(A) signal flow graph metathod of goal programming

Abstract

Goal programming is a powerful technique for achieving multiple, conflicting objectives under a complex set of constraints. The mathematical formulation of a goal programming problem results in a large, sparse linear system and the simplex method has been the traditional approach to solution. This thesis presents an interactive method, which is a variation of signal flow graph method, for the solution of a goal programming problem. It differs from the usual graph theoretic methods, which are based on Gaussian elimination. By the development of a new technique, concerning searching method it significantly reduces the time involved in the evaluation of loops and paths under of the traditional graph theoretic approach. The computational efficiency of the signal flow graph over the simplex method and/or the graph theoretic approach depends on the problems involved and the ratio of addition vs multiplication time. The computational advantages of signal flow graph method over others are tabulated for various and set of factors-basic variables, non-basic variables, reduced cost vector resources. It indeed shows that the method developed in this thesis can be used for a wide range of problems with the noted computational edge. Due to the nature of the new algorithm, an interactive approach can be taken in solving a goal programming problem, which was difficult under the existing algorithms. The interactive approach does not concern it self with the minimization of iteration steps during the solution process but it deals with the uncertainty of priority factors and sensitivity analysis. Hence the new method not only achieves computational efficiency but also opens up new procedures for goal programming.