In this paper, we develop two Economic Order Quantity (EOQ) models for quadratic time-varying demand. It is assumed that successive replenishment cycle lengths are in arithmetic progression and γ the rate of reduction of successive cycle lengths. The model with shortages is studied first. The corresponding results for the model without shortages are derived next. Decision variables are determined numerically for given input parameters. Optimum costs for both the models are also calculated. Computational results show that the model with shortages allowed is economically beneficial. Finally, sensitivity analysis is performed to study the effect of changes in input parameters on the optimal cost.