Scheduling job classes on uniform machines

  • Authors:

  • Enrique Gerstl;Gur Mosheiov

  • Affiliations:

  • School of Business Administration, The Hebrew University, Jerusalem 91905, Israel;School of Business Administration, The Hebrew University, Jerusalem 91905, Israel

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2012

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Abstract

We study a scheduling problem with job classes on parallel uniform machines. All the jobs of a given class share a common due-date. General, non-decreasing and class-dependent earliness and tardiness cost functions are assumed. Two objectives are considered: (i) minmax, where the scheduler is required to minimize the maximum earliness/tardiness cost among all the jobs and (ii) minmax-minsum, where the scheduler minimizes the sum of the maximum earliness/tardiness cost in all job classes. The problem is easily shown to be NP-hard, and we focus here on the introduction of simple heuristics. We introduce LPT (Largest Processing Time first)-based heuristics for the allocation of jobs to machines within each class, followed by a solution of an appropriate non-linear program, which produces for this job allocation an optimal schedule of the classes. We also propose a lower bound, based on balancing the load on the machines. Our numerical tests indicate that the heuristics result in very small optimality gaps.