Video-on-Demand (VOD) or near-VOD services are expected to grow significantly over time, providing diverse programs for home entertainment, learning and training, news-on-demand, and other applications. These services require large bandwidth resources. We present a model for bandwidth allocation in a tree network with limited link capacities, where a server at the root node repeatedly broadcasts copies of various programs. The time intervals between successive broadcasts of each program can be increased at subsequent nodes, or the video quality can be decreased, thus providing different service performance to different nodes while satisfying the capacity constraints. The model is formulated as an equitable resource allocation problem with a lexicographic minimax objective function and tree-like ordering constraints. We present a lexicographic minimax algorithm that allocates each link’s bandwidth among the programs carried on the link. The algorithm repeatedly solves minimax problems, and fixes some variables at their optimal value after the solution of each such problem. The algorithm for solving the minimax problems uses a bisection search to find the minimax solution with the minimal decision variable values. The model also provides an ordered list of links from the most critical link to the least critical link, a useful feature for capacity expansion planning decisions.