Single machine and group scheduling with random learning rates

This study mainly considers the scheduling problems with learning effects, where the learning rate is a random variable and obeys a uniform distribution. In the first part, we introduce a single machine model with location-based learning effects. We have given the theoretical proof of the optimal solution for the five objective functions. In the second part, we study the problem with group technology. Both intra-group and inter-group have location-based learning effects, and the learning rate of intra-group jobs follows a uniform distribution. We also give the optimal ranking method and proof for the two problems proposed.