Dynamic parametric bounds on efficient outcomes in interactive multiple criteria decision making problems

Bounds on efficient outcomes in interactive multiple criteria decision making problems are derived. Bounds are dynamic, i.e., they become stronger with the growing number of explicitly identified outcomes. They are also parametric with respect to weighting coefficients. Computational cost to calculate bounds is negligible. Bounds of the sort offer a breakthrough for prohibitive size and/or solution time bottlenecks by allowing a decision maker to interact with an approximation of the underlying mathematical model rather than the model itself. Possible applications of bounds to existing interactive decision making algorithms are discussed. Illustrative numerical examples are given.