Perishable Production Inventory System with a Level Dependent Demand and offering Discount during Production run

This paper presents a comprehensive analysis of a perishable production inventory system with level-dependent demand, focusing on the application of a discount during the production phase. The model assumes no shortage, and the production rate exceeds the rate of demand, which is treated as a function of the inventory level. Throughout the entire cycle, deterioration is taken into account, and inventory is categorized into undecayed and decayed portions over different phases. A discount is applied to the un-decayed inventory during production run, which influences holding and decay costs. The aim is to develop a profit function in terms of quantity that incorporates these factors and optimize inventory policies. Analytical expressions for total cost and profit are derived. The results offer practical insights for improving profitability in inventory systems with perishable items under the given assumptions. Some numerical illustrations are derived and few tables and graphs are constructed in order to better representation of the results. Sensitivity analysis is performed in order to exhibit the model’s relevance to real-world situations, especially in controlling and managing perishable goods.