Single-machine scheduling with past-sequence-dependent setup times and time-dependent learning effect

Abstract

This paper studies the single-machine scheduling problem with time-dependent learning effect and setup times considerations. The time-dependent learning effect means that the processing time of a job is defined by a function of the total normal processing time of the already processed jobs. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved in polynomial time, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.