Job sequencing with uncertain and controllable processing times

In this paper, a single machine scheduling problem is considered. The jobs' processing times are controllable (i.e., they may take any value within a certain range) and non-precisely defined. They are treated as linguistic variables, whose values are expressed by means of fuzzy numbers. The objective function to be minimised is: (a) the mean flow time cost plus the mean processing cost, and (b) the maximum flowtime cost plus the total processing cost. The problem is modelled as an assignment problem and is solved optimally with respect to the defuzzification strategy used.