A Decomposable Computer Oriented Method for Solving Interval LP Problems

Sharmin Afroz; M. Babul Hasan

doi:doi:10.11648/j.pamj.20130205.13

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A Decomposable Computer Oriented Method for Solving Interval LP Problems

Sharmin Afroz, M. Babul Hasan

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 5)

Received: 26 September 2013 Accepted: Published: 30 October 2013

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Abstract

The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 5)
DOI	10.11648/j.pamj.20130205.13
Page(s)	162-168
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), 2024. Published by Science Publishing Group

Keywords

LP, ILP, DILP Computer Program

References

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[3]	Charners, A. Frieda Granot and F. Philips (1977), " An Algorithm for Solving Interval Linear Programming Problems ", Operation Research, Vol. 25, No.4, pp. 688-695.
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[5]	Dantzig, G.B. and P. Wolfe (1961), "The Decomposition Algorithm for Linear Programming", Econometrica, Vol. 29, No.4.
[6]	Sweeny, D.J. and R.A. Murphy (1979), "A Method of Decomposition for Integer Programs", Operations Research, Vol. 27, No.6, pp. 1128-1141.
[7]	Hasan, M.B. and J.F. Raffensperger (2007), "A Decomposition Based Pricing Model for Solving a Large-Scale MILP Model for an Integrated Fishery", Hindawi Publishing Corporation, Journal of Applied Mathematics and Decision Sciences, Vol. 2007, Article ID 56404, 10 pages.
[8]	Winston, W.L. (1994), "Linear Programming:Applications and Algorithm", Duxbury press, Belmont, California, U.S.A.
[9]	Dantzig, G.B. (1963), "Linear Programming and Extensions", Princeton University Press, Princeton, U.S.A..
[10]	A B M Rezaul Karim, B M Ikramul Haque, Anisur Rahman & Muhammad Mofisur Rahman (2006), "Linear Programming", First Edition
[11]	Robert Fourer, David M.Gay & Brian W.Kernighan, "A Modeling Language for Mathematical Programming", Secondt Edition.
[12]	Don, E. (2000), "Theory and Problems of Mathematica", Schaum’s Outline Series, Mc. GRAW-HILL
[13]	Zangwill, W.i. (1967), " A Decomposable Non- Linear Programming Approach", Operations Research, Vol. 15, No.6, pp. 1068-1087.
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[17]	Oliver Aberth (1997), " The Solution of Linear Interval Equations by a Linear Programming Method", Linear Algebra and Its Applications 259,pp. 271-279.
[18]	Radimir Viher (2003), " Interval Method for Interval Linear Program", Mathematical Communications 8, pp. 23-33.
[19]	Nakahara Y., M. Sasaki and M. Gen (1992), " On the Linear Programming Problems withInterval Coefficients", Computer and Industrial Engineering, Vol. 23, pp. 301-304.

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APA Style

Sharmin Afroz, M. Babul Hasan. (2013). A Decomposable Computer Oriented Method for Solving Interval LP Problems. Pure and Applied Mathematics Journal, 2(5), 162-168. https://doi.org/10.11648/j.pamj.20130205.13

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ACS Style

Sharmin Afroz; M. Babul Hasan. A Decomposable Computer Oriented Method for Solving Interval LP Problems. Pure Appl. Math. J. 2013, 2(5), 162-168. doi: 10.11648/j.pamj.20130205.13

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AMA Style

Sharmin Afroz, M. Babul Hasan. A Decomposable Computer Oriented Method for Solving Interval LP Problems. Pure Appl Math J. 2013;2(5):162-168. doi: 10.11648/j.pamj.20130205.13

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@article{10.11648/j.pamj.20130205.13,
  author = {Sharmin Afroz and M. Babul Hasan},
  title = {A Decomposable Computer Oriented Method for Solving Interval LP Problems},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {5},
  pages = {162-168},
  doi = {10.11648/j.pamj.20130205.13},
  url = {https://doi.org/10.11648/j.pamj.20130205.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130205.13},
  abstract = {The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.},
 year = {2013}
}

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TY  - JOUR
T1  - A Decomposable Computer Oriented Method for Solving Interval LP Problems
AU  - Sharmin Afroz
AU  - M. Babul Hasan
Y1  - 2013/10/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130205.13
DO  - 10.11648/j.pamj.20130205.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 162
EP  - 168
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130205.13
AB  - The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.
VL  - 2
IS  - 5
ER  -

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Author Information

Sharmin Afroz

Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
M. Babul Hasan

Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh

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APA Style

Sharmin Afroz, M. Babul Hasan. (2013). A Decomposable Computer Oriented Method for Solving Interval LP Problems. Pure and Applied Mathematics Journal, 2(5), 162-168. https://doi.org/10.11648/j.pamj.20130205.13

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ACS Style

Sharmin Afroz; M. Babul Hasan. A Decomposable Computer Oriented Method for Solving Interval LP Problems. Pure Appl. Math. J. 2013, 2(5), 162-168. doi: 10.11648/j.pamj.20130205.13

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AMA Style

Sharmin Afroz, M. Babul Hasan. A Decomposable Computer Oriented Method for Solving Interval LP Problems. Pure Appl Math J. 2013;2(5):162-168. doi: 10.11648/j.pamj.20130205.13

Copy | Download

@article{10.11648/j.pamj.20130205.13,
  author = {Sharmin Afroz and M. Babul Hasan},
  title = {A Decomposable Computer Oriented Method for Solving Interval LP Problems},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {5},
  pages = {162-168},
  doi = {10.11648/j.pamj.20130205.13},
  url = {https://doi.org/10.11648/j.pamj.20130205.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130205.13},
  abstract = {The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - A Decomposable Computer Oriented Method for Solving Interval LP Problems
AU  - Sharmin Afroz
AU  - M. Babul Hasan
Y1  - 2013/10/30
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130205.13
DO  - 10.11648/j.pamj.20130205.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 162
EP  - 168
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130205.13
AB  - The purpose of this paper is to develop a computer oriented decomposition program for solving Interval Linear Programming (ILP) Problems. For this, we first analyze the existing methods for solving ILP problems. We also discuss the main stricter of Decomposable Interval programming (DIP) problems. Then a decomposable algorithm is analyzed for solving DIP problems. Using “Mathematica”, we develop a computer oriented program for solving such problems. We present step by step illustration of a numerical example to demonstrate our technique.
VL  - 2
IS  - 5
ER  -

Copy | Download