The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems
Pure and Applied Mathematics Journal
Volume 5, Issue 1, February 2016, Pages: 1-8
Received: Sep. 20, 2015;
Accepted: Oct. 27, 2015;
Published: Jan. 25, 2016
Views 4632 Downloads 156
Geleta Tadele Mohammed, Department of Mathematics, Addis Ababa University, College of Computational and Natural Science, School of Graduate Studies, Addis Ababa, Ethiopia
Birhanu Guta Hordofa, Department of Mathematics, Addis Ababa University, College of Computational and Natural Science, School of Graduate Studies, Addis Ababa, Ethiopia
Most of real world decision making problems have multiple objectives, which cannot be optimized simultaneously due to the conflicting nature of the objectives. Such problems can be solved by various methods to obtain the best-compromise solutions. Modified Sequential Linear Goal Programming (MSLGP) method can be used to solve Multiple Objective Linear programming Problems. In this paper, the use of existing single objective Linear Programming (LP) techniques is there, and the information required for MSLGP in each iteration are taken from the previous iteration. In this study, there is a great Revised Multi-phase Simplex Algorithm, which is used to solve MSLGP Accordingly within small number of computations as much as possible. This method is illustrated by some numerical examples, and provides ‘best compromise’ solution.
Geleta Tadele Mohammed,
Birhanu Guta Hordofa,
The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems, Pure and Applied Mathematics Journal.
Vol. 5, No. 1,
2016, pp. 1-8.
A. Charnes, W. W. Cooper, J. Harrald, K. Karwana and W. Wallace, A goal inter val programming model for resource allocation in a marine environment protection problem, Journal of Envir. Econ. Mgmt., Vol. 3 (1976), pp. 347−362.
J. P. Ignizio, Linear Programming in Single and Multiple Objective Systems, Prentice−Hall, Englewood Chiffs, New Jersey, 1982.
J. P. Ignizio, Multi-objective mathematical programming via the MULTIPLEX model and algorithm, European Journal of Operational Research, Vol. 22 (1985), pp. 338346.
J. P. Ignizio, Introduction to Linear Goal Programming, Severely Hills, CA, Saga, 1972..J. P. Ignizio, Adaptive Antenna Array Study, Boeing Company, RWA− 5557, 1966.  S. M. Lee, Goal Programming for Decision Analysis, Auerback, Philadelphia, 1972.
C. Romero, M. Tamiz and D. F. Jones, Goal programming, compromise programming and reference point method formulations: linkages and utility interpretation, Journal of Operational Research Society, Vol. 49 (1998), pp. 986−991.
C. Romero, Extended lexicograpic goal programming: a unifying approach, Omega, Vol. 29 (2001), pp. 63−71.
M. Tamiz, D. F. Jones and E. El−Darzi, A review of goal programming package and its applications, Annals of Operations Research, Vol. 58 (1995), pp. 39−53.
M. Tamiz, D. F. Jones and C. Romero, Goal programming for decision making: an overview of the current state-of-the-art, European Journal of Operational Research, Vol. 111 (1998), pp. 569−58.
M. P. Biswal and Srikumar Acharya (2008) Some modifications on sequential linear goal programming, Journal of Interdisciplinary Mathematics, 11:3, 415−427.
S. Acharya, ∗ S. Nanda and B.B. Mishra Solving Multi-Choice Linear Goal Programming problem with preemptive priorities.