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Journal Articles European Journal of Operational Research Year : 2008

Lower bound for the earliness-tardiness scheduling problem on parallel machines with distinct due dates

Safia Kedad-Sidhoum
Yasmin Agueda Rios Solis
  • Function : Author
Francis Sourd
  • Function : Author

Abstract

This paper addresses the parallel machine scheduling problem in which the jobs have distinct due dates with earliness and tardiness costs. New lower bounds are proposed for the problem, they can be classed into two families. First, two assignment-based lower bounds for the one-machine problem are generalized for the parallel machine case. Second, a time-indexed formulation of the problem is investigated in order to derive efficient lower bounds throught column generation or Lagrangean relaxation. A simple local search algorithm is also presented in order to derive an upper bound. Computational experiments compare these bounds for both the one machine and parallel machine problems and show that the gap between upper and lower bounds is about 1.5%.

Dates and versions

hal-01185211 , version 1 (19-08-2015)

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Safia Kedad-Sidhoum, Yasmin Agueda Rios Solis, Francis Sourd. Lower bound for the earliness-tardiness scheduling problem on parallel machines with distinct due dates. European Journal of Operational Research, 2008, 189 (3), pp.1305-1316. ⟨10.1016/j.ejor.2006.05.052⟩. ⟨hal-01185211⟩
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