Bi-criterion single machine scheduling problem with a past-sequence-dependent setup times and learning effect

This paper considers the bi-criterion single machine scheduling problem of n jobs with a past-sequence-dependent setup times (PSD) and learning effect (LE) together. The two objectives considered are the total completion time (TC) and total absolute differences in completion times (TADC). We consider only the objective TC, we obtain an unique optimal sequence (solution). We study the objective TADC to obtain a unique optimal sequence (solution). If both the TC and TADC are considered together, a set of optimal sequences that performs well with respect to both the objectives TC and TADC would be obtained. This set of optimal sequences is the minimum set of optimal sequences (MSOS). Our purpose in this paper is to find this minimum set of optimal sequences (MSOS) that performs well with respect to both the objectives TC and TADC.