Rack Locations in the Mobile-Rack Picking System: Comparison
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Please note this is a comparison between Version 2 by Rita Xu and Version 1 by MengYue Zhai.

移动式货架拣选系统（MRPS）中货架的灵活移动，显著提高了具有“一单多品”特点的电商订单的拣选效率，也带来了如何在仓库中放置货架的挑战性问题。这是因为每个货架在MRPS中的位置直接影响订单拣选过程中货架需要移动的距离，进而影响订单拣选效率。

The flexible movement of racks in the mobile-rack picking system (MRPS) significantly improves the picking efficiency of e-commerce orders with the characteristics of “one order multi–items” and creates a challenging problem of how to place racks in the warehouse. This is because the placement of each rack in the MRPS directly influences the distance that racks need to be moved during order picking, which in turn affects the order picking efficiency.

  • mobile-rack picking system
  • rack location optimization
  • degrees of rack heat and relevance

1. Introduction

The rapid development of electronic commerce in recent years has posed substantial implications and challenges for warehouse operation management. Given the demanding timeliness and large-scale, diverse, small-batch nature of customer orders, the urgent resolution of the problem of implementing precise and efficient order picking operations is a critical concern for every warehouse enterprise [1,2][1][2]. The MRPS, operating as a semi-automated picking system, provides a fresh way to address this problem [3]. This system deviates from the traditional fixed rack storage system as its racks are smaller in size and can be moved to any desired position within the warehouse. The picking operation is executed by the robot, which carries the rack to the picking station, thereby implementing the “parts to picker” mode. Instead of being stored in a fixed location like a traditional warehouse, each Stock Keeping Unit (SKU) can be scattered and put on numerous mobile racks, each rack holding varying amounts of different categories of SKUs [4,5][4][5]. The MRPS significantly improves the flexibility of SKUs storage and efficiently addresses the difficulty of e-commerce order picking by allowing for the relocation of racks in the warehouse [6]. As a result, it is highly desired by numerous e-commerce warehousing enterprises. Presently, e-commerce giants such as JD, Walmart, and Alibaba have embraced MRPS [7]. Nevertheless, this system also gives rise to the challenge of optimizing rack location. The positioning of each rack in the MRPS directly affects the distance traveled by the robots during order picking, thereby impacting the efficiency of the order picking. How can the arrangement of the rack in the warehouse be periodically adjusted, taking into account the regularity of customer orders and the categories and quantities of SKUs stored on the rack, with the objective of minimizing the travel distance of robots? This is a challenging problem that every MRPS decision-maker faces, especially when dealing with e-commerce order picking, in order to maximize efficiency and leverage the system’s advantages. This problem is accompanied by the emergence of MRPS, which restricts the development of a new generation of order picking systems. It is different from the location optimization problem in the fixed rack storage system, its solution surpasses the applicability of existing theoretical methods, and its NP-Hard characteristics significantly amplify the problem’s difficulty, especially when addressing large-size customer orders [8,9][8][9].

