Solution of Generalized Fuzzy Assignment Problem with Restriction on Costs under Fuzzy Environment

To solve the problems of Engineering and Management Science Generalized Assignment Problem (GAP) plays a very important role. The GAP is a classical example of a difficult combinatorial optimization problem that has received considerable attention over the years due to its widespread applications. In many instances it appears as a substructure in more complicated models, including routing problems, facility location models, knapsack problems, computer networking applications etc. Recently, Fuzzy Generalized Assignment Problem (FGAP) became very popular because in real life, data may not be known with certainty. So, to consider uncertainty in real life situations fuzzy data instead of crisp data is more advantageous. In this paper, cost for assigning the j-th job to the i-th person is taken as triangular fuzzy numbers. Further we have put a restriction on the total available cost which makes the problem more realistic and general. The problem is solved by modified Fuzzy Extremum Difference Method (FEDM) for initial Basic Feasible Solution (BFS) and to test the optimality Modified Distribution Method (MODI) method is used. The same fuzzy problem has been transformed into crisp one using Yager’s Ranking Method [17] and has been solved by EDM [9] for initial BFS and then for optimal solution LINGO 9.0 is used.