Minimizing the makespan on a single machine with learning and unequal release times

The importance of the ready times can be found in Wafer fabrication with the presence of unequal ready times. It is sometimes advantageous to form a non-full batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. On the other hand, there is a significant involvement of humans in scheduling environments; the amount of learning activities is high. Hence it seems to be reasonable to consider learning in scheduling environments. However, research with learning and release times is relatively unexplored. Motivated by this observation, this paper deals with a single-machine problem with the learning effect and release times where the objective is to minimize the makespan. This paper proposes a branch-and-bound algorithm and three two-stage heuristic algorithms for the problem. The computational experiments show that the branch-and-bound algorithm can solve instances up to 25 jobs, and the best one with the average error percentage of the proposed heuristics is less than 0.05%.