DESIGN AND IMPLEMENTATION OF AUTOMATED SOFTWARE FOR THE PUSH AND PULL METHOD OF SOLVING LINEAR PROGRAMMING PROBLEMS

ABSTRACT

This research work focused on solving Linear Programming Problems with the objective of identifying and reducing the computational complexities or complications involved in solving these problems. In this work, we presented two algorithms; the Standard Simplex method and a newer solution algorithm called Push and Push algorithm. The Simplex method has been one of the oldest and the best methods for efficiently solving Linear Programming (LP) problems until recently. In this work, a manual and computerized comparison for the Simplex algorithm and the Push and Pull algorithm has been achieved. We presented an automated software for the Simplex and the Push and Pull algorithms for solving a wide range of Linear Programming problems, in which the computational comparison of the two methods was carried out. The software was developed using Visual Basic 6.0 on a Visual Studio .NET Framework 3.5 and on a Windows Vista operating system. This research work was carried out using the theoretical methodology. The software was designed using an algorithm called, Algorithm Implementation Modules. In the course of this work, we found out that for LP Problems with ≤ constraints (Maximization cases), the computational complexity slightly differed, though the Push and Pull method still exhibits less number of computations, while for LP Problems with  constraints (Minimization cases), the computational complexity greatly differed; with the Push and Pull method having much lesser number of computations. We, therefore, concluded that the Push and Pull method is a preferable alternative to the Simplex method in solving LP problems.