One machine scheduling problem with fuzzy random due-dates

In many classical or basic scheduling models, jobs' processing times and due-dates are crisp values. Recently, they have been formulated as uncertain values in some more actual models. That is the introduction of "fuzziness". However, in a real situation of decision making, there exists uncertainty that can not be described only by fuzziness. In this paper, we propose an n-job, one machine scheduling model, where due-dates for jobs are fuzzy random variables. In the model, jobs' processing times are crisp, and we assign satisfaction levels to jobs' completion times according to membership functions. They are non-increasing functions, but their support positions depend upon the expected due-dates, which are exponentially distributed random variables.