Valid inequalities for the single arc design problem with set-ups

Agostinho Agra, Mahdi Doostmohammadi, Quentin Louveaux

Research output: Contribution to journalArticlepeer-review


We consider a mixed integer set which generalizes two well-known sets: the single node fixed-charge network set and the single arc design set. Such set arises as a relaxation of feasible sets of general mixed integer problems such as lot-sizing and network design problems. We derive several families of valid inequalities that, in particular, generalize the arc residual capacity inequalities and the flow cover inequalities. For the constant capacitated case we provide an extended compact formulation and give a partial description of the convex hull in the original space which is exact under a certain condition. By lifting some basic inequalities we provide some insight on the difficulty of obtaining such a full polyhedral description for the constant capacitated case. Preliminary computational results are presented.

Original languageEnglish
Pages (from-to)17-35
Number of pages19
JournalDiscrete Optimization
Early online date25 Jan 2015
Publication statusPublished - 31 May 2015


  • facet-defining inequalities
  • mixed integer programming
  • valid inequalities


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