This paper presents a continuous EPQ model of deteriorating items with shortages. Also in this paper, an inventory policy for an item is presented with inflation and selling price dependent demand under deterministic and random planning horizons allowing shortages with an immediate part payment to the wholesaler. In this study inventory models under the finite and random planning horizons have been formulated with respect to the retailer’s point of view for maximum profit. The GRG method is used to find the optimal solutions and the corresponding maximum profits for the different sets of given numerical data.