Abstract: This research delves into optimizing inventory systems by incorporating stochastic lead-time, price-dependent demand, and advance payment strategies to reflect real-world uncertainties and improve supply chain efficiency. Traditional models often assume deterministic lead-times and static demand, which do not account for the variability and dynamic nature of actual market conditions. Our model integrates a stochastic lead-time distribution to handle delivery time variability and models demand as a function of selling price to capture consumer behavior's sensitivity to pricing. Additionally, advance payment options are included to explore their financial implications on inventory costs and ordering decisions. Using advanced mathematical techniques and heuristic algorithms, we derive optimal ordering policies that minimize total costs, including ordering, holding, shortage, and advance payment costs. Sensitivity analysis highlights the impact of key parameters such as lead-time variability, price elasticity, and advance payment terms on system performance. The findings demonstrate that considering these factors enhances the robustness of inventory management strategies and provides financial benefits by mitigating risks associated with uncertain lead-times and optimizing cash flow alignment with the inventory cycle.

Keywords: Inventory Optimization, Stochastic Lead-Time, Price-Dependent Demand, Advance Payment Strategies, Demand Forecasting, Cost Minimization, Sensitivity Analysis

| DOI: 10.17148/IARJSET.2025.12737