Linear plus fractional multiobjective programming problem with homogeneous constraints using fuzzy approach

We develop an algorithm for the solution of multiobjective linear plus fractionalprogramming problem (MOL+FPP) when some of the constraints are homogeneous innature. Using homogeneous constraints, first we construct a transformation matrix Twhich transforms the given problem into another MOL+FPP with fewer constraints. Then,a relationship between these two problems, ensuring that the solution of the originalproblem can be recovered from the solution of the transformed problem, is established.We repeat this process of transformation until all the homogeneous constraints areremoved. Then, we discuss the multi objective programming part, for which fuzzyprogramming methodology is proposed which works for the minimization of perpendiculardistances between two hyper planes (curves) at the optimal points of the objectivefunctions. A suitable membership function is defined with the help of the supremumperpendicular distance. A compromised optimal solution is obtained as a result of theminimization of the The supremum perpendicular distance. The corresponding optimalsolution to the original problem is obtained using the transformation matrix. Finally, anexample is given to illustrate the proposed model.