This paper proposes a genetic algorithm (GA) as a heuristic for multilevel lot sizing, combined with the Bit_Mod heuristic developed in this context, and invoking adaptive probabilities for crossover and mutation. The influence of various parameters under fired and rolling horizons is detailed. Design of experiments methodology is used in this connection. In the rolling horizon, the behaviour of the GA and other reties are compared with and without freezing the plan. The performance of the GA is compared with the cost-modified Wagner Whitin algorithm and cost-modified silver meal methods. The superiority of the proposed method is discussed, and case studies are given.