An evolutionary algorithm for pure fuzzy flowshop scheduling problems

The pure flowshop scheduling problem is here investigated from a perspective considering the uncertainty associated with the execution of shop floor activities. Being the flowshop problem is NP complete, a large number of heuristic algorithms have been proposed in literature to determine an optimal solution. Unfortunately, these algorithms usually assume a simplifying hypothesis: the problem data are assumed as deterministic, i.e. job processing times and the due dates are expressed through a unique value, which does not reflect the real process variability. For this reason, some authors have recently proposed the use of a fuzzy set theory to model the uncertainty in scheduling problems. In this paper, a proper genetic algorithm has been developed for solving the fuzzy flowshop scheduling problem. The optimisation involves two different objectives: the completion time minimisation and the due date fulfilment; both the single and multi-objective configurations have been considered. A new ranking criterion has been proposed and its performance has been tested through a set of test problems. A numerical analysis confirms the efficiency of the proposed optimisation procedure.