Stochastic Vendor-Buyer Inventory Model Analysis

This document is a research article that presents an analytical method for proving the uniqueness of the optimal solution for a stochastic vendor-buyer inventory model that includes defective items. The authors develop a rigorous approach to locate the optimal solution, addressing the limitations of previous iterative methods. The article discusses the assumptions and notations relevant to the model, including the vendor's production rate, reorder points, and the treatment of defective items. It also reviews prior research on inventory systems, highlighting various models and their contributions to the field. The findings aim to provide a solid analytical basis for decision-makers in inventory management, facilitating the identification of minimum average costs associated with defective items. The research underscores the importance of a robust solution mechanism in practical applications, helping practitioners construct more effective inventory models to meet real-world challenges.