Preemptive scheduling on uniform machines to minimize mean flow time

• Published in: Computers & operations research Vol. 36; no. 10; pp. 2816 - 2821
• Main Authors: Kravchenko, Svetlana A., Werner, Frank
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.10.2009; Elsevier; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Exact sciences and technology; Flows in networks. Combinatorial problems; Job shops; Linear programming; Mathematical programming; Maximum flow; Operational research and scientific management; Operational research. Management science; Parallel uniform machines; Polynomial algorithm; Production scheduling; Scheduling, sequencing; Studies; Linear programming; Parallel uniform machines; Polynomial algorithm; Maximum flow; Preemption; Parallel machines; Scheduling; Polynomial method; Source sink relationship; Optimal flow; Completion time
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2008.12.010

A set of jobs has to be scheduled on parallel uniform machines. Each machine can handle at most one job at a time. Each job becomes available for processing at its release date. All jobs have the same execution requirement, and each machine has a known speed. The processing of any job may be interrupted arbitrarily often and resumed later on any machine. We want to find a schedule that minimizes the sum of completion times, i.e., we consider problem Q | r j , p j = p , pmtn | ∑ C j whose complexity status was open. In this paper, we give a polynomial algorithm for the above problem. The algorithm is based on a reduction of the scheduling problem to a linear program. The crucial condition for implementing the proposed reduction is the known order of job completion times.