Convergence and Validation of Interactive Methods in MCDM: Simulation Studies

A wide array of interactive methods, or (more correctly perhaps) methods of progressive articulation of preference, are available to the MCDM practitioner. In some cases (such as the Zionts-Wallenius method) it can be proved that the procedures converge in the sense of terminating after a finite number of iterations. In other instances, no such convergence can be demonstrated, and such methodologies must be classed as heuristics. It is, however, by no means evident that mathematical convergence is either necessary or sufficient to demonstrate the practical validity of a procedure. Practical validity requires that within a very small number of iterations, the decision maker is enabled to gain sufficient understanding of the decision Space and the necessary trade-offs, to have confidence in and be satisfied with the Solution selected at that stage with the help of the method. In this paper we review Simulation studies, in which interactive methods of both the value function and goal programming types have been implemented in hypothetical computer-generated decision contexts. The results of these Simulation studies provide a substantial level of Validation for both types of interactive methods, but do also provide warnings of how careless implementation of these methods can lead to very poor results.