A Progressive Algorithm for Modeling and Solving Multiple-Criteria Decision Problems

We consider a decision maker (DM) who has a set of possible decision alternatives, from which one (a “best”) is to be chosen. However, all decision alternatives are not at the DM's disposal initially, nor is full knowledge of his/her utility/value function. Therefore, the DM evaluates only the available subset of all decision alternatives, from which he/she chooses a most preferred one. Obviously, this decision is not necessarily “globally” best. Two natural questions arise: How good is the most preferred solution? What are the chances of finding better solutions by considering additional alternatives? We describe and illustrate a general progressive algorithm and the supporting theory for modeling and solving this problem when alternatives are introduced dynamically.