Relating reference points and weights in multiple objective linear programming

A frequent problem for decision makers analysing decisions involving multiple objectives is the identification and selection of the most preferred option from the set of non-dominated solutions. Two techniques, weighted sum optimization and reference point optimization, have been developed to address this problem for multiobjective linear programming problems (MOLP). In this paper, we examine the relationship between these two techniques. We demonstrate that the values of the dual variables associated with auxiliary constraints of the reference point technique are equal to the weight values used to compute the same non-dominated solution via the weighted sum technique. This insight will enable the development of new interactive solution procedures for MOLPs which allow the decision maker to readily switch from one method to the other during the search for the most preferred non-dominated solution. The advantages of the approach are discussed in the paper.