Abstract
In a scheduling problem with controllable processing times the job processing time can be compressed through incurring an additional cost. We consider the identical parallel machines max flow time minimization problem with controllable processing times. We address the preemptive and non-preemptive version of the problem. For the preemptive case, a linear programming formulation is presented which solves the problem optimally in polynomial time. For the non-preemptive problem it is shown that the First In First Out (FIFO) heuristic has a tight worst-case performance of 3−2/m, when jobs processing times and costs are set as in some optimal preemptive schedule.
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Supported by Swiss National Science Foundation project 20-63733.00/1, “Resource Allocation and Scheduling in Flexible Manufacturing Systems”, and by the “Metaheuristics Network”, grant HPRN-CT-1999-00106.
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Mastrolilli, M. Notes on Max Flow Time Minimization with Controllable Processing Times. Computing 71, 375–386 (2003). https://doi.org/10.1007/s00607-003-0029-z
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DOI: https://doi.org/10.1007/s00607-003-0029-z