An inventory model for two-parameter Weibull deteriorating items with quartic demand and no shortages

This paper develops an inventory model for deteriorating items in which the deterioration rate follows a two-parameter Weibull distribution. The demand rate is assumed to be a quartic function of time, making the model more flexible and better suited to modern supply chain environments. The model assumes that shortages are not permitted and that all demand is satisfied instantaneously. The quartic demand function captures different phases of demand behaviour, including initial growth, accelerated growth due to promotional activities, demand saturation, and a subsequent decline in growth. The objective of the study is to minimize the total inventory cost and to investigate the effects of the demand coefficients and Weibull parameters on the optimal cost. Owing to the quartic demand structure and the nonlinear time-dependent deterioration rate, a closed-form analytical solution cannot be obtained. To address this limitation, the fourth-order Runge–Kutta method is employed to solve the resulting nonlinear differential equations. This numerical approach provides an efficient, stable, and accurate solution framework and offers sufficient flexibility for sensitivity analysis and practical implementation. A numerical example illustrates the model’s applicability. The total inventory cost, cycle length, and average cost are computed using Python, and a sensitivity analysis is performed to examine the effects of the demand coefficients and Weibull parameters on the optimal solution and various inventory cost components.