Two extended formulations for the virtual network function placement and routing problem

Given a bi-directed graph modeling telecommunication network, and set of origin-destination pairs representing traffic requests (commodities) along with their associated Service Function Chains (SFCs), the Virtual Network Placement Routing Problem (VNFPRP) aims to find, for each commodity, one latency-constrained routing path that visits required Functions in specific order. The function installation costs together node activation have be minimized. In this paper, we present two extended Mixed Integer Programming (MIP) formulations model VNFPRP. For formulation define master problem, pricing Lagrangian bound branching scheme, order derive an efficient Branch-and-Price algorithm. We also provide several families valid inequalities strengthen LP-relaxation bounds. Computational results are reported comparing performance algorithms compact MIP its Branch-and-Benders-cut implementation on SNDlib instances networks.