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In classical scheduling theory job processing times are constant. However, there are many situations where processing time of a job depends on the starting time of the job in the queue. This paper reviews the rapidly growing literature on single machine scheduling models with time dependent processing times. Attention is focused on linear, piecewise linear and non-linear processing time functions for jobs. We survey known results and introduce new solvable cases. Finally, we identify the areas and give directions where further research is needed.
Alidaee et al. (Thu,) studied this question.