MOPS-Mathematical OPtimization System

This paper discusses a software system for solving large scale linear and mixed-integer optimization models. The system in its present form is the result of several years of research and development. The first functional version of MOPS was completed in 1987 for the IBM 6150 (a predecessor of the RS/6000) under AIX. A benchmark model from the Petroleum industry with 5563 rows and 6181 columns was solved with MOPS in 5 hours. The newest version solves this model in 6.51 minutes on a MS-DOS PC with i80486 processor (25Mhz). This paper discusses only LP optimization. The MIP optimizer in MOPS is a prototype version which will undergo major changes in the future. The paper describes algorithmic aspects, implementation issues and numerical results on Netlib and other real-life LP models. Sophisticated LP optimizers-although simple from a mathematical point of view-are algorithmically very complex. The discussion is therefore limited to a few fundamental issues that the paper feels are important.