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The paper proposes and investigates the problem of the reconfiguration of cloud and bandwidth resources in Multi-Provider Network Function Virtualization architectures where the Cloud Infrastructures (CI) are managed by different Providers and interconnected by an elastic optical network. The resource reconfiguration is performed by taking into account the different costs charged by the Infrastructure Providers (InP) of the CIs and by exploiting the advantages of the adaptive optical modulation. The objective is to minimize the total cost given by the sum of three components: i) the cloud resource cost; ii) the bandwidth costs; iii) the reconfiguration costs characterized by the revenue loss of the Telecommunication Service Provider due to the degradation of the Quality of Service occurring during the reconfiguration of the optical circuits. We define and investigate a heuristic of polynomial complexity. The application of …