AN INTERACTIVE PAIRED COMPARISON METHOD FOR MULTIPLE CRITERIA DECISION MAKING OPTIMIZATION (MOLP)
Abstract
In this dissertation a man-machine interactive mathematical programming method based on the theory of Multiple Objective Linear Programming (MOLP) simplex method is presented for solving multiple criteria problems involving a single decision maker. The composite function or overall utility function of the Decision Maker (DM) is unknown explicitly but it is assumed to be implicitly a linear function. To solve the multiple objective problem, the DM is requested to provide his strength of preferences for a pair of utility efficient extreme point solutions. The DM should respond with strong preference, weak preference, or naive indifferences (undecided) to a comparison of two alternatives. A theory for paired comparisons has been developed where the utility function is linear, and there exist some linear constraints on the weights associated with the DM's utility function. The relation of paired comparisons and MOLP simplex method is identified and established. Also, a theory for implementing the DM's strengths of preferences is developed to assist in a faster and better estimation of his implicit preferences. In comparison to the widely used Zionts-Wallenius (Z-W) method for MOLP problems, the following advantages are given for the Paired Comparison method: (i) concept of "utility efficiency" and its advantages over "trade-off" efficiency"; (ii) a solution to the problem of decreasing utility of the Z-W method; (iii) a theory for strength of preferences and its application; (iv) a better handling of DM's undecided preferences; and (v) a theory and an approach for handling the problem of inconsistency of the DM. Detailed computational results comparing the Paired Comparison simplex method and the Z-W method are discussed. Also, several numerical examples illustrating the theoretical contributions are provided. An implementation and evaluation of Multiple Criteria Decision Making (MCDM) mathematical programming for the United States glass industry energy system is also provided as a case study.
Degree
Ph.D.
Subject Area
Industrial engineering
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