Rights statement: This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 251, 1, 2015 DOI: 10.1016/j.ejor.2015.11.001
Accepted author manuscript, 365 KB, PDF document
Available under license: CC BY-NC-ND: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem
AU - Letchford, Adam
AU - Salazar Gonzalez, Juan Jose
N1 - This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 251, 1, 2015 DOI: 10.1016/j.ejor.2015.11.001
PY - 2016/5/16
Y1 - 2016/5/16
N2 - The sequential ordering problem (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernandez & Salazar introduced a multi-commodity flow (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables and adding valid equations. We then use polyhedral projection, together with some known results on flows, cuts and metrics, to derive new families of strong valid inequalities for both problems. Finally, we give computational results, which show that our findings yield good lower bounds in practice.
AB - The sequential ordering problem (SOP) is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes. Hernandez & Salazar introduced a multi-commodity flow (MCF) formulation for a generalisation of the SOP in which the vehicle has a limited capacity. We strengthen this MCF formulation by fixing variables and adding valid equations. We then use polyhedral projection, together with some known results on flows, cuts and metrics, to derive new families of strong valid inequalities for both problems. Finally, we give computational results, which show that our findings yield good lower bounds in practice.
KW - sequential ordering
KW - travelling salesman problem
KW - multi-commodity flows
KW - metrics
KW - polyhedral combinatorics
U2 - 10.1016/j.ejor.2015.11.001
DO - 10.1016/j.ejor.2015.11.001
M3 - Journal article
VL - 251
SP - 74
EP - 84
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 1
ER -