# Designing Automated Logistics Warehouse Stackable Bidirectional Infinite-Loop Modules
## 1 Introduction  
The online market is currently experiencing a significant surge, driven by advancements in information technology, and is actively shaping new global consumption trends, particularly in response to the impact of COVID-19. This evolving trend has led to a noticeable increase in the volume of small orders for various products, highlighting the growing importance of same-day delivery services [1]. Notably, same-day delivery services for fresh food, considered essential, have gained considerable attention in Korea, with their scale consistently expanding alongside the spread of COVID-19. Consequently, efficient logistics systems have become crucial, making the expansion and innovation of automated logistics warehouses indispensable [2]. In particular, there is a growing interest in logistics warehouses responsible for the selection and retrieval of ordered goods from inventories [3]. While the importance of warehouse management has been emphasized in the past, traditional warehouses were primarily perceived as places for storing goods. However, recent years have seen a rapid increase in logistics volume in Korea, particularly under the influence of services like same-day delivery. The ability to quickly locate and process goods within warehouses has thus become paramount. Moreover, owing to the escalating land prices in metropolitan areas of Korea, driven by dense population centers, the demand for warehouses that maximize space utilization and operational efficiency has surged [4, 5]. These logistics warehouses, primarily concentrated in the Seoul Capital Area, are undergoing modernization and evolving into logistics warehouses that incorporate artificial intelligence to create new added value [6]. Major e-commerce and logistics companies, such as Coupang, C] Logistics, and Lotte Mart in Korea, Amazon in the United Statesof America, Ocalo in the United Kingdom, DHL in Germany, and JD.COM in China, are expanding their investments in automated warehouses as a crucial strategy to enhance their competitiveness [7]. However, existing automated logistics warehouses face limitations in achieving both spatial efficiency and increased speed of logistics operations. These limitations stem from constraints based on horizontal expansion, complexity of stacked systems, and high land prices in densely populated areas [8]. Logistics warehouses prioritize quick delivery and accessibility, leading to the concentration of most warehouses in metropolitan and other densely populated regions. Given the characteristics of these areas, land prices are exorbitant, which increases warehouse construction costs and makes it increasingly challenging to secure new spaces nearby. Consequently, the issue of space utilization in existing warehouses becomes a pivotal consideration, accompanied by several constraints. First, the expansion of logistics warehouses in confined spaces primarily relies on horizontal expansion [9]. However, securing additional land in surrounding areas in densely populated regions is a formidable challenge. Additionally, the expansion of stacked systems presents its own set of challenges. Constructing high-rise buildings must account for various variables, including structural stability, fire and safety regulations, and logistics operational efficiency. Therefore, simply adding floors to warehouses is a limited solution. These challenges are critical factors influencing the efficient operation of logistics warehouses [8]. The present study introduces a novel warehouse design aimed at overcoming the shortcomings of horizontal and stacked expansion approaches. This innovative design not only boosts spatial efficiency and logistics operation speed but also offers a strategic solution to alleviate space acquisition and cost-related challenges in warehouse location decisions within densely populated areas. Our warehouse design centers around a stackable bidirectional infinite-loop module to facilitate both horizontal and vertical expansion.