Designing a video-on-demand (VoD) system is in essence an optimization task aimed at minimizing the cost of communication and storage in the corresponding network. The decision variables of this problem are the locations of the nodes plus the content which should be cached in each node. Furthermore, an assignment strategy is needed to determine, for each customer, which node should be contacted for each video file. While this problem is categorized in the general group of network optimization problems, its specific characteristics demand a new solution to be sought for it. In this paper, inspired by the success of fuzzy optimization for similar problems in coding, a fuzzy objective function is derived which is heuristically shown to minimize the communication cost in a VoD network, while controlling the storage cost as well. Then, an iterative algorithm is proposed to find an optimum solution to the proposed problem. After addressing the mathematical details of the proposed method, a sample problem is presented followed by the solution produced for it by the proposed method. This solution is then extensively analyzed.