Computational experiments in the formulation of linear product-mix and non-convex production-investment models

Mathematical programming problems often contain many “balance equations”. It is possible to transform a given formulation by the elimination of balance equations; these eliminations generate different formulations which are equivalent in the sense that the same optimum can be derived from them. Some equivalent formulations for product-mix decisions were generated and solved by using APEX-III, CDC's commercial package for mathematical programming. The results show that for today's powerful software one should not trust mathematical programming folklore which states that CPU-time rises roughly in proportion to the cube of the number of constraints; a far better explanation of computational effort is possible by taking the number of constraints as well as the number of nonzeros into account.