Scheduling problems with the nonlinear effects of learning and deterioration

In this paper, we present both nonlinear job deterioration and nonlinear learning which exist simultaneously. Job deterioration and learning co-exist in many realistic scheduling situations. By the effects of learning and deterioration, we mean that the processing time of a job is defined by the increasing function of its execution start time and position in the sequence. The following objectives are considered: single-machine makespan and sum of completion times (square) and the maximum lateness. For the single-machine case, we derive polynomial time optimal solutions. For the case of an m-machine permutation flowshop, we present polynomial time optimal solutions for some special cases of the problems to minimize makespan and total completion time.