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Video-on-demand (VOD) services are expected to grow significantly over time, providing diverse programs for home entertainment, distance instruction, news on demand, and other applications. These services require large bandwidth resources. We present a model for a tree network where each node may have demands for multiple different VOD program families, where each program family is an aggregation of similar programs. The decision variables include location of VOD servers and assignment of program families to servers. The model considers cost of servers, cost of assigning program families to servers, and cost of link bandwidths used to broadcast programs. The objective is to minimize the sum of all these costs. The model is formulated as an integer program. We develop a dynamic programming formulation with multiple state variables and an algorithm that solves this model. Starting from the end nodes of the tree network, the algorithm determines optimal solutions to subtrees, eventually reaching the root node with the central server, thus providing an optimal solution to the entire network.