A binary integer linear program with multi-criteria and multi-constraint levels

This paper introduces a mathematical formulation of a binary integer linear program with multi-criteria and multi-constraint levels (MC²) by using the framework of MC² linear programming. A branch-and-bound procedure is developed to solve such MC² binary integer linear programming problems. In this branch-and-bound procedure, an MC² linear programming problem is adopted for the relaxation of each subproblem in the branches. The upper bound of a subproblem is defined as the expected objective value of its relaxation problem having a probability distribution over parameters of multi-criteria and multi-constraint levels. A numerical example is used to demonstrate the applicability of the proposed method in solving MC² binary-integer-linear programming problems.