## 2 Research Context  
Our focus is on two primary streams of literature: (i) optimally performing inventory control under a periodic review (R, s, S) inventory system and (ii) environmental and economic performance of SCs related to inventory control. The periodic review (R, s, S) inventory system is widely present in the literature and practice, being the dominant ordering policy in modern companies with implemented business information systems such as Material Requirement Planning or Enterprise Resource Planning [13; 14]. A company working under an (R, s, S) inventory system reviews inventory levels at equidistant time intervals R. According to the control rule, only if the current inventory position x reaches the level equal to or below the reorder point s, a replenishment order of order-up-to level S \(-\) x is placed. However, since there are no simple procedures or algorithms for determining the optimal s and S levels in particular real-world situations, they are usually set manually, without algorithmic determination [15; 16]. Inventory models are generally classified by several factors: inventory policy type, demand type, response to excess demand, cost structure, etc. The literature review will follow these segments. To our knowledge, the vast body of literature on (R, s, S) inventory systems does not describe any model that addresses all the influential factors jointly considered in this paper. The goal of an inventory system is to meet customer demands adequately. Works of [17; 18] recognize that SC performance measures can be seen from two main perspectives: quantitative and qualitative. Quantitative is measured by costs, FRs, inventory levels, resources, and capacity utilization. The fill rate, defined as the percentage of demand that can be fulfilled from stock, is the industry's most commonly used service metric [19]. In contrast, the qualitative perspective of SC performance is measured by customer satisfaction, information, material flow integration, SC resilience, product quality, etc. Some authors, such as [20], emphasize the importance of performing research on multiple criteria approaches, trading off costs and service measures, and simultaneously including sustainability measures. That approach is implemented in this study. However, a common concept in the literature is that inventory can be managed from a customer service or cost minimization perspective [21]. An extensive review of [20] recognizes that 85% of 394 papers studying multi-echelon inventory systems analyze cost minimization problems, even though putting the company objectives into a single cost function is often difficult or unrealistic. While some costs are easy to quantify, others, such as penalty costs related to lost sales and loss of goodwill, are more challenging to estimate. Managers often prefer setting a service constraint, such as FR, over defining shortage costs due to the difficulty in accurately quantifying those costs [22; 23]. This complexity contributes to the more frequent use of service-level constraints in practice. However, in research, shortage costs are preferred because they allow for a comprehensive total cost perspective, which makes the comparison between different policies easier [24]. On the other hand, service level constraints are more commonly found in a practical, competitive business environment, with customer satisfaction often being a differentiation strategy among competitors [25; 26]. Service constraints imposed on periodic review inventory models can be found in several research papers, such as [25; 27; 28; 29]. One key inventory management strategy concern is how a company handles excess demand and temporary stockouts. The company can either backorder the item and expedite replenishment or treat it as lost sales. While backordering is commonly discussed in the literature, research [30] indicates that in a real-world environment, only 15% of customers in an out-of-stock situation will delay their purchase and wait for the product to become available again.