On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems

Effanga Effanga Okon; Edwin Frank Nsien

doi:doi:10.11648/j.sjams.20190702.12

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On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems

Effanga Effanga Okon, Edwin Frank Nsien

Published in Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 2)

Received: 1 April 2019 Accepted: 23 May 2019 Published: 10 June 2019

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Abstract

Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 7, Issue 2)
DOI	10.11648/j.sjams.20190702.12
Page(s)	15-20
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), 2019. Published by Science Publishing Group

Keywords

Multi-objective, Single Objective, Linear Programming, Pareto Optimal Solution, Weight, Non-inferior Solution

References

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[3]	Khanjarpanah, H and Pishvaee, M. S (2017): A fuzzy robust programming approach to multi-objective portfolio optimization problem under uncertainty. International Journal of Operations Research. Inderscience Online, Vol. 12, Issue 1.
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[6]	Steuer, R. E. (1977). An interactive multi-objective linear programming procedure. TIMS Stud. Management Science, 6, 225–239.
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[8]	Korhonen, P. & Laakso, J. (1986). A visual interactive method for solving the multi-criteria problem. European Journal of Operations Research, 24, 277–287.
[9]	Gardiner, L. R. & Steuer, R. E. (1994). Unified interactive multi-objective programming. European Journal of Operations Research, 74, 391–406.
[10]	Stewart, J. (1999). Concepts of interactive programming. Advances in MCDM models, Algorithms. Theory and Applications, Kluwer Academic Publishers, Boston. 299 pp.
[11]	Branke, J; Deb, K; Miettinen, K. & Slowinsk (2008). Mult-objective optimization: Interactive and Evolutionary Approaches. Springer-verlag Bellin Heidenlbetg. 481 pp.
[12]	Sadrabadi, M. R. & Sadjadi, S. J. (2009). A new interactive method to solve multi- objective linear programming problems. J. Software Engineering & Application, 2, 23 –247.
[13]	De, P. K. & Yadav, B. (2011). An algorithm for obtaining optimal compromise solution of a mult-objective fuzzy linear programming problem. International Journal of Computer Application, 17, 20–24.
[14]	Augusto, O; Bennis, F., and Caro, S. (2012). A new method for decision making in multi-objective optimization problems. Pesquisa Operational, 32 (2): 331-339.
[15]	Zeleny, M. (1974). Linear Multi-objective Programming. Springer, berlin- Heidelberg- New York.
[16]	Trafalis, T. B., Mishina, T. and Foote, B. L. (1999). An interior point multi-objective programming approach for production planning with uncertain information. Computers and Industrial Engineering, 37, 631–648.
[17]	Eiselt, H. A; Pederzoli G. & Sandblom C. L. (1987): Continuous optimization models. Walter de Gruyter, New York.

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APA Style

Effanga Effanga Okon, Edwin Frank Nsien. (2019). On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems. Science Journal of Applied Mathematics and Statistics, 7(2), 15-20. https://doi.org/10.11648/j.sjams.20190702.12

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ACS Style

Effanga Effanga Okon; Edwin Frank Nsien. On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems. Sci. J. Appl. Math. Stat. 2019, 7(2), 15-20. doi: 10.11648/j.sjams.20190702.12

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AMA Style

Effanga Effanga Okon, Edwin Frank Nsien. On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems. Sci J Appl Math Stat. 2019;7(2):15-20. doi: 10.11648/j.sjams.20190702.12

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@article{10.11648/j.sjams.20190702.12,
  author = {Effanga Effanga Okon and Edwin Frank Nsien},
  title = {On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {2},
  pages = {15-20},
  doi = {10.11648/j.sjams.20190702.12},
  url = {https://doi.org/10.11648/j.sjams.20190702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190702.12},
  abstract = {Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.},
 year = {2019}
}

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TY  - JOUR
T1  - On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems
AU  - Effanga Effanga Okon
AU  - Edwin Frank Nsien
Y1  - 2019/06/10
PY  - 2019
N1  - https://doi.org/10.11648/j.sjams.20190702.12
DO  - 10.11648/j.sjams.20190702.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 15
EP  - 20
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20190702.12
AB  - Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.
VL  - 7
IS  - 2
ER  -

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Author Information

Effanga Effanga Okon

Department of Statistics, University of Calabar, Calabar, Cross River State, Nigeria
Edwin Frank Nsien

Department of Mathematics/Statistics, University of Uyo, Uyo, Akwa Ibom State, Nigeria

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APA Style

Effanga Effanga Okon, Edwin Frank Nsien. (2019). On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems. Science Journal of Applied Mathematics and Statistics, 7(2), 15-20. https://doi.org/10.11648/j.sjams.20190702.12

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ACS Style

Effanga Effanga Okon; Edwin Frank Nsien. On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems. Sci. J. Appl. Math. Stat. 2019, 7(2), 15-20. doi: 10.11648/j.sjams.20190702.12

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AMA Style

Effanga Effanga Okon, Edwin Frank Nsien. On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems. Sci J Appl Math Stat. 2019;7(2):15-20. doi: 10.11648/j.sjams.20190702.12

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@article{10.11648/j.sjams.20190702.12,
  author = {Effanga Effanga Okon and Edwin Frank Nsien},
  title = {On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {7},
  number = {2},
  pages = {15-20},
  doi = {10.11648/j.sjams.20190702.12},
  url = {https://doi.org/10.11648/j.sjams.20190702.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20190702.12},
  abstract = {Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On Technique for Generating Pareto Optimal Solutions of Multi-objective Linear Programming Problems
AU  - Effanga Effanga Okon
AU  - Edwin Frank Nsien
Y1  - 2019/06/10
PY  - 2019
N1  - https://doi.org/10.11648/j.sjams.20190702.12
DO  - 10.11648/j.sjams.20190702.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 15
EP  - 20
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20190702.12
AB  - Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.
VL  - 7
IS  - 2
ER  -

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