A periodic review inventory model for deteriorating items in which time is treated as a discrete variable is developed. The model is developed under deterministic but time dependent demands and instantaneous delivery. Deterioration is assumed to be a constant fraction of the on hand inventory and partial returns are allowed for the deteriorated items. The solution procedures for obtaining the optimal order quantities which maximize the total profit in the scheduling period are presented for the cases of back orders and lost sales. Finally, when the additional orders are allowed, an efficient solution algorithm determining the initial and additional order quantities and additional ordering time is developed. Some numerical examples are also presented to illustrate the results.