With the increasing environmental concerns and legislative pressures, the focus on incorporating ecologically sustainable practices into inventory management systems has grown, leading to the emergence of green inventory management. However, this field is not without its challenges, with numerous conflicting real-world constraints and goals. A comprehensive literature review targeting green inventory management operating under a periodic review inventory system was conducted to identify research gaps and potential directions for future research. Despite the growing interest in the field, this review highlighted the scarcity of relevant studies. Out of the 1272 papers reviewed, only 16 studies, or 1.3%, met the criteria for exploring periodic review inventory systems while simultaneously considering environmental and economic aspects. These studies were further analyzed in detail and categorized according to key classification criteria. The future research directions highlighted the need for additional studies on periodic review inventory systems operating under stochastic market demand in the context of green supply chain management. The standardization of emission calculation methodologies was also emphasized as a crucial step towards aligning inventory management practices with the aim of increasing inventory management efficiency and the related improvement in the environmental performance of supply chains.

This research employs numerical simulations and scenario analysis to assess a supply chain model’s economic and environmental performance operating under stochastic market demand, with inventory levels managed by a periodic review (R, s, S) inventory system. The inventory model in this research is designed to determine the minimal inventory levels required to achieve predefined fill rates across various operational constraints. The supply chain’s inventory model simulates optimal responses to normally distributed market demand within 365-day periods characterized by mean and two levels of demand variability through two fill rate levels, two workweek schedules, 15 review periods, and 16 lead times. By conducting an extensive analysis of the 192000 simulation experiments of the supply chain under periodic review (R, s, S) inventory system, complex influences between system variables and economic outcomes of supply chain operation measured by ordering, transportation, holding, penalty, and total costs along with greenhouse gas emissions arising from inventory-related transportation according to the ISO 14083 standard are analyzed. The insights from this research have significant practical implications, providing valuable guidance for supply chain managers, researchers, and freight companies offering guidance for improving economic and environmental performance.

This paper develops explicit equations for setting the reorder point s and the order-up-to level S in a periodic-review (R, s, S) inventory policy in a lost-sales environment. The objective is to support direct policy parameterization from demand level, demand variability, review period, lead time, and type-II unit fill-rate target. A long-horizon discrete-event simulation was combined with exhaustive enumeration of integer policy pairs to construct a policy-consistent reference dataset of five million observations. Symbolic regression was then used to convert this simulation-derived reference map into compact closed-form equations for both policy parameters. Over the full tested domain, the equations achieved R² = 0.941 for the reorder point s and R² = 0.989 for the order-up-to level S. On the common domain where analytical comparison is possible, the proposed equations reduced mean absolute error by approximately 65% for the reorder point and 85% for the order-up-to level. The equations also remain directly evaluable at the finite-horizon zero-lost-sales boundary corresponding to a 100% fill rate, where standard normal-loss logic has no finite safety-factor solution. The study provides an interpretable, auditable equation system for initial estimation of policy parameters for periodic-review lost-sales inventory policies within the tested normal-demand domain.