This is thesis concerned with the inventory has deteriorating item in aimed area as Republic of Yemen where the collected data from the study area includes the two types of deteriorating items as first the deteriorating item which it has only the deterioration character second one the item has two characters as deterioration and break-ability rates simultaneously, so that there are many inventory models both first and second especially when the inventory level, not equal zero before any replenishment, the important thing the proposed mathematical models for inventory are developed in a general way for any inventory satisfied the assumptions and conditions
