Most of the works about flowshop scheduling problems assume that the problem data are known exactly in advance or the common approach to the treatment of the uncertainties in the problem is the use of probabilistic models. However, the evaluation and optimization of the probabilistic model is computationally expensive and rational only when the descriptions of the uncertain parameters are available froth the historical data. In addition, as in many real-world situations, a certain amount of delay on due dates may be tolerated in most situations although they are handled as crisp dates in most of the previous papers. In this paper we deal with a flowshop scheduling problem with fuzzy processing times and flexible due dates. Schedules are generated by a proposed algorithm in the context of ant colony optimization metaheuristic approach. We use the necessity measure as a confidence measure with which the occurrence of the nontardy schedule can be guaranteed to be certain.