This article presents an integer linear model for the hop constrained node survivable network design problem. The formulation is focused on networks represented by undirected graphs with not rooted demands, considering costs in arcs and in optional (Steiner) nodes, too. | Yugoslav Journal of Operations Research 27 (2017), Number 4, 427–438 DOI: A FORMULATION FOR A HOP CONSTRAINED SURVIVABLE NETWORK DESIGN PROBLEM Graciela FERREIRA Facultad de Ingenier´ıa, Universidad de la Rep´ublica Montevideo, Uruguay gferreira@ Sergio NESMACHNOW Facultad de Ingenier´ıa, Universidad de la Rep´ublica Montevideo, Uruguay sergion@ Franco ROBLEDO Facultad de Ingenier´ıa, Universidad de la Rep´ublica Montevideo, Uruguay frobledo@ Received: May 2016 / Accepted: March 2017 Abstract: This article presents an integer linear model for the hop constrained node survivable network design problem. The formulation is focused on networks represented by undirected graphs with not rooted demands, considering costs in arcs and in optional (Steiner) nodes, too. The proposed model allows setting different values of parameters for constraints between each pair of terminal nodes, including hop length and number of node disjoint paths constraints. This work includes calculating lower and upper bounds to the optimal solution. Since this kind of problems are NPhard, it is useful to combine the presented formulation with heuristic methods in order to solve effectively large problem instances. The model was tested over the graphs with up to 85 nodes and 148 arcs, in order to validate it in cases with known solution. Keywords: Network Design, Hop Constrained, Survivability. MSC: 90B06, 90C05, 90C08. 1. INTRODUCTION In network design, the survivability property enables the network to maintain a certain level of network connectivity and quality of service under failure conditions. Survivability 428 G. Ferreira, S. Nesmachnow, F. Robledo / A formulation for a HCSNDP has been considered as one of the critical requirements in network planning and design [5]. It often involves considering design requirements on the network topology, or in the case of communication networks, constraints could be associated with protocol,
