A WIN-WIN approach to multiple objective linear programming problems

Interactive decision making arose as a means to overcome the uncertainty concerning the decision maker's (DM) value function. So far the search is confined to nondominated alternatives, which assumes that a win-lose strategy is adopted. The purpose of this paper is to suggest a complementary interactive algorithm that uses an interior point method to solve multiple objective linear programming problems. As the algorithm proceeds, the DM has access to intermediate solutions. The sequence of intermediate solutions has a very interesting characteristic: all of the criteria are improved, that is, a solution (x(2)) over tilde, that follows another solution (x(1)) over tilde, has the values of all objectives greater than those of (x(1)) over tilde. This WIN-WIN feature allows the DM to reach a nondominated solution without making any trade-off among the objective functions. However, there is no impediment in proceeding with traditional multiobjective methods.