Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties

In this paper we consider parallel identical machines scheduling problems with deteriorating jobs. In this model, job processing times are defined by functions of their starting times. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remains polynomially solvable under the proposed model.