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.