Compound sets in mathematical programming modeling languages

This paper presents a series of simple but realistic examples in which common algebraic indexing conventions are not so convenient. In particular, it analyzes the difficulties caused by the conventions that each model component must have a fixed number of indices and that the order of the indices is significant to their meaning. To deal with these difficulties compensating extensions to algebraic notation are proposed. The proposed notation is compared to existing notation in terms of the human abilities to understand, maintain and verify model descriptions.