Online scheduling of weighted equal-length jobs with hard deadlines on parallel machines

  • Authors:

  • Sven O. Krumke;Alfred Taudes;Stephan Westphal

  • Affiliations:

  • University of Kaiserslautern, Department of Mathematics, P.O. Box 3049, Paul-Ehrlich-Str. 14, 67653 Kaiserslautern, Germany;Vienna University of Economics and Business Administration, Institute for Production Management, Austria;University of Kaiserslautern, Department of Mathematics, P.O. Box 3049, Paul-Ehrlich-Str. 14, 67653 Kaiserslautern, Germany

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2011

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Abstract

We consider the problem of scheduling a maximum profit selection of equal length jobs on m identical machines. Jobs arrive online over time and the goal is to determine a non-preemptive schedule which maximizes the total profit of the scheduled jobs. Let the common processing requirement of the jobs be p0. For each job j"i, i=1,...,n we are given a release time r"i (at which the job becomes known) and a deadline r"i+p+@d"i. If the job is scheduled and completed before the deadline, a profit of w"i is earned. Upon arrival of a new job, an online algorithm must decide whether to accept the job or not. In case of acceptance, the online algorithms must provide a feasible starting date for the job. Competitive analysis has become a standard way of measuring the quality of online algorithms. For a maximization problem, an online algorithm is called c-competitive, if on every input instance it achieves at least a 1/c-fraction of the optimal (''offline'') profit. We give lower bounds for the competitivity of online algorithms and propose algorithms which match this lower bound up to a constant factor.