Preemptive scheduling in the presence of transportation times

Abstract

In this paper, we consider the problem of scheduling n independent jobs preemptively on m identical parallel machines, to minimize the total completion time (makespan). Each job J i ( i = 1 , n ¯ ) has a processing time p i and the transportation of an interrupted job from a machine M j to another machine M j ′ requires d jj ′ units of time. We propose a linear programming formulation in real and binary decision variables and we prove that the problem is NP-hard. Some subproblems are analyzed and solved by polynomial algorithms. Finally we present some heuristics and give some lower bounds of the makespan.