Solution algorithms for the makespan minimization problem with the general learning model

Most of the papers devoted to scheduling problems with the learning effect concern the Wright’s learning curve. On the other hand, the study about learning has pointed out that the learning curve in practice is very often an S-shaped function, which has not been considered in scheduling. Thus, in this paper, a single processor makespan minimization problem with an S-shaped learning model is investigated. We prove that this problem is strongly NP-hard even if the experience provided by each job is equal to its normal processing time. Therefore, to solve this problem, we prove some eliminating properties that are used to construct a branch and bound algorithm and some fast heuristic methods. Since the proposed algorithms are dedicated for the general case, i.e., where job processing times are arbitrary non-increasing experience dependent functions, their efficiency is verified numerically for the S-shaped model.