SOME SCHEDULING PROBLEMS WITH PAST SEQUENCE DEPENDENT SETUP TIMES UNDER THE EFFECTS OF NONLINEAR DETERIORATION AND TIME-DEPENDENT LEARNING

This paper studies scheduling problems which include a combination of nonlinear job deterioration and a time-dependent learning effect. We use past sequence dependent (p-s-d) setup times, which is first introduced by Koulamas and Kyparisis [Eur. J. Oper. Res. 187 (2008) 1045-1049]. They considered a new form of setup times which depend on all already scheduled jobs from the current batch. Job deterioration and learning co-exist in various real life scheduling settings. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and a function of the total normal processing time of jobs scheduled prior to it. The following objectives are considered: single machine makespan and sum of completion times (square) and the maximum lateness. For the single-machine case, we derive polynomial-time optimal solutions.