In this paper, we study the problem of minimizing the maximum total completion time per machine on m parallel and identical machines. We prove that the problem is strongly NP-hard if m is a part of the input. When m is a given number, a pseudo-polynomial time dynamic programming is proposed. We...

This paper considers the scheduling problems with the objective of minimizing the total completion time on two parallel identical machines with given unavailable periods. The jobs are assumed to be nonresumable. If there is one unavailable period on one of the two machines, we prove that SPT has...