Fuzzy generalized assignment problem with credibility constraints

In this paper, we firstly discuss some properties with respect to the credibility constraints. After that, we construct a new class of fuzzy generalized assignment problem with credibility constraints, in which the cost and time are uncertain and assumed to be characterized by fuzzy variables with known possibility distributions. The problem is a very changeable combinational optimization and it is always different to solve the programming problems using the classical algorithms. In some special cases, we can transform the objective and the credibility constraints into the equivalent linear form by means of the results that we deduce. As a consequence, we can solve it with standard software. Finally, we present one application example encountered by the Canadian Department of Transportation to demonstrate the proposed method.