W e consider a periodic-review perishable inventory system with multiple demand classes, each characterized by a different lost-sales cost and the least freshness requirement. Demands of different classes in the same period could be correlated, while demands across periods are independent but not necessarily identical. In each period, the firm jointly makes the decisions regarding demand fulfillment, production/ordering, and disposal. The objective is to minimize the total discounted expected cost over the entire planning horizon including linear ordering cost, inventory holding/lostsales cost, expiration cost, and disposal cost. By establishing new properties of multimodularity, we explore some monotonicity and bounded sensitivity properties of the optimal policies. The optimality analysis enables us to propose a novel approximation approach, called adaptive approximation approach, which can be recursively calculated through a singledimension dynamic program. Numerical studies demonstrate that our proposed approximation approach is nearly optimal with the average optimality gap 0.30% and significantly outperforms the existing heuristics in the literature.