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This paper studies a two-dimensional two-stage guillotine cutting stock problem which includes determination of how the items should be cut from stock panels in an optimal way, by developing and applying different solution approaches. An integer programming model with new features is proposed. A random key based genetic algorithm is utilized to obtain feasible solutions, and by applying a local search within the algorithm, a hybrid structure is acquired. Besides, a novel two-stage math-heuristic solution method is proposed. In the first stage of this method, a relaxation of the problem is solved; in the second, this solution is improved. The time to obtain the results of the developed two-stage math-heuristic solution approach is significantly lower than the other methods given in the article. Optimal solution values were obtained in 26 of 30 test problems taken from the literature with the proposed mathematical model, in 14 with mathematical programming based heuristic method, and in 16 with a random key based genetic algorithm. [ABSTRACT FROM AUTHOR]