2. Rack Locations in the Mobile-Rack Picking System

在存储分配方面，传统的手动拣货系统只需要确定In terms of storage assignment, the traditional manual order picking system solely requires determining the storage position of the SKU在货架上的存储位置。这是因为货架具有固定的存储位置，并且拣货员在通道中行走以从货架中检索 SKU。换句话说，这是一个为SKU分配存储位置的问题[10]。s on the rack. This is because the racks have fixed storage locations, and pickers walk in the channels to retrieve SKUs from the racks. In other words, it is a problem of assigning storage locations to SKUs [10]. Hausman等人率先比较了三种存储分配策略：随机分配、基于完全周转率的分配和基于类的周转分配[11]。随后， et al. were the first to compare three storage assignment strategies: random assignment, full turnover-based assignment, and class-based turnover assignment [11]. Subsequently, Kuo等人分配了存储位置，目的是通过减少客户等待时间来提高仓库利用率和客户满意度[12]。 et al. assigned the storage locations with the objective of increasing warehouse utilization and customer satisfaction by reducing customer waiting time [12]. Glock和 and Grosse研究了仓库拣选成本最低的存储分配问题[13]，而sse studied the problem of storage assignment with the lowest warehouse picking cost [13], while Bortolini等人则基于最佳货架稳定性优化了 et al. optimized SKU存储位置[14]。上述研究的目标设定方法比较常见。此外，一些学者通过分析产品本身的某些属性来优化s storage locations based on the best rack stability [14]. The objective-setting methods of the above studies are relatively common. In addition, some scholars optimized SKU的存储位置：s storage locations by analyzing certain attributes of the products themselves: Caron等人提出了一种基于 et al. proposed a storage strategy based on the Cube-per-Order Index（COI）的存储策略[15]。 (COI) [15]. Li 和and Nof 提出了一种存储优化方法，根据其属性对 SKU 进行分类proposed a storage optimization method to classify the SKUs based on their attributes [16]. [16]。Yang 和and Nguyen 开发了一种结合主成分分析的约束聚类方法，以满足聚类存储 SKU 的需求，同时考虑实际存储约束developed a constrained clustering method integrated with principal component analysis to meet the need of clustering stored SKUs with the consideration of practical storage constraints [17]. Since there is a certain correlation between different [17]。由于在实践中不同SKU之间存在一定的相关性，并且它们经常同时购买，因此其他学者也考虑了这种相关性：s in practice and they are often purchased at the same time, other scholars take this correlation into consideration: Pan等使用同时购买SKU的频率来量化产品之间的相关性[18]。 et al. used the frequency of simultaneous purchases of SKUs to quantify the correlation between products [18]. Xiao 和and Zheng 建议根据相关性对所有 SKU 进行分类，然后将它们与分类的存储位置进行匹配proposed to classify all SKUs based on correlation and then match them with classified storage locations [19]. [19]。Jane和 and Laih提出根据关联关系对SKU进行分类，相似的SKU被随机放置在同一个区域[20]。 proposed to classify SKUs according to association relationships, and similar SKUs are randomly placed in the same area [20]. 在The above research focuses on the problem of storage assignment under the traditional “picker-to-parts” model. Within the MRPS系统中，机器人使用“零件到拣选机”拣选模式将货架从存储区运送到拣选站。与此同时，拣货员站在拣选站不动，从货架上取回 SKU 以完成订单的拣选。拣选完成后，机器人需要将货架从拣选站运回空位进行存储[21]。因此， system, the robot transports the racks from the storage area to the picking station using the “parts-to-picker” picking mode. Meanwhile, the pickers stand still at the picking station, retrieving the SKUs from the racks to fulfill the orders’ picking. After picking is completed, the robot needs to transport the racks from the picking station back to the empty location for storage [21]. Therefore, the storage assignment problem of MRPS的存储分配问题可以分为 can be divided into SKUs存储机架优化和机架位置优化。一些学者采用两阶段求解思路来研究MRPS的存储分配问题。第一阶段采用关联分析方法和聚类方法对SKU进行关联聚类，使经常同时购买的SKU可以存储在同一个货架上，实现存储在货架上的SKU在整体相关性上最大化。在第二阶段，Li等人提出了一种基于货架周转率的新型分散存储策略，旨在分散存放周转率较高的货架，以避免同时在高频作业区域出现大量AGV的拥堵和堆积[22]。 storage racks optimization and rack location optimization. Some scholars have used a two-stage solution idea to study the storage assignment problem of MRPS. In the first stage, correlation analysis methods and clustering methods are used to perform correlation clustering on SKUs, so that SKUs that are often purchased at the same time can be stored on the same rack, and to realize that the SKUs stored on racks are maximized in overall relevance. In the second stage, Li et al. proposed a new scattering storage strategy based on rack turnover rate, aiming to decentralize the storage of racks with higher turnover rates to avoid congestion and accumulation of a large number of AGVs in high-frequency operating areas at the same time [22]. Yuan等人考虑了机架周转率、机架之间的相关性和车道内的工作平衡，构建了最小化机器人总行程距离的优化模型，并设计了一种结合贪婪算法和改进的模拟退火的混合算法[23]。