On some single-machine scheduling with sequence-dependent set-up times

In machine scheduling problems one of the important versions is the single-machine scheduling. The single-machine plus single-criterion is its simplest and most typical one including many famous NP-complete or -hard problems. With the single-criterion usually taking makespan as a popular choice, the single-machine deals with N jobs whose setup times are dependent or independent on the job sequences. Some single-machines with sequence-dependent setup times have been be transformed into the travelling salesman problem (1-TSP) in the literature, whereas in this paper one of its versions is reduced into the k-travelling salesman problem (k-TSP), an extension of the 1-TSP