Parallel machines scheduling with deteriorating and learning effects

In this paper parallel identical machines scheduling problems with deteriorating jobs and learning effects are considered. In this model, job processing times are defined by functions of their starting times and positions in the sequence. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. We show that the problems remain polynomially solvable under the proposed model.