INTERACTIVE DECISION MAKING INVOLVING INTEGER BICRITERION PROBLEMS - ALGORITHMS AND APPLICATION
Abstract
Decisions with multiple criteria are quite prevalent in government, industry and other organizations. Analytical thinking along with mathematical formulations of the problem has been very helpful in developing solution procedures for these problems. This dissertation concentrates on developing algorithms to solve a bicriterion mathematical programming (BIMP) problem with integer variables. Algorithms developed in this research are of three types--completely interactive, partly interactive and non-interactive. Four methods, along with the necessary theoretical foundations, have been developed in this research. First, we develop an interactive paired comparison method (PCM) that requires the Decision Maker to express preferences between a pair of efficient solutions. The efficient solutions are generated by solving a single objective problem with weights assigned to each objective. However, when there exist more than two optimal solutions to the single objective problem, the interactive PCM is not guaranteed to generate all efficient solutions. Hence, a second interactive algorithm is developed that uses the 'Tchebycheff norm' approach to generate the efficient points. This approach is shown to converge better under certain qualifying assumptions on the criteria space. We then present a non-interactive method, called decomposition method, that identifies all the efficient points of the BIMP problem. Finally we develop a 'hybrid method', that combines the best features of both the interactive PCM and the decomposition method. The hybrid method is partly interactive. An application of the BIMP problem to the selection of bayesian acceptance plans in quality control has also been presented. The quality control problem is formulated as a BIMP problem with Average Lot Inspection Cost (ALIC) and Average Outgoing Quality (AOQ) as the two conflicting criteria. The interactive PCM using a Tchebycheff norm for generation of efficient points is used to solve the BIMP problem. Computer software is also developed to solve the quality control problem; it has been successfully implemented on an IBM 3081 system. An experiment to test the potential of the software has been completed using Industrial Engineering students from a quality control course and a practicing quality control manager. The results and conclusions of this experiment are also discussed.
Degree
Ph.D.
Subject Area
Industrial engineering
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