Preemptive scheduling in the presence of transportation times

Authors:
Mourad Boudhar;Amina Haned
Affiliations:
Faculty of Mathematics, USTHB University, BP 32 Bab-Ezzouar, El-Alia 16111, Algiers, Algeria;Faculty of Mathematics, USTHB University, BP 32 Bab-Ezzouar, El-Alia 16111, Algiers, Algeria
Venue:
Computers and Operations Research
Year:
2009

Citing 5
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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"j"j"^"' 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.