Asian Journal of Pure and Applied Mathematics

This study develops a fuzzy inventory model for a single deteriorating item under quartic time-dependent demand and a two-parameter Weibull deterioration process, assuming zero lead time, instantaneous replenishment, and no shortages. Uncertainty in the demand and deterioration parameters is represented through triangular fuzzy numbers. The corresponding α-cut formulation yields lower and upper inventory systems governed by nonlinear time-dependent differential equations. Because the interaction between quartic demand and Weibull deterioration does not provide a convenient closed-form solution, the fourth-order Runge–Kutta method is employed to obtain numerical inventory trajectories over the replenishment cycle. The resulting holding, purchasing, ordering, and deterioration costs are evaluated from the numerical solutions, and the Graded Mean Integration Representation method is used to defuzzify the fuzzy total and average inventory costs. Numerical examples are considered for both non-fuzzy and fuzzy cases, and a one-at-a-time sensitivity analysis is performed by varying selected demand, deterioration, and cost parameters by ±20% while holding the remaining parameters constant. The results indicate that the optimal cycle length and inventory costs respond more strongly to changes in selected demand and cost parameters than to changes in the Weibull deterioration parameters within the ranges examined. The model therefore provides a numerical framework for analysing replenishment and cost decisions when demand and deterioration parameters are imprecisely specified.