@article{PessoaUchoade Arag{\~a}oetal.2010,
  author    = {Pessoa, Artur and Uchoa, Eduardo and de Arag{\~a}o, Marcus Poggi and Rodrigues, Rosiane},
  title     = {Exact algorithm over an arc-time-indexed formulation for parallel machine scheduling problems},
  journal   = {Mathematical Programming Computation},
  volume    = {2},
  number    = {3-4},
  publisher = {Springer Science and Business Media LLC},
  issn      = {1867-2949},
  doi       = {10.1007/s12532-010-0019-z},
  pages     = {259 -- 290},
  year      = {2010},
  abstract  = {This paper presents an exact algorithm for the identical parallel machine scheduling problem over a formulation where each variable is indexed by a pair of jobs and a completion time.We show that such a formulation can be handled, in spite of its huge number of variables, through a branch cut and price algorithm enhanced by a number of practical techniques, including a dynamic programming procedure to fix variables by Lagrangean bounds and dual stabilization. The resulting method permits the solution of many instances of the P||\sum{wj Tj} problem with up to 100 jobs, and having 2 or 4 machines. This is the first time that medium-sized instances of the P||\sum{wj Tj} have been solved to optimality.},
  language  = {en}
}