Preference Order Dynamic Programming

Abstract

The dynamic programming recursive procedure has provided an efficient method for solving a variety of multi-stage decision problems in which the objective is measured by a real valued utility function. In this paper we propose that the real valued objective function be replaced by preference relations. Sufficient conditions are given on the structure of the preference relations to insure that the recursive dynamic programming procedure yields an optimal sequence of decisions. The solution method is well adapted to an interactive mode of implementation in which there is a dialogue between the decision maker and a source of information and analysis (e.g., a computer). The “computer” collects, analyzes, and presents information on a set of alternatives to the decision maker who then communicates to the “computer” his choice of the best alternatives in the set. The process is repeated, stage by stage, thus generating an optimal sequence of decisions. The approach should be particularly useful in dealing with multi-stage decision problems involving design and/or operation of facilities and multi-period public projects where a variety of desiderata must be considered (i.e., a simple cost or benefit function is inadequate).