Mathematical Theory and Modeling www.iiste.org ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online) Vol.3, No.13, 2013 9 Comparisons of Linear Goal Programming Algorithms U.C. Orumie 1 , D.W Ebong 2 1 Department of Mathematics/Statistics, University of Port-Harcourt, Nigeria. 2 Department of Mathematics/Statistics, University of Port-Harcourt, Nigeria amakaorumie@yahoo.com & daniel.ebong@uniport.edu.ng ABSTRACT: Lack of an efficient algorithm capable of reaching a compromised solution within a reasonable time is a major setback in the use of goal programming. Orumie and Ebong newly developed an alternative method of solving goal programming problem utilizing modified simplex procedures. This algorithm is compared in terms of accuracy and time requirements with existing algorithms by Lee and by Ignizio. Computational times for 10 goal programming models of various sizes are presented. Number of iteration per problem, total entries per problems is used as benchmark for the comparisons. The new method by Orumie and Ebong (2011) have better computational times in all the problem solution and proved the best since there is a reduction in computational time in all the problems solved. Keywords: Goal Programming, Lee’s modified simplex, Ignizio’s Sequential, Orumie and Ebong method 1. INTRODUCTION Goal programming (GP) technique was initially developed by Charnes and Cooper (1961) for linear system in which conflicting goals were included as constraints. Their goal programming models are restricted to only those utilizing a single objective priority. The model is thus; . ) . . . 2 , 1 ( , ) ( min 1 m i b d d x a that such d d p z lexi i i i j ij i i = = - + + = + - + - . Further development took place by Ijiri (1965) who defined a preemptive priority levels to handle goals in their order of importance. The objective function represents the sum of disutilities for a particular program, and it is this weighted sum which is minimized to give the optimal solution. Lee (1972) and Ignizio (1976) brought the technique into common usage as an operational research tool. Goal programming quickly rose to become the most popular technique within the field of multi-criteria decision making (MCDM). This led to large number of applications being reported in the literature from the mid-1970 onwards. Ignizio (1978) described Lee (1972) and Ignizio (1976) approaches as a significant improvement over the sequential simplex technique, since it requires fewer pivots (in general) and eliminates the need for the construction of new constraints at each sequence. Authur and Ravindran (1978) described Lee (1972) as the widely used goal programming algorithm whereas Schniederjans and kwaks (1982) echoed that Lee (1972) and Ignizio (1976) are the most commonly used goal programming solution methods, , but that both methods require columns in the simplex tableau for positive and negative deviational variables. Both methods require separate objective function rows for each priority level, all of which add immensely to the computational time of their solution method. Ignizio (1976) developed a GP solution approach known as multiphase (linear) GP method that