Linear Programming Optimization on Microcomputers

Abstract

ABSTRACT A common type of mathematical optimization is Linear Programming (LP). An LP solution of aquifer influence functions has recently been reported by Gadjica, etal.1 (1987) and Targac, etal.2 Their LP matrices were large and sparse (only 3% of the elements were non-zero) and were solved on main frame computers. Another recent application of LP is equation-of-state matching of laboratory PVT data3. This problem leads to a smaller, denser LP matrix. Three methods of LP solution were investigated on microcomputers: (1) the simplex method, (2) the revised simplex method, and (3) the symmetric method. These methods were run on several LP problems ranging from a small dense matrix to large sparse matrices. The different methods have different characteristics which affect the speed, storage requirements and simplicity of coding. The simplex method is straightforward, but usually is slower and requires more storage than the other methods. The results of this study are tabulated with running times and storage requirements for the various LP methods and microcomputers. The computers range from the IBM XT to the Compaq 386. This information serves as a documentation of the LP codes and should be useful for an engineer interested in using LP codes on a microcomputer.