The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems

Geleta Tadele Mohammed; Birhanu Guta Hordofa

doi:doi:10.11648/j.pamj.20160501.11

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The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems

Geleta Tadele Mohammed, Birhanu Guta Hordofa

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 1)

Received: 20 September 2015 Accepted: 27 October 2015 Published: 25 January 2016

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Abstract

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.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 1)
DOI	10.11648/j.pamj.20160501.11
Page(s)	1-8
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Multiple Objectives Linear Programming, Modified Sequential Linear Goal Programming, Revised Multi-Phase Simplex Algorithm for MSLGP Algorithm

References

[1]	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.
[2]	J. P. Ignizio, Linear Programming in Single and Multiple Objective Systems, Prentice−Hall, Englewood Chiffs, New Jersey, 1982.
[3]	J. P. Ignizio, Multi-objective mathematical programming via the MULTIPLEX model and algorithm, European Journal of Operational Research, Vol. 22 (1985), pp. 338346.
[4]	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. [6] S. M. Lee, Goal Programming for Decision Analysis, Auerback, Philadelphia, 1972.
[5]	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.
[6]	C. Romero, Extended lexicograpic goal programming: a unifying approach, Omega, Vol. 29 (2001), pp. 63−71.
[7]	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.
[8]	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.
[9]	M. P. Biswal and Srikumar Acharya (2008) Some modifications on sequential linear goal programming, Journal of Interdisciplinary Mathematics, 11:3, 415−427.
[10]	S. Acharya, ∗ S. Nanda and B.B. Mishra Solving Multi-Choice Linear Goal Programming problem with preemptive priorities.

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APA Style

Geleta Tadele Mohammed, Birhanu Guta Hordofa. (2016). The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems. Pure and Applied Mathematics Journal, 5(1), 1-8. https://doi.org/10.11648/j.pamj.20160501.11

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ACS Style

Geleta Tadele Mohammed; Birhanu Guta Hordofa. The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems. Pure Appl. Math. J. 2016, 5(1), 1-8. doi: 10.11648/j.pamj.20160501.11

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AMA Style

Geleta Tadele Mohammed, Birhanu Guta Hordofa. The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems. Pure Appl Math J. 2016;5(1):1-8. doi: 10.11648/j.pamj.20160501.11

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@article{10.11648/j.pamj.20160501.11,
  author = {Geleta Tadele Mohammed and Birhanu Guta Hordofa},
  title = {The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.pamj.20160501.11},
  url = {https://doi.org/10.11648/j.pamj.20160501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.11},
  abstract = {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.},
 year = {2016}
}

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TY  - JOUR
T1  - The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems
AU  - Geleta Tadele Mohammed
AU  - Birhanu Guta Hordofa
Y1  - 2016/01/25
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160501.11
DO  - 10.11648/j.pamj.20160501.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160501.11
AB  - 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.
VL  - 5
IS  - 1
ER  -

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Author Information

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

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APA Style

Geleta Tadele Mohammed, Birhanu Guta Hordofa. (2016). The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems. Pure and Applied Mathematics Journal, 5(1), 1-8. https://doi.org/10.11648/j.pamj.20160501.11

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ACS Style

Geleta Tadele Mohammed; Birhanu Guta Hordofa. The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems. Pure Appl. Math. J. 2016, 5(1), 1-8. doi: 10.11648/j.pamj.20160501.11

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AMA Style

Geleta Tadele Mohammed, Birhanu Guta Hordofa. The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems. Pure Appl Math J. 2016;5(1):1-8. doi: 10.11648/j.pamj.20160501.11

Copy | Download

@article{10.11648/j.pamj.20160501.11,
  author = {Geleta Tadele Mohammed and Birhanu Guta Hordofa},
  title = {The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.pamj.20160501.11},
  url = {https://doi.org/10.11648/j.pamj.20160501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160501.11},
  abstract = {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.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - The Modified Sequential Linear Goal Programming Method for Solving Multiple Objectives Linear Programming Problems
AU  - Geleta Tadele Mohammed
AU  - Birhanu Guta Hordofa
Y1  - 2016/01/25
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160501.11
DO  - 10.11648/j.pamj.20160501.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160501.11
AB  - 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.
VL  - 5
IS  - 1
ER  -

Copy | Download