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Video-on-demand (VoD) is the entertainment source that, in the future, will likely overtake regular television in many aspects. Although many companies have deployed working VoD services, some aspects of the VoD should still undergo further improvement in order for it to reach to the foreseen potentials. An important aspect of a VoD system is the underlying network in which it operates. According to the huge number of customers in this network, it should be carefully designed to fulfill certain performance criteria. This process should be capable of finding optimal locations for the nodes of the network as well as determining the content that should be cached in each one. 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, which is inspired by the successful use of fuzzy optimization in similar problems in other fields, a fuzzy objective function that is heuristically shown to minimize the communication cost in a VoD network is derived while also controlling the storage cost. Then, an iterative algorithm is proposed to find a locally optimal solution to the proposed objective function. Capitalizing on the unrepeatable tendency of the proposed algorithm, a heuristic method for picking a good solution from a bundle of solutions produced by the proposed algorithm is also suggested. This paper includes a formal statement of the problem and its mathematical analysis. In addition, different scenarios in which the proposed algorithm can be utilized are discussed.