A DETERMINISTIC INVENTORY MODEL WITH QUARTIC DEMAND AND EXPONENTIALLY DISTRIBUTED DETERIORATION RATE UNDER SHORTAGES

Abstract

This study formulates a deterministic inventory model for perishable items under a quartic time-dependent demand function and exponentially distributed deterioration. Complete backlogging of shortages is assumed within each replenishment cycle. The inventory dynamics are represented by differential equations over the positive stock and shortage intervals, and closed-form expressions are obtained using appropriate boundary conditions. The Total Inventory Cost (TIC) per unit time is derived and optimized through first-order optimality conditions to determine the optimal cycle length and shortage duration.Numerical experiments are conducted to verify the analytical results, and graphical analysis confirms the convexity and stability of the cost structure. Sensitivity analysis shows that demand coefficients and principal cost parameters significantly affect the optimal solution, whereas deterioration parameters exert comparatively minor influence. Two structural extensions incorporating variable holding cost and variable ordering cost further demonstrate the adaptability and robustness of the proposed framework for managing time-sensitive and deteriorating inventories.