To solve assembly line balancing problem (ALBP) an integer-programming model is proposed. This model takes into consideration assignment, cycle time, zoning, and precedence constraints. The proposed model has solved the single ALBP with deterministic and stochastic task time. The model aims at optimizing four objectives which are the number of stations, mean absolute deviation, line efficiency, and probability of line stopping. The proposed model has been solved using genetic algorithms, which are applied to a number of benchmark problems then comparing results with the best-known results. The experimental study indicates that the developed approach is competent and capable of solving practical problems.