A reference direction approach to multiple objective integer linear programming

We propose the use of a reference direction/reference point approach to solving multiple objective integer linear programming problems. The reference direction/reference point is determined by the aspiration levels for the criteria that the decision-maker wants to improve. Within this framework, two methods are developed, viz., a pure integer method that operates entirely with integer solutions and a continuous/integer method that works with continuous solutions and finds an integer solution closest to the continuous solution in terms of the achievement scalarizing function. Obviously, the pure integer method is time consuming. We therefore propose a decision support system that combines the two methods. This way the advantages of each method can be used to their fullest extent. We illustrate the proposed decision support system with a numerical example.