An interactive sorting method for additive utility functions

In this paper, we consider the problem of placing alternatives that are defined by multiple criteria into preference-ordered categories. We consider a method that estimates an additive utility function and demonstrate that it may misclassify many alternatives even when substantial preference information is obtained from the decision maker (DM) to estimate the function. To resolve this difficulty, we develop an interactive approach. Our approach occasionally requires the DM to place some reference alternatives into categories during the solution process and uses this information to categorize other alternatives. The approach guarantees to place all alternatives correctly for a DM whose preferences are consistent with any additive utility function. We demonstrate that the approach works well using data derived from ranking global MBA programs as well as on several randomly generated problems.