Effect of Optimization Tool Approach on Linear Programming Methods to Optimize Mathematical Manipulation
Citation
MLA Style: Mrs. Yogita D. Shahakar , Mr. Deepak A.. Shahakar"Effect of Optimization Tool Approach on Linear Programming Methods to Optimize Mathematical Manipulation" International Journal of Engineering Trends and Technology 67.8 (2019): 53-58.
APA Style:Mrs. Yogita D. Shahakar , Mr. Deepak A.. Shahakar. Effect of Optimization Tool Approach on Linear Programming Methods to Optimize Mathematical ManipulationInternational Journal of Engineering Trends and Technology, 67(8), 53-58.
Abstract
The main target of this work is based on the effect of optimization tools on linear programming methods to optimize the mathematical calculations. Linear programming plays an important role in our lives. There are various methods to solve LPP, such as simplex, dual-simplex, Big-M , two phase and graphical method. In this, an approach is presented to solve LPP by considering the optimization tool of MATLAB and compare it with tabular methods of LPP. The complexity reduction is done by eliminating the large number of steps. By using proposed technique, the calculation part has been completely avoided and we can achieve the results in considerable duration. The objective function of linear programming problem (LPP) involves in the maximization and minimization problem with the set of linear equalities and inequalities constraints. By using optimization tool in MATLAB used for LPP, reduced to form of Linear programming (LP) problem. So practically, for large number of constraints & variables, it is not possible to solve these problems by tabular method.. It takes more computation time & iterations.. By using proposed technique, we can achieve the results in considerable duration & exact optimum solution.
Reference
[1] Nikolaos Ploskas & Nikolaos Samaeas “Linear Programming Using MATLAB (Springer Optimization & its applications)” 1st edition 2017.
[2] Singereshu S. Rao, “Engineering Applications: Theory & Practice”, Fourth Edition ,John Wiley & Sons.
[3] D.S. Hira. and P.K. Gupta. Operations research, Seventh revised Edition 2014. ISBN: 81-219-0281-9 .
[4] Taha, H. A. , “ Operations Research An Introduction ” , Macmillan publishing co., Inc. United States , 1982..
[5] E.R. Barnes, A Variation on Karmarkar`s Algorithm for Solving Linear Programming problems, Mathematical Programming 36, 1986, p. 174-182 .
[6] Hillier, Frederick S and Lieberman, Gerald. Introduction to Operations Research. 2005. Boston: McGraw-Hill. ISBN: 0-07-123828-X.
[7] Barnes,J, W, and R.M. Crisp, “Linear Programming: A Survey of General Purpose Algorithms,”AIIE Transactions,
[8] Namrata Tripathi & Namita Shrivastav “Optimization problem solved by different platform say optimum toolbox (MATLAB) & Excel solver” International Research Journal of Engineering & Technology. vol 4 , issue 9 sep 2017 .
[9] Optimization in Practice with MATLAB, Achille Messle.
[10] D. Gay, A Variant of Karmarkar`s Linear Programming Algorithm for Problems in Standard form, Mathematical Programming 37 (1987) 81-90
[11] E.D. Anderson and K.D. Anderson. Presolving in Linear Programming, Mathematical Programming, 71 (1995), pp. 221-245.
[12] Charles Copper & Henderson,1963, An Introduction to Linear programming, John Willy,New York.
[13] Optimization Toolbox™ 4 User’s Guide.
[14] Cesar Parez Lopez “MATLAB Optimization Technique: Springer.
Keywords
Linear programming problem, optimization tools, optimal solution, Tabular Method.