Single machine scheduling with time-dependent deterioration and exponential learning effect

In this paper we consider the single machine scheduling problems with time-dependent deterioration and exponential learning effect, i.e., the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. We consider the following objective functions: the makespan, the sum of the δ  th (δ⩾0)(δ⩾0) power of job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the sum of the δth power of job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.