Copyright © 2013 Pengfei Xue and Yulin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We consider a single-machine scheduling problem with upper bounded actual
processing time and upper bounded maintenance time under deteriorating effect. The actual
processing time of a job is a position-dependent power function. If the actual processing time
of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the
maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance
should also be paid. The maintenance duration studied in the paper is a position-dependent
exponential function. The objective is to find jointly the optimal maintenance frequency and
the optimal job sequence to minimize the total cost, which is a linear function of the makespan
and the total tardiness. We show that the studied scheduling problem can be transformed as a
classic assignment problem to solve. There is also shown that a special case of the scheduling
problem can be optimally solved by a lower order algorithm.