Prescriptions for radiation therapy are given in terms of dose-volume constraints (DVCs). Solving the fluence map optimization (FMO) problem while satisfying DVCs often requires a tedious trial-and-error for selecting appropriate dose control parameters on various organs. In this paper, we propose an iterative approach to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. This algorithm, starting from arbitrary initial parameter values, gradually updates the values through an iterative solution process toward optimal solution. This method finds appropriate parameter values through the trade-off between OAR sparing and target coverage to improve the solution. We compared the plan quality and the satisfaction of the DVCs by the proposed algorithm with two nonlinear approaches: a nonlinear FMO model solved by using the L-BFGS algorithm and another approach solved by a commercial treatment planning system (Eclipse 8.9). We retrospectively selected from our institutional database five patients with lung cancer and one patient with prostate cancer for this study. Numerical results show that our approach successfully improved target coverage to meet the DVCs, while trying to keep corresponding OAR DVCs satisfied. The LBFGS algorithm for solving the nonlinear FMO model successfully satisfied the DVCs in three out of five test cases. However, there is no recourse in the nonlinear FMO model for correcting unsatisfied DVCs other than manually changing some parameter values through trial and error to derive a solution that more closely meets the DVC requirements. The LP-based heuristic algorithm outperformed the current treatment planning system in terms of DVC satisfaction. A major strength of the LP-based heuristic approach is that it is not sensitive to the starting condition.