Single-Machine Scheduling Problems with General Learning Effects and Deterioration Jobs

This paper considers a scheduling model with general learning effects and deteriorating jobs simultaneously, where the actual processing time of a job is a function depends not only on the start time of the job, but also on the total normal processing times of jobs in front of it in the sequence. It shows that the optimal schedule for the single-machine scheduling problem to minimize makespan is obtained by the longest processing time first (LPT) rule. For the problem to minimize total complete time, we use the smallest processing time first (SPT) rule as a heuristic algorithm and analyze its worst-case bound.