Cost minimization in production inventory mode for linearly deteriorating items with overtime production and lifetime demand

This paper presents a production inventory model specifically designed for linearly decaying items. The model incorporates parameters such as price, stock, lifetime demand rate, and constant holding costs, alongside the inclusion of an overtime production facility to meet customer demand and prevent shortages. The primary objective is to minimize various inventory-related costs within the system. The model is mathematically formulated through a system of differential equations, which are subsequently solved to yield optimal production and inventory strategies. By integrating an overtime manufacturing process, the producer is able to minimize the total gross inventory cost. The effectiveness of the model is further analyzed through sensitivity analysis, showcasing the optimal parameter values and demonstrating its robustness and efficiency.