Minimizing makespan in a single-machine scheduling problem with a learning effect and fuzzy processing times

Abstract

In scheduling problems with learning effects, most research assumes that processing times are deterministic. This paper studies a single-machine scheduling problem with a position-based learning effect and fuzzy processing times where the objective is to minimize the makespan. 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. Two different polynomial-time algorithms are developed for the problem. The first solution methodology is based on the fuzzy chance-constrained programming, whereas the second is based on a method to rank fuzzy numbers. Computational experiments are then conducted in order to evaluate the performance of the algorithms.