上述研究同时考虑了 et al. considered rack turnover rate, relevance between racks, and work balance in the lanes to construct an optimization model for minimizing the total travel distance of robots and designed a hybrid algorithm that combines a greedy algorithm and improved simulated annealing [23]. The above research considered both the two sub-problems of SKU存储优化和货架位置优化这两个子问题。然而，在s storage optimization and rack location optimization. However, in the real operation of the MRPS的实际运行中，SKU在货架上的存储分配和货架位置的调整是两类不同时间频率不同的工作，因此它们属于两个不同层次的问题。, the storage assignment of SKUs on the rack and the adjustment of the rack position are two types of work with different frequencies at different times, so they belong to two different levels of the problem. 考虑到机架存储位置的决策对机架的移动距离和机器人的工作量有重要影响，近年来许多学者对Considering that the decision of rack storage location has an important impact on the moving distance of the rack and the workload of the robot, many scholars have conducted research on the RLOP of RMFS的RLOP进行了研究。 in recent years. Weidinger等人通过计算货架与拣选站之间的移动距离，将货架定位问题形式化为特殊的间隔调度问题，并引入了一种基于自适应大邻域搜索的数学方法来求解该问题。研究表明，当目标是最小化货架和拣选站之间的距离时，简单的货架定位策略（如最短路径存储）可以获得更好的结果[8]。 et al. formalized the rack location problem as a special interval scheduling problem by calculating the movement distances between racks and picking stations and introduced a mathematical approach based on adaptive large neighborhood search to solve the problem. It is shown that a simple rack location strategy like the shortest path storage can gain better results when the objective is to minimize the distance between the racks and the picking stations [8]. Yuan et al. developed a fluid model to analyze the performance of velocity-based storage policies. They characterized the maximum possible improvement from applying a velocity-based storage policy in 等人开发了一个流体模型来分析基于速度的存储策略的性能。他们描述了与随机存储策略相比，应用基于速度的存储策略可能带来的最大改进。结果表明，具有两个或三个类的基于类的存储可以实现大部分潜在好处，并且这些好处随着机架速度的变化而增加[5]。comparison to the random storage policy. The result showed that class-based storage with two or three classes can achieve most of the potential benefits and that these benefits increase with greater variation in the rack velocities [5]. Merschformann等人介绍了几种机架重新定位策略，如随机策略、固定策略和最近策略[24]。 et al. introduced several rack repositioning policies such as random policy, fixed policy, and nearest policy [24]. Cai等人将机架位置分配问题与路径规划决策相结合，以最小化机器人的总行程时间[25]。 et al. integrated the rack location assignment problem with the path planning decisions to minimize the total travel time of robots [25]. Zhuang et al. investigated the rack storage and robot assignment to racks problem during order processing. They formulated this problem with the objective of minimizing the makespan of this system and developed a matheuristic decomposition approach based on a rolling horizon framework and the simulated annealing method. In the above study, the storage location of the rack is constantly chang等人研究了订单处理过程中的货架存储和机器人分配给货架的问题。他们提出了这个问题，目的是最小化该系统的制造跨度，并开发了一种基于滚动水平框架和模拟退火方法的数学分解方法。在上述研究中，货架的存储位置不断变化，并且每个完成的拣选都可以将货架分配到新的存储位置。ing, and the rack may be assigned to a new storage location for each completed pick. Merschformann 等人证明，与固定策略相比，在许多情况下采用可变存储位置是有利的。这种方法有效地减少了机器人的行进时间，使它们能够迅速完成后续任务。但是，这种策略可能会导致不再有用的货架存储在非常显眼的存储位置，这可能会导致拥塞问题，并在以后的订单拣选过程中进一步增加机器人的移动距离。此外，在订单拣选过程中，每次使用货架后分配新的存储位置将大大增加智能操作系统的计算负担[26\ et al. demonstrated that employing variable storage locations is advantageous in numerous scenarios compared to a fixed strategy. This approach effectively minimizes the traveling time of robots, enabling them to promptly accomplish subsequent tasks. However, this strategy may result in no longer useful racks being stored in very prominent storage locations, which is likely to cause problems with congestion and further robot travel distances during order picking later. Moreover, assigning a new storage location after each rack use during the order picking process will greatly increase the computational bu201227]。rden of the intelligent operating system [26][27]. 在实际情况下，客户对订单的交货时间和成本要求越来越高。由于销售、季节、产品生命周期和周转率等变量的影响，In actual situations, customers have increasingly higher requirements on the delivery time and cost of their orders. Owing to the impact of variables like sales, seasons, product life cycles, and turnover rates, rack locations in MRPS中的货架位置必须定期更改，以适应这些变化并满足客户需求。鉴于机器人运送到拣选站的货架始终存储大量 SKU，本文在客户订单的 SKU 组合与货架上的 SKU 组合之间建立了相关性。通过分析客户订单数量中披露的SKU订购规则，以及每个货架上存在的SKU的类别和数量，可以确定每个货架的使用频率。随后，可以合理分配货架位置，以适应未来的订单拣选需求。 must be changed on a regular basis in order to accommodate these changes and satisfy customer demands.

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