[Biswas, 2(11): November, 2013] ISSN: 2277-9655 Impact Factor: 1.852 http: // www.ijesrt.com(C)International Journal of Engineering Sciences & Research Technology [3142-3145] IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Convexity in Linear Fractional Programming Problem Anita Biswas *1 , Smita Verma 2 *1 Assistant Professor, TRUBA College of Engineering & Technology, Indore, India 2 Assistant Professor, S.G.S. Institute of Technology & Science, Indore, India anitabiswas89@yahoo.com Abstract Linear programming is a mathematical programming technique to optimize performance under a set of resource constraints as specified by organization. Linear fractional programming is a generalization of linear programming. The objective functions in linear programs are linear functions while the objective function in a linear fractional program is a ratio of two linear functions. In his paper an attempt is made to solve the convexity in linear fractional programming problem by taking CCR model, which states that the collection of all feasible solution to CCR model constitutes a convex set whose extreme points correspond to the basic feasible solutions. Keywords: Fractional programming, CCR model, Convexity. Introduction Linear programming is a mathematical modeling technique designed to optimize the usage of limited resources. Successful application of linear programming exist in the areas of military, industry, agriculture, transportation, economics, health systems and even behavioral and social sciences[4], while a linear fractional programming (LFP) problem is one whose objective function has a numerator and a denominator. Several methods to solve this problem have been proposed so far [6]. Charnes and Kooper [1] have proposed a method which depends on transferring the LFP problem to an equivalent linear program. Linear Fractional Programming Hungarian mathematician Bela Martos formulated and considered a so called hyperbolic programming problem in the year 1960, which in the English language special literature is referred as linear fractional programming problems. In a typical case the common problem of LFP may be formulated as follows [3]: Given objective function  =   = ∑        ∑         where D(x)>0 Which must be maximized (or minimized) subject to ∑     ≤     , =1,2,3,………………………%  ∑     ≥    , =%  + 1, %  +2,…………………% ( ∑     =    ,  = % ( +1, % ( +2,………………….%   ≥ 0, + = 1,2, … … … … … … . . , A linear programming problem is said to be in general form if all constraints are ≤ (less than) inequalities and all unknown variables are non- negative, that is  =   = ∑        ∑         → Maximize (minimize) Subject to∑     ≤     , =1,2,3,………………………% - > 0, ∀01 Relationship with Linear programming It is obvious that if all 2  = 0, + = 1,2, … … … . , and 2 3 =1 then linear fractional programming problem becomes a linear programming problem. This is a reason why we say that a linear fractional programming problem is a generalization of an linear programming problem.