Enhancing performance of capacity‐constrained (S, T) inventory models with backlogging under random and discrete demand-lead time conditions

Inventory management plays a critical role in optimizing supply chain operations, especially under uncertain demand and lead time conditions. This thesis introduces an innovative model for a capacity‐restricted (S, T) inventory policy with lost sales, designed to tackle the complexities arising from discrete and stochastic demand as well as variable lead times. Unlike traditional models that assume infinite replenishment capacity or deterministic parameters, this study incorporates real-world constraints, such as finite storage capacity and probabilistic demand patterns, to provide a more practical framework.The proposed model is developed using advanced stochastic modeling techniques, enabling a more accurate representation of inventory behavior under uncertain conditions. Analytical methods are applied to derive performance metrics, including stockout probabilities, expected costs, and service levels. Additionally, the model integrates a simulation-based approach to validate its effectiveness across various scenarios, such as fluctuating demand, limited replenishment capacity, and varying lead time distributions.The results demonstrate that the proposed (S, T) policy significantly improves inventory performance by balancing cost efficiency with service reliability, particularly in environments where lost sales directly impact profitability. This study advances inventory management by proposing a flexible and scalable framework to support decision‐making in environments characterized by uncertainty. Practical implications for industries such as retail, manufacturing, and food services are also discussed, highlighting the model's versatility in addressing inventory challenges across diverse sectors.