## 1 Introduction  
Currently, organizations in the global market optimize their warehouses to improve production capacity and distribution, reduce lead and delivery times, and maintain sufficient inventory to meet seasonal demand [1, 2]. In this highly competitive global market, various organizations and industries must become extremely efficient and must implement continuous improvement methods to maintain their performance indices [3, 4].  
Successful businesses are employing technological advances in monitoring, storing, and shipping goods worldwide to eliminate waste, reduce cost, and improve customer service [5, 6]. In addition, companies incorporate effective supply chain logistics and lean manufacturing techniques integrated with Industry 4.0 principles, which improve product delivery and increase customer satisfaction, leading to viability and improved profit margins [7].  
Various chain management techniques have been implemented to monitor the warehouse and maximize inventory to leverage the storage of the products [8]. Warehouse management plays a crucial role in the successful operation of businesses. The global market relies on innovative techniques to improve the workflows in the warehouses of various industries [4]. For example, the implementation of radio frequency identification (RFID) tags on the products, through which serial numbers or bar codes are scanned in the system, allows the product location to be identified along with an estimated delivery time [9]. Furthermore, various inventory management software applications are available for maintaining proper inventory. This software provides the required information when the replenishment of the stock is needed to restore the inventory in the organization's warehouse [5]. To establish a workflow, optimize the process, and increase the workforce efficiency within the industry or production plant, different decision-making approaches are available: optimization-based, i.e., linear programming, genetic algorithm; simulation-based, i.e., discrete event; and multi-criteria decision-making analysis (MCDA), i.e., weighted sum approach (WSA), analytic hierarchy process (AHP), and technique for order preference by similarity to ideal solution (TOPSIS) [10; 11; 12; 13; 14].  
This study focuses on improving supplier warehouse utilization and maximizing implant warehouse utilization by optimizing the storage space for current product demands. Key considerations include storage space utilization, rack layout, the number of units per shelf, warehouse dimensions, and layout. In addition, this study aims to provide maximum quantities for product storage and decision-making guidance to determine the best placement of the product for optimal product storage, retrieval, and shipping to the customer.  
Therefore, the objectives of this study are summarized as the following:  
* Implement a linear programming (LP) model to determine the maximum quantity of boxes that can be stored on the respective rack of the warehouse;
* Identify criteria that can maximize the utilization of the warehouse;
* Develop a decision-making model based on the criteria concerning the storage rack to optimize the ranking of box placement.  
To achieve these objectives, this study integrates both the optimization- and MCDA-based methods. The dimensional data regarding the warehouse and product box are analyzed to formulate the LP model. The best possible solution from this model maximizes the quantities of the boxes stacked on the shelves within the facility. Furthermore, the type and number of products that can be placed on the shelves are defined. Then, the most suitable and effective placement for the product can be obtained through the decision-making tool, which is developed by integrating the rough AHP method with the rough TOPSIS method [15]. Rough set theory plays a vital role in handling the uncertainties and provides appropriate decisions by removing the vagueness of the experts' opinions.