Flowshop scheduling with a general exponential learning effect

This paper investigates flowshop scheduling problems with a general exponential learning effect, i.e., the actual processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The objective is to minimize the makespan, the total (weighted) completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times, respectively. Several simple heuristic algorithms are proposed in this paper by using the optimal schedules for the corresponding single machine problems. The tight worst-case bound of these heuristic algorithms is also given. Two well-known heuristics are also proposed for the flowshop scheduling with a general exponential learning effect.