Learning effect and deteriorating jobs in the single machine scheduling problems

This paper studies the single machine scheduling problems with learning effect and deteriorating jobs simultaneously. In this model, the processing times of jobs are defined as functions of their starting times and positions in a sequence. It is shown that even with the introduction of learning effect and deteriorating jobs to job processing times, the makespan, the total completion time and the sum of the k$k$th power of completion times minimization problems remain polynomially solvable, respectively. But for the following objective functions: the total weighted completion time and the maximum lateness, this paper proves that the shortest weighted processing time first (WSPT) rule and the earliest due-date first (EDD) rule can construct the optimal sequence under some special cases, respectively.