Two methods for the solution of the mixed binary problem: A comparison of their computational efficiency

Our main objective is to solve the following problem: min cx + dy, s.t. Ax + By = b, y ≥ 0, x ∈ [0, 1]. Gomory's algorithm for the integer mixed problem and a lift and project cutting plane algorithm for mixed 0–1 problems due to Balas, were implemented. Balas's method uses in an explicit way the binary character of the variables. A comparison between the two methods with respect to the number of cuts and the execution time is done.