Approximation Schemes for Scheduling Jobs with Common Due Date on Parallel Machines to Minimize Total Tardiness

Authors:
Mikhail Y. Kovalyov;Frank Werner
Affiliations:
Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus;Otto-von-Guericke-Universität, Fakultät für Mathematik, PSF 4120, 39016 Magdeburg, Germany
Venue:
Journal of Heuristics
Year:
2002

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Abstract

The problem of scheduling n nonpreemptive jobs having a common due date d on m, m ≥ 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms {Aϵ} and {Bϵ} are presented such that (T0 − T*)/(T* + d) ≤ ϵ holds for any problem instance and any given ϵ 0, where T* is the optimal solution value and T0 is the value of the solution delivered by Aϵ or Bϵ. Algorithms Aϵ and Bϵ run in O(n2m/ϵm−1) and O(nm+1/ϵm) time, respectively, if m is a constant. For m = 2, algorithm Aϵ can be improved to run in O(n3/ϵ) time.