A decision maker will allocate his goods to appearing customers during the given periods. There are finite types of customers. Each type of customer appears with a given probability at the beginning of each period. When the customer appears, the decision maker sells some of his goods to acquire the expected reward which depends on the number of goods sold and the type of appearing customer. Unsold goods at the end of each period perish at the beginning of next period with some probability. The objective is to find a sequence of optimal number of goods to be sold which maximizes the total expected reward. Some properties of an optimal policy are investigated and some simple examples are presented.