The ongoing roll-out of 5G networks paves the way for many fascinating applications such as virtual reality (VR), augmented reality (AR), and autonomous driving. Moreover, 5G enables billions of devices to transfer an unprecedented amount of data at the same time. This transformation calls for novel technologies like multi-access edge computing (MEC) to satisfy the stringent latency and bitrate requirements of the mentioned applications. The main challenge pertaining to MEC is that the edge MEC nodes are usually characterized by scarce computational resources compared to the core or cloud, arising the challenge of efficiently utilizing the edge resources while ensuring that the service requirements are satisfied. When considered with the users’ mobility, this poses another challenge, which lies in minimization of the service interruption for the users whose service requests are represented as service function chains (SFCs) composed of virtualized network functions (VNFs) instantiated on the MEC nodes or on the cloud. In this paper, we study the problem of joint user association, SFC placement, and resource allocation, employing mixed-integer linear programming (MILP) techniques. The objective function of this MILP-based problem formulation are to minimize (i) the service provisioning cost, (ii) the transport network utilization, and (iii) the service interruption. Moreover, a heuristic algorithm is proposed to tackle the scalability issue of the MILP-based algorithms. Finally, comprehensive experiments are performed to draw a comparison between these approaches.