Scheduling two parallel machines with a single server: the general case

This paper considers the problem of scheduling two-operation non-preemptable jobs on two identical semiautomatic machines. A single server is available to carry out the first (or setup) operation. The second operation is executed automatically, without the server. The general problem of makespan minimization is NP-hard in the strong sense. In earlier work, we showed that the equal total length problem is polynomial time and we also provided efficient and effective solutions for the special cases of equal setup and equal processing times. Most of the cases analyzed thus far have fallen into the category of regular problems. In this paper we build on this earlier work to deal with the general case. Various approaches will be considered. One may reduce the problem to a regular one by amalgamating jobs, or we may apply the earlier heuristics to (possibly regular) job clusters. Alternately we may apply a greedy heuristic, a metaheuristic such as a genetic algorithm or the well known Gilmor...

• Type: Journal
• Year: 2006
• Where: COR
• Authors: Amir H. Abdekhodaee, Andrew Wirth, Heng-Soon Gan
• Keywords: COR 2006, Earlier Work, General Problem, Identical Semiautomatic Machines