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Volume 2, Issue 5, October 2013, Page: 162-168
A Decomposable Computer Oriented Method for Solving Interval LP Problems
Sharmin Afroz, Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
M. Babul Hasan, Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
Received: Sep. 26, 2013;       Published: Oct. 30, 2013
DOI: 10.11648/j.pamj.20130205.13      View  3530      Downloads  121
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.
Keywords
LP, ILP, DILP Computer Program
To cite this article
Sharmin Afroz, M. Babul Hasan, A Decomposable Computer Oriented Method for Solving Interval LP Problems, Pure and Applied Mathematics Journal. Vol. 2, No. 5, 2013, pp. 162-168. doi: 10.11648/j.pamj.20130205.13
Reference
[1]
Ravindran, Philips & Solberg (2000), "Operations Research", John Wiley and Sons, Second Edition, New York, U.S.A.
[2]
Ganesh Chandra Ray, D., Md. Elias Hossain (2008), "Linear Programming," 3rd edition, Titas Publications, Dhaka-1100.
[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.
[4]
Ben-Isreal, A. and P.D. Robers (1970), " A Decomposable Method for Interval Linear Programming ", Management Science, Vol. 16, No.5, pp. 374-387.
[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.
[14]
Sanders, J.L. (1965), " A Nonlinear Decomposable Principle ", Operation Research, Vol. 13, No.2, pp. 266-271.
[15]
Rober P. D. and A. Ben-Isreal (1970) , " A Suboptimization Method or Interval Linear Programming: A New Method for Linear Programming", Linear Algebra and Its Applications 3, pp. 383-405.
[16]
Gunn E. A. and G. J. Anders (1981), "A Comparison of Interval Linear Programming with Simplex Method", Linear Algebra And Its Applications, 38, pp. 149-159.
[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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