期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 251, 期 1, 页码 74-84出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2015.11.001
关键词
Sequential ordering; Travelling salesman problem with; precedence constraints; Multi-commodity flows; Metrics; Polyhedral combinatorics
资金
- Ministerio de Economia y Competitividad, Spain [MTM2012-36163-C06-01]
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. (C) 2015 Elsevier B.V. All rights reserved.
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