Scheduling with past-sequence-dependent setup times and learning effects on a single machine

Abstract

In this paper, we study the single-machine scheduling problems with learning effect and setup time considerations. 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). The objective functions are to minimize the sum of the quadratic job completion times, the total waiting time, the total weighted completion time, the maximum lateness, the total absolute differences in waiting times, and the sum of earliness penalties subject to no tardy jobs, respectively. We show that the sum of the quadratic job completion times minimization problem, the total waiting time minimization problem, the total absolute differences in waiting times minimization problem, and the sum of earliness penalties minimization problem subject to no tardy jobs 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 some special cases.