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Recently, learning scheduling problems have received increasingattention. However, the majority of the research assume that theactual job processing time is a function of its position. This paperdeals with the single-machine scheduling problem with asum-of-processing-time-based learning effect. By the effect ofsum-of-processing-time-based learning, we mean that the processingtime of a job is defined by total normal processing time of jobs infront of it in the sequence. We show that the single-machinemakespan problem remains polynomially solvable under the proposedmodel.  We show that the total completion time minimization problemfor a≥1 remains polynomially solvable under the proposedmodel.  For the case of 0<a<1, we show that an optimal schedule ofthe total completion time minimization problem is V-shaped with respect to normal job processing times

Single-Machine Scheduling Problems with a Sum-of-Processing-Time-Based Learning Function