A solution approach for a multi-objective fuzzy generalized assignment problem

Abstract

We consider a multi-objective generalized assignment problem in which the costs are fuzzy numbers. The generalized assignment problem has gained its significance in the fuzzy environment. We have represented the fuzzy numbers in their parametric form and then solved it through ones assignment method. To the best of our knowledge, most of the authors have obtained the solution by converting the problem to its crisp form. We have recommended an algorithm where we have used the ranking method and arithmetic operations to obtain a desirable solution without converting to an equivalent crisp form. The solution we acquired is represented in terms of location index and fuzziness index functions which enables the decision maker to decide his/her preference of solution. An example is given to explain the proposed methodology.