Content Delivery Network (CDN) has evolved to overcome a network bottleneck and improve user perceived Quality of Service (QoS). A CDN replicates contents from the origin server to replica servers to reduce the overload of the origin server. CDN providers would try to achieve an acceptable performance at the least cost including the storage space or processing power. In this paper, we introduce a new optimization model for the CDN design problem considering the user perceived QoS and single path (non-bifurcated) routing constraints and analyze the computational complexity for some special cases.