Single-machine scheduling with a position-based learning effect and fuzzy processing times

In scheduling problems with learning effects, most researches assume that processing times are deterministic. This paper considers a single-machine scheduling problem with a position-based learning effect and fuzzy processing times, simultaneously. The position-based learning effect of a job is assumed to be a function of its position. The processing times are considered to be triangular fuzzy numbers. A polynomial time algorithm is proposed for the problem where the objective is to minimize the total completion time. The solution procedure is based on applying the shortest processing time rule to triangular fuzzy processing times. Computational results show that our model gives better results than the model ignoring the uncertainty.