Minimizing the earliness/tardiness costs on parallel machine with learning effects and deteriorating jobs: a mixed nonlinear integer programming approach

In this study, we introduce a mixed nonlinear integer programming formulation for parallel machine earliness/tardiness (ET) scheduling with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we propose that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The model can easily provide the optimal solution to problems involving about eleven jobs and two machines