TITLE:
Single Machine Scheduling with Time-Dependent Learning Effect and Non-Linear Past-Sequence-Dependent Setup Times
AUTHORS:
Yuling Yeh, Chinyao Low, Wen-Yi Lin
KEYWORDS:
Scheduling, Time-Dependent Learning, Setup Time, Past-Sequence-Dependent, Total Completion Time
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.1,
January
28,
2015
ABSTRACT: This paper studies a single machine
scheduling problem with time-dependent learning and setup times. Time-dependent
learning means that the actual processing time of a job is a function of the
sum of the normal processing times of the jobs already scheduled. The setup
time of a job is proportional to the length of the already processed jobs, that
is, past-sequence-dependent (psd) setup time. We show that the addressed
problem remains polynomially solvable for the objectives, i.e., minimization of
the total completion time and minimization of the total weighted completion
time. We also show that the smallest processing time (SPT) rule provides the
optimum sequence for the addressed problem.