# SOLVING PURE INTEGER PROGRAMMING PROBLEMS WITHOUT USING GOMORIAN CONSTRAINT BY USING CMI METHOD

#### Authors:

S. Cynthiya Margaret Indrani,N.Srinivasan,

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.08.00043

#### Keywords:

CMI Method,LPP,IPP,Optimal Solution,Reduction technique,

#### Abstract

The objective of this paper is to solve pure integer programming problems without using Gomorian constraints. In this, CMI method is used for solving linear programming problems instead of simplex method. In CMI method, there is no need to calculate net evaluations, which is essential and mandatory in pre-existing methods. By discarding the calculation of net evaluations, the iterations in the procedure gets reduced or remains atmost equal in number. After getting a non-integer value in final CMI table, here we use a reduction technique instead of adding Gomorian constraint to get the integer solution directly.The main advantage of using this reduction technique is to avoid using, any additional constraints and the Dual simplex method for getting an integer solution. With the elimination of the above processes, the integer solutions are arrived very easily. Hence this new approachof pure integer programming problemensures time conservation at various levels in deriving the optimal solutions.  This proposed method is illustrated withexamples.

#### Refference:

I G.B. Dantzig, Maximization of linear function of variables subject to linear inequalities Koop man cowls commission Monograph, 1951).

II Handy A.Taha: ‘Operations Research An Introduction’ 8th edition by Pearson Publication.

III Kalpana Lokhande; Pranay.Khobragade and .W. Khobragade: Alternative approach to simplex method, International journal of engineering and innovative Technology, volume 4, Issue 6, pg: 123-127.

IV P.Pandian and M.Jayalakshmi: A new approach for solving a class of pure integer linear programming problems, International journal of advanced engineering technology.

V S.Cynthiya Margaret Indrani and Dr.N.Srinivasan: ‘CMI –M Technique for the solution of linear Programming problem,’ International Journal of Research and Analytical Reviews, October 2018, Volume-5, Issue-4.Pg-76-82ded.

VI S.Cynthiya Margaret Indrani and Dr.N.Srinivasan: ‘CMI Method for the solution of linear formulating problem’, Journal of Emerging Technologies and Innovative Research, September 2018, Volume 5, Issue 9, Pg. 248-253.