Two-machine flowshop scheduling with past-sequence-dependent setup times and general learning effects

Abstract

This paper provides a continuation of ideas presented by Yin et al. [Yin et al., Some scheduling problems with general position-dependent and time-dependent learning effects, Inform. Sci. 179 (2009) 2416–2425]. In this paper, we study a two-machine flowshop scheduling model with proportional job processing times and a general learning effect simultaneously. In particular, we show that the problems to minimize makespan and sum of the kth power of completion times can be solved in polynomial time. We also show that the problems to minimize total weighted completion time, maximum lateness and maximum tardiness can be solved in polynomial time under certain conditions.