Single machine scheduling models with fuzzy parameters and precedence constraints

A methodology for modelling the single machine scheduling problems with fuzzy parameters and precedence constraints is proposed based on credibility measure. For a given set of jobs to be processed on a single machine, it is assumed that the processing times and the due dates are nonnegative fuzzy numbers and all the weights are positive, crisp numbers. Based on credibility measure, three sequencing problems and a goal programming model are formulated. Genetic algorithm is utilized to find optimal solutions in a short period of time. Illustrative numerical example is also given. Simulation results show that the proposed models and the genetic algorithm are effective, which can deal with the considered single machine fuzzy scheduling problems.