Abstract
We study the directed network design problem with relays (DNDPR) whose aim is to construct a minimum cost network that enables the communication of a given set of origin-destination pairs. Thereby, expensive signal regeneration devices need to be placed to cover communication distances exceeding a predefined threshold. Applications of the DNDPR arise in telecommunications and transportation. We propose two new integer programming formulations for the DNDPR. The first one is a flow-based formulation with a pseudo-polynomial number of variables and constraints and the second is a cut-based formulation with an exponential number of constraints. Fractional distance values are handled efficiently by augmenting both models with an exponentially-sized set of infeasible path constraints. We develop branch-and-cut algorithms and also consider valid inequalities to strengthen the obtained dual bounds and to speed up convergence. The results of our extensive computational study on diverse sets of benchmark instances show that our algorithms outperform the previous state-of-the-art method based on column generation.
Original language | English |
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Article number | 102005 |
Pages (from-to) | 1-17 |
Number of pages | 17 |
Journal | Omega |
Volume | 91 |
Early online date | 16 Nov 2018 |
DOIs | |
Publication status | Published - Mar 2020 |
Funding
This work was partly supported by the Vienna Science and Technology Fund through project ICT15-014.
Funders | Funder number |
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Vienna Science and Technology Fund | ICT15-014 |
Keywords
- Integer Programming
- Layered Graphs
- Networks
- Telecommunications