A bi-reference procedure for interactive multiple criteria programming

The paper presents an interactive procedure to search the set of nondominated outcomes of a multiple criteria linear programming problem. The procedure requires the decision maker to specify the worst outcome. Then, the ideal outcome is identified, and the improvement direction from the worst to ideal outcomes is constructed. A trial solution is found by moving from a current solution along the improvement direction, while maximizing the step size. For a trial solution, the decision maker is requested to partition the set of objective functions into three categories: those to be improved, those which may remain unchanged, those which may be relaxed. Based on this partition, the procedure displaces the worst and ideal outcomes, calculates the new improvement direction, and the entire process is repeated. The method terminates when two successive trial solutions are reasonably similar.