In systems of general assembly line with material handling, line-side buffers need to be carefully assigned to a limited number of material delivers (drivers) for part delivery to avoid production stoppage due to material shortage. Such a problem is referred to as line-side buffer assignment problem (LBAP). In this paper, we focus on fixed zoning version of LBAP. We formulate the problem, prove its NP-hardness, and propose an algorithm based on two structural characteristics of the LBAP problem-one being the analogousness between our problem and the parallel machine scheduling (PMS) problem and the other being the monotonicity of the system throughput in the course of assigning line-side buffers to drivers. The developed algorithm globally converges with probability one when there exist feasible assignments. The algorithm is tested on a real system, and the results show that it is effective for solving the LBAP problem.