Single-machine scheduling with time window-dependent processing times

In the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coe cient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models considered in previous papers on scheduling problems with time dependent processing times. Various computational complexity results are presented for the makespan criterion, which show that the problem is NP-hard, even with 2 time windows. Solving procedures are also proposed for some special cases.