Solving a time-indexed formulation for an unrelated parallel machine scheduling problem by preprocessing and cutting planes
RAIRO. Operations Research, Tome 55 (2021), pp. S1747-S1765

We consider a time-indexed formulation for the unrelated parallel machine scheduling problem. We show that all polyhedral knowledge known from the single machine problem (in particular, valid inequalities) is applicable to this formulation. We present new facet-inducing valid inequalities and a preprocessing technique involving fixing variables based on reduced costs. We combine both techniques in a basic cutting-plane algorithm and test the performance of the resulting algorithm by running it on randomly generated instances.

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DOI : 10.1051/ro/2020031
Classification : 90B35
Keywords: Unrelated machine scheduling, time-indexed formulation, valid inequalities, cutting plane algorithm, variable fixing 
@article{RO_2021__55_S1_S1747_0,
     author = {Berghman, Lotte and Spieksma, Frits C. R. and T{\textquoteright}kindt, Vincent},
     title = {Solving a time-indexed formulation for an unrelated parallel machine scheduling problem by preprocessing and cutting planes},
     journal = {RAIRO. Operations Research},
     pages = {S1747--S1765},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     doi = {10.1051/ro/2020031},
     mrnumber = {4223119},
     zbl = {1469.90076},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2020031/}
}
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Berghman, Lotte; Spieksma, Frits C. R.; T’kindt, Vincent. Solving a time-indexed formulation for an unrelated parallel machine scheduling problem by preprocessing and cutting planes. RAIRO. Operations Research, Tome 55 (2021), pp. S1747-S1765. doi: 10.1051/ro/2020031

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