Scheduling jobs with linear model of simultaneous ageing and learning effects

In the paper, we introduce some new scheduling model in which learning and aging effects are both considered simultaneously. In this model the actual processing time of the jobs depends only on its position in a schedule and can be described by the piecewise linear function. For single-processor problem with introduced model, we show that the problem of minimizing the makespan criterion for independent jobs with release dates is strongly NP-hard, but some special cases of this problem are polynomially solvable. Based on those special cases, we propose 4 heuristic algorithms and we experimentally examine their usefulness for solving the general problem.