Asian Research Journal of Mathematics

This study develops a single-item, continuous-review economic order quantity (EOQ) model for a deteriorating product with a demand rate that varies linearly over time. The deterioration rate is represented as a triangular fuzzy number to reflect epistemic uncertainty arising from limited observations or expert judgement. The inventory-depletion differential equation is solved in exact closed form, yielding analytical expressions for the inventory level, order quantity, holding-cost integral, and quantity lost through deterioration. A structural identity is established showing that the deteriorated quantity equals the deterioration rate multiplied by the holding-cost integral, which reduces the total-cost function to a compact form. The fuzzy total cost is defuzzified using the α-cut and signed-distance method to obtain a crisp equivalent cost function. A closed-form second-derivative analysis, together with a generalised-convexity ratio argument, establishes strict pseudo-convexity of the defuzzified cost with respect to cycle length and therefore a unique global optimum. Three numerical illustrations demonstrate the solution procedure, while the sensitivity analysis examines the effects of demand, cost, deterioration, and fuzzy-spread parameters on the optimal policy. The results indicate that the minimum cost is most responsive to the initial demand rate and ordering cost, whereas changes in the demand growth rate, deterioration cost, modal deterioration rate, and fuzzy spread have comparatively smaller effects. The model provides an analytically tractable replenishment framework for deteriorating items under imprecise deterioration information.