Composite primary keys are what you want where you want to create a many to many relationship with a fact table. For example, you might have a holiday rental package that includes a number of properties in it. On the other hand, the property could also be available as a part of a number of rental packages, either on its own or with other properties. In this scenario, you establish the relationship between the property and the rental package with a property/package fact table. The association between a property and a package will be unique, you will only ever join using property_id with the property table and/or package_id with the package table. Each relationship is unique and an auto_increment key is redundant as it won't feature in any other table. Hence defining the composite key is the answer.