## 1 Introduction  
Warehousing involves the storage of raw materials, components, work in progress (WIP), and finished goods. It has consistently been recognized as a crucial element within the supply chain and within logistics. A well-designed and effectively managed warehousing system can yield significant benefits, such as reducing the risk of running out of stock, mitigating the bullwhip effect, and decreasing the lead time of the final products [1]. Over recent decades, advancements in automation have led to the proliferation of fully automated solutions like automated storage and retrieval systems (AS/RSs) and automated vehicle storage and retrieval systems (AVS/RSs) across various industrial environments [2]. An AS/RS comprises two essential components: (i) a storage area that can be subdivided and (ii) multiple automated machines responsible for material movement within and outside the storage area. Compared to traditional manual warehouses, AS/RSs offer unreliable advantages, including labor savings, an increased storage capacity, a reduced throughput time, and a decreased occurrence of errors, damage, and risks for operators. However, the success of AS/RS implementation relies on the efficiency and alignment of the control policies with the needs of the industrial system. A well-designed AS/RS must autonomously address various challenges, such as scheduling retrieval and storage operations, assigning stock items to customer orders, allocating delivery trucks to output points, and determining routing for operations involving storage and retrieval machines, among others [3]. Despite their complexity, and owing to their numerous benefits, AS/RSs have rapidly gained traction across diverse sectors in recent decades. One industry where AS/RSs are becoming increasingly prevalent is the steel industry. According to an analysis by the World Steel Association ([[https://www.worldsteel.org/](https://www.worldsteel.org/)]([https://www.worldsteel.org/](https://www.worldsteel.org/)), accessed on 15 January 2024), this industry is at the heart of global development. In 2017, the steel industry achieved sales of USD 2.5 trillion and generated USD 500 billion in value. For every USD 1 added within the steel industry, an additional USD 2.50 of value-added activity is supported across other sectors of the global economy due to purchases of raw materials, goods, energy, and services. This generates over USD 1.2 trillion in value. In terms of employment, this analysis study confirmed that the steel industry employs more than 6 million people, and for every 2 jobs in the steel sector, 13 more jobs are supported throughout its supply chain, resulting in a total of around 40 million jobs. AS/RSs used in the steel sector significantly differ from those implemented in other environments, such as AS/RSs for pallets [2], miniloads [4], shuttle-based AS/RSs [5], etc. These differences predominantly stem from the fact that, in the steel sector, the systems are designed to handle unconventional stock-keeping units and typically heavier and bulkier items (e.g., slabs, blooms, billets, tubes and bundles, metal sheet bundles, etc.). Consequently, solutions proposed for other AS/RSs are often impractical for systems intended for the steel sector. One of the most prevalent AS/RSs in the steel sector is the shuttle-lift-crane (SLC)-based AS/RS (SLC-AS/RS) (Figure 1): a fully automated system specifically designed for storing bundles of long metal bars or tubes, wherein the stored items themselves act as the unit loads (i.e., the bundles themselves). To the best of the authors' knowledge, the SLC-AS/RS has received limited attention in the scientific literature despite its significance in this industry. Thus, this paper contributes to partially filling this gap. Managing the handling of metal bar bundles involves several constraints related to the weight and quality of goods, complicating operational decisions. Previous work by [PERSON] et al.