Inventory Model for Defective and Deteriorating Items With Two Production Rates, Stochastic Demand, and Payment Delay Within A Finite Horizon

An inventory production model is developed specifically for managing deteriorating items, encompassing the presence of defective items within the production process. Within this framework, demand is modelled as stochastic, following the Wiener process. Notably, the planning horizon is constrained to a finite timeframe. Additionally, the model incorporates the assumption of shortages, two distinct production rates, reflecting the dynamic nature of real-world manufacturing operations. Furthermore, the impact of delays in payments for raw materials, from the manufacturer to the supplier, is also accounted. The resolution of the stochastic integral is achieved through the rigorous application of the Riemann integral method. The model is solved, and the optimal cost is calculated demonstrating effective management strategies. A numerical example is solved, followed by sensitivity analysis to illustrate practical applications. This article offers an approach to optimize inventory management under complex real-world constraints.