The advantages of the orthogonal frequency division multiplexing (OFDM) are high spectral efficiency, resiliency to RF interference, lower multi-path distortion and others. To further utilize the vast channel capacity of the multiuser OFDM, one has to find the efficient adaptive subcarrier and bit allocation among users. In this paper, we propose a 0-1 integer programming model formulating the optimal subcarrier and bit allocation problem of the multiuser OFDM. We proved that the continuous relaxation of our formulation is tighter than the previous convex optimization formulation based on perspective function and the Lagrangian dual bound of our formulation is equivalent to the linear programming relaxation bound. The proposed Lagrangian dual is seperable with respect to subcarriers and allows an efficient dual maximization algorithm. We compared the performance of the integer programming formulation and the Lagrangian dual of our formulation and the continuous relaxation and the primal heuristic proposed in [3]. Computer simulation on a system employing M-ary quadrature amplitude modulation (MQAM) assuming a frequency-selective channel consisting of three independent Rayleigh multipaths is carried out with the optimal subcarrier and bit allocation solution generated by the 0-1 integer programming model.