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We study the optimal scheduling problem for delay minimization subject to traffic demand, transmit power and Signal-to-Noise-plus-Interference Ratio (SNIR) constraints in rate-controlled Ultra-Wideband (UWB) wireless networks. We first formulate the Linear Programming (LP) problem where the number of variables is exponential in the number of the links. We then propose the heuristic algorithm called Exclusion Region and Utility Maximization based Column Generation Method (EXUM-CGM) to solve the problem rapidly and efficiently. In EXUM-CGM, we decompose the large scale problem into two sub-problems, Restricted Master Problem (RMP) and Pricing Problem (PP). We adapt the exclusion region concept commonly used in UWB systems to the initialization of the RMP. Since the PP formulation is a non-linear integer programming problem, we propose a heuristic algorithm based on utility maximization. Through the simulations, we show that EXUM-CGM decreases the runtime of the exponential LP problem significantly while achieving very close-to-optimal solutions.