。最后通过实验测试验证了模型和算法的有效性,分析了两种批次创建方法的适用性,并通过灵敏度分析给出了合理的周转箱数量配置建议。本研究可为采用“货到人”拣选系统的企业通过订单分批优化进一步提高AGV拣选效率提供理论依据和实践指导。     

Facility placement with sub-aisle design in an existing layout

In this paper, we consider the integration of facility placement in an existing layout and the configuration of one or two connecting sub-aisles. This is relevant, for example, when placing a new machine/department on a shop floor with existing machines/departments and an existing aisle structure. Our work is motivated by the work of Savas et al. [Savas, S., Batta, R., Nagi, R., 2002. Finite-size facility placement in the presence of barriers to rectilinear travel. Operations Research 50 (6), 1018–1031], that considered the optimal planar placement of a finite-size facility in the presence of existing facilities. Our work differs from theirs in that we consider material handling to be restricted to the aisle structure. We do not allow the newly placed facility to overlap with existing facilities or with the aisle structure. Facilities are rectangular and travel is limited to new or existing aisles. We show that there are a finite number of candidate placements for the new facility. Algorithms are developed to find the optimal placement and the corresponding configurations for the sub-aisles. Complexity of the solution method is analyzed. Also, a numerical example is provided to explore the impact of the number of sub-aisles added.     

“货到人”拣选系统机器人任务分配的鲁棒双层规划模型

在电商“货到人”拣选系统中,如何调度系统中的机器人并对任务进行合理地分配决定着整个系统的运行效率与成本。分析“货到人”拣选系统作业流程,建立机器人数量配置、机器人调度与机器人任务分配的双层规划模型。上层模型以批量订单完成总成本最小为目标函数,以机器人调度为决策变量,构建整数规划模型;下层模型以机器人完成所有任务的平均空闲率最小为目标函数,以任务分配为决策变量,考虑机器人在完成任务过程中由于调度、避障、路径规划等导致的行走距离不确定因素,构建鲁棒优化模型。上层的调度结果制约了下层的最小平均空闲率,下层的任务分配结果影响上层的最小成本,上下层结果共同决定机器人配置决策。利用遗传算法求解模型,通过实例仿真验证了模型的有效性。