## 2 Research Context
The lost sales environment analyzed in this study is particularly prevalent in highly competitive sectors such as retail, service, machinery spare parts, and online sales [30; 31; 32]. The periodic review (R, s, S) inventory system is rarely studied in a context with lost sales [25]. As recognized by [33], adding a service-based constraint to an inventory model with lost sales makes the model more realistic for retail inventory modeling but makes computation and analysis more difficult. Few publications have studied this problem, and this paper aims to contribute to this field. Our study assumes normally distributed market demand, a type with a vast application under various settings in both practice and research on inventory control. Normally distributed market demand is frequently analyzed in the inventory management-related literature in various settings, examples of which can be found in the works of [34; 35; 36; 37; 38; 39]. Operating in workweek schedules other than under a seven-day, although common in business practice, is scarce in the relevant scientific literature. The studies [37; 40] recognize the synchronicity of working time as one of the influential factors of inventory management in SCs. The work of [41] acknowledges only partially non-working conditions, i.e., the EOQ inventory model with defined open and closed hours. The study of [42] considers the influence of non-working days in inventory models for perishable goods regarding waste and costs. Based on simulations, they conclude that including non-working day constraints in the replenishment process slightly reduces food waste. They also found that a store open seven days a week instead of six decreases food spoilage by 18.6%. In the study of [43], authors develop a new hybrid discrete-time perishable inventory model that incorporates time-varying demand and closing days based on the Weibull distribution. The work [37] considers the non-working days at the manufacturer level of the SC model working under a periodic review (R, s, S) inventory system. However, it does not compare WSs with and without non-working days, as carried out in this study, which increases analysis complexity and provides conclusions relevant to practitioners and scientists. Finally, the study [44] explores optimizing the number of bikes in bike-sharing systems by considering the differences in the WS based on an inventory system (s, S) and an iterative optimization algorithm. As previously mentioned and confirmed in the study of [5], there is an evident lack of relevant literature that simultaneously tackles environmental and economic considerations of periodic review inventory systems. One of only a few such papers is the research [45], where the optimization criteria are environmental benefits and costs. The work of [46] compared the forest-based biomass SC's main parameters for two inventory control systems via simulation modeling. Their results imply that selecting an inventory system significantly impacts the total cost and carbon emissions and only has a minor effect on demand fulfillment. In the work of [37], multi-criteria decisions are made in an SC echelon based on inventory levels, emissions calculated according to the EN 16258 [47] norm, and total costs. Many studies investigate environmental and cost considerations related to inventory control models other than periodic review (R, s, S) inventory systems. Most common are the papers investigating the economic order quantity (EOQ) model, which substantially differs from the inventory model in this research. Among others, works of [48; 49; 50] extend the traditional definition of EOQ by including an environmental approach to the green economic order quantity model. In green inventory management, the traditional focus on economic factors, usually measured by costs, is supplemented by an environmental perspective, typically assessed through emissions. A key topic is understanding how inventory-related decisions affect costs and emissions.