A study of Quadratic Programming with Fractional and Fuzzy Variables

Abstract

The main theme of this thesis is to solve the special types of quadratic programming newlineproblems in fuzzy environment. The special quadratic problems are those problems newlinewhich have Bilevel, Trilevel and Multilevel hierarchical decision makers. Here, we newlineused these Bilevel, Trilevel and Multilevel programming problems in such a way that newlineobjective function of each level is taken in the ratio form and this ratio also has numerator newlineand denominator as the quadratic function under the linear constraints. Such newlinetypes of problems are termed as the Bilevel, Trilevel and Multilevel quadratic fractional newlineprogramming problems. The various introductory terms and their literature work is newlineexplained in the first chapter of this thesis. newlineIn Chapter 2, we have solved a Bilevel Quadratic Fractional Programming newlineProblem through Fuzzy Goal Programming approach in a new way. Bilevel is a newlinespecial case of multilevel optimization hierarchy with two decision levels. First of all, newlinewe have constructed two Bilevel Quadratic Programming problems from one Bilevel newlineQuadratic Fractional Programming Problem by separating the numerator and denominator newlinein fractional objective function of each decision maker. Then, we have solved newlineboth Bilevel Quadratic Programming problems separately and thus constructed a solution newlineprocedure for given Bilevel Quadratic Fractional Programming Problem. newlineIn Chapter 3, we have formulated a Bi-level Quadratic Fractional programming newlineProblem related to supply and demand of a local industry and after that we newlinehave solved this formulated Bi-level Quadratic Fractional programming problem by using newlinea modified fuzzy goal programming approach. In this solution procedure while newlinemaking a fuzzy goal programming model for first level, membership functions of both newlinenumerators and denominators are inserted in that model and after finding a compromised newlinesolution, new membership functions are selected to be constrained in the fuzzy newlinegoal programming model for second level of hierarchy. This procedure is very helpful newlinein finding the cooperative solution f