Virtualization paradigms like cloud computing, software defined networking (SDN), and network functions virtualization (NFV) provide advantages with respect to aspects like flexibility, costs, and scalability. However, management and orchestration of the resulting networks also introduce new challenges. The placement of services, such as virtual machines~(VMs), virtualized network functions~(VNFs), or SDN controllers, is a multi-objective optimization task that confronts operators with a multitude of possible solutions that are incomparable among each other. The goal of this work is to investigate mechanisms that enable automated decision making between such multi-dimensional solutions. To this end, we investigate techniques from the domain of multi-attribute decision making that aggregate the performance of placements to a single numeric score. A comparison between resulting rankings of placements shows that many techniques produce similar results. Hence, placements that achieve good rankings according to many approaches might be viable candidates in the context of automated decision making. In order to illustrate the functionality of the different scoring mechanisms, we perform a case study on a single network graph and a fixed number of objectives and service instances. Additionally, we present aggregated results from broad evaluations on the Internet Topology Zoo and a larger number of objectives as well as varying numbers of service instances. These allow making more reliable statements about the mechanisms' performance and agreement.