A new approach to two-machine flow shop problem with uncertain processing times

This paper deals with the problem of optimization of job sequence in a two-machine flow shop problem in the presence of uncertainty. It is assumed that the processing times of jobs on the machines are described by triangular fuzzy sets. A new optimization algorithm based on Johnson's algorithm for deterministic processing times and on an improvement of McCahon and Lee's algorithm is developed and presented. In order to compare fuzzy processing times, McCahon and Lee use mean values of their corresponding fuzzy sets. It is shown that this approach cannot fully explore possible relationships between fuzzy sets. In order to overcome this drawback we consider different fuzzy sets determined by lambda-cuts of the fuzzy processing times. Extensive experiments show that the new algorithm gives better solutions with respect to makespan than existing McCahon and Lee's algorithm.