An efficient linearization approach for mixed-integer problems

Abstract

Oral and Kettani previously developed a linearization technique, published in Management Science in 1990 and in Operational Research in 1992, for solving quadratic and cubic mixed-integer problems. For a quadratic problem with n 0–1 variables, their method would introduce n additional continuous variables and n auxiliary constraints. For a cubic problem with n 0–1 variables, their method would introduce 3 n additional continuous variables and 3 n auxiliary constraints. This linearization approach of Oral and Kettani has been accepted as the most efficient linearization technique published, requiring the least number of additional continuous variables and auxiliary constraints. However, their method is difficult to extend for linearizing higher order polynomial terms that appear in mixed-integer problems, and in addition, all constraints should be kept as linear. This note proposes a new general model for linearizing various orders of mixed-integer problems which cannot be solved by Oral and Kettani's model when the order is higher than three. Some computational results show that the proposed model is more efficient than Oral–Kettani's method because it uses less additional variables and auxiliary constraints to linearize the same size of mixed-integer problems. In addition, the proposed model can be easily applied to polynomial mixed-integer terms that appear in the objective function and/or constraints.