Abstract:

In this paper, we consider combining time and position dependent effects on a single machine subject to deteriorating maintenance activities.  The actual processing time of the job is a function of its position.  We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The proposed two problems can be solved in polynomial time by using the matching algorithm. Finally, the makespan problems can be solved by the group balance principle under some certain conditions.

Key words: scheduling, time-dependent and position-dependent, maintenance activities, matching algorithm, the group balance principle