An interactive algorithm for multicriteria decision making: the attainable reference point method

An interactive algorithm, the attainable reference point method, is proposed for finding a satisfactory solution to a general multicriteria decision making problem. The decision-maker is only required to modify the reference value of the satisfactory objectives to generate a new attainable reference point in each iteration step. The lexicographic weighted Tchebycheff program associated with the attainable reference point is constructed to guarantee the efficiency of all the discussed points. The value of the unsatisfactory objective chosen by the decision-maker is improved to be satisfactory. Thus its reference value does not need to be modified again in later iterations, and a satisfactory solution can be derived in finite steps. A numerical example is presented to demonstrate the feasibility and efficiency of the proposed method