Service chains consist of a set of network services, such as firewalls or application delivery controllers, which are interconnected through a network to support various applications. While it is not a new concept, there has been an extremely important new trend with the rise of Software-Defined Network (SDN) and Network Function Virtualization (NFV). The combination of SDN and NFV can make the service chain and application provisioning process much shorter and simpler. In this paper, we study the provisioning of service chains jointly with the number/location of Virtual Network Functions (VNFs). While chains are often built to support multiple applications, the question arises as how to plan the provisioning of service chains in order to avoid data passing through unnecessary network devices or servers and consuming extra bandwidth and CPU cycles. It requires choosing carefully the number and the location of the VNFs. We propose an exact mathematical model using decomposition methods whose solution is scalable in order to conduct such an investigation. We conduct extensive numerical experiments, and show we can solve exactly the routing of service chain requests in a few minutes for networks with up to 50 nodes, and traffic requests between all pairs of nodes. Detailed analysis is then made on the best compromise between minimizing the bandwidth requirement and minimizing the number of VNFs and optimizing their locations using different data sets.