Single Machine Scheduling with a Time-Dependent Learning Effect and Fuzzy Due Dates

In this paper, a single machine scheduling problem with a time-dependent learning effect is studied considering the imprecise or fuzzy nature of due dates. The time-dependent learning effect of a job is assumed to be a function of the sum of the normal processing times of the already processed jobs. The fuzzy due dates of jobs are defined by membership functions with respect to the satisfaction of job completion times. The objective is to find a job sequence maximizing the minimum satisfaction degree. We show the problem is polynomially solvable under certain conditions.