2002 Volume 15 Issue 1 Pages 41-49
In this paper we consider the scheduling problem of minimizing the maximum completion time (i.e., the makespan) for a two-machine robotic unit of flowshop type, in which each of n jobs is processed on the first machine and later on the second machine. There is an intermediate station between the two machines for intermediate operations such as washing, chip disposal, cooling, drying and/or quenching. If only permutation schedules are allowed (i.e., sequences of jobs on the two machines have to be the same), the problem can be solved in polynomial time, although non-permutation problem (i.e., the original problem) is NP-hard in the strong sense. It is already known that, if the optimal permutation schedule is used as an approximate solution for the non-permutation problem, it gives a maximum completion time within twice the optimal. In this paper, we present a different approximate algorithm which is based on a relaxation to the single-machine problem with delivery times, and show that its non-permutation schedule also gives a maximum completion time within twice the optimal. Moreover, we examine its approximation performance by means of numerical experiments, comparing with the optimal permutation scheduling.