<p>Network function virtualization (NFV) is a transformative networking paradigm that leverages virtualization and cloud computing technologies to transform physical network functions, traditionally deployed on proprietary hardware middleboxes, into virtualized network functions (VNFs). This task is achieved by implementing these network functions in software that runs as virtual machines (VM) on commercial hardware within high-performance data centers, known as network function virtualization infrastructures (NFVIs). The softwareization of network appliances offers numerous advantages such as flexible provisioning and streamlined management of service function chains, reduced capital and operational expenditure (CAPEX and OPEX), and improved service delivery. However, efficient resource allocation for requested service function chains remains one of the most significant challenges in NFV. This process generally involves three stages: VNF chain composition (VNF-CC), VNF mapping, and scheduling. This study addresses the challenges of VNFs mapping and scheduling problems and proposes a novel multi-phase heuristic algorithm to solve these issues in a large-scale network. Our objective is to minimize the mapping cost by optimizing the server utilization and the makespan of the scheduled services. We developed a generator for physical resources and the corresponding network graphs for different scenarios to evaluate and compare the algorithm. Additionally, to simulate different numbers of VNFs and network service (NS) scenarios, we generated multiple VNF forwarding graphs. The proposed approach demonstrates improved server utilization and achieves a reduced makespan, thereby enhancing overall network efficiency.</p>