Single Machine Scheduling Problems with Time-dependent Learning Effects

In traditional scheduling problems, most literature assumes that the processing time of a job is fixed. However, there are many situations where the processing time of a job depends on the starting time or the position of the job in a sequence. In such situations, the actual processing time of a job may be more or less than its normal processing time if it is scheduled later. This phenomenon is known as the ‘‘learning effect’’. In this study, we introduce a time-dependent learning effect into a single-machine scheduling problems. We consider the following objective functions: (i) maximum tardiness, (ii) number of tardy jobs (iii) maximum tardiness subject to the number of tardy jobs (iv) number of tardy jobs subject to maximum tardiness. A nonlinear programming model are developed for problems which belongs to NP-hard class. Also the model is tested on an example. According to the best of our knowledge, no works exists on the optimal solutions for four problems were examined.