Network Function Virtualization along with Network Service Chaining envision a reduction in the respective cost that end users, service providers, and network operators are experiencing, while providing complete and high quality services. However, the vast range of available services and the service on-demand model, creates dynamic traffic conditions that necessitates a flexible and automatic network platform to redirect traffic according to network conditions. In this paper, we study the problem of deploying service chains, consisting of a number of virtualized network functions (VNFs), in a SDN enabled data center network, where a random number of users are associated with each service chain. To this end, appropriate resource management algorithms are introduced for the placement of VNFs satisfying server affinity and latency constraints. The interconnection of the VNFs is facilitated by an SDN controller, which periodically recalculates the routing paths to adjust to the dynamic traffic conditions.