DEMO seminar on "On Two-Stage Multiobjective Linear Programs: Formulations and Solution Methods"

Topic: On Two-Stage Multiobjective Linear Programs: Formulations and Solution Methods

Abstract: Many decision-making problems under uncertainty are resolved in a two-stage decision process. Strategic decisions being here-and-now decisions are made in the first stage while tactical/operational decisions being wait-and-see decisions are made in the second stage. For example, in engineering design, a two-stage decision-making structure is common because certain high-level design decisions must be made to allow further development of physical or simulation models from which additional low-level design decisions can be made accordingly. For example, the selection of a design configuration is conducted in the first stage whereas the second stage deals with the decisions in terms of product utilization and applicability in various scenarios.
Two-stage multiobjective linear programs (TSMOLPs) model two-stage decision processes under uncertainty having conflicting linear objectives and linear constraints at every stage. Addressing the worst-case uncertainty scenario, the TSMOLP is transformed into the two-stage robust counterpart (TSrMOLP) whose efficient solutions are the robust-efficient solutions for the original problem.
The TSrMOLP can be studied in two ways. One goal is to compute the first-stage feasible solutions that are efficient with respect to the first and second-stage objectives. The other goal is to recognize the first- and second-stage decision makers' preferences and develop an interactive procedure to compute a first-stage feasible solution that is the most preferred efficient solution with respect to the first- and second-stage objectives.
The assumptions on discrete or continuous uncertainty and the number of second-stage objectives, and the application of weighted-sum scalarization transform the TSrMOLP into single-objective optimization problems (SOPs) of an increasing level of difficulty. The SOPs' optimal solutions provide exact or approximate efficient solution to the TSrMOLP. Solution approaches using Benders' decomposition, a Parametric Linear Programming solver, and the Biconvex Approximate Simplex method are given and illustrated with biobjective examples.


Bio: Margaret M. Wiecek is Professor of Mathematical Sciences in the School of Mathematical and Statistical Sciences and has held joint professorship with the Department of Mechanical Engineering at Clemson University in Clemson, South Carolina. She has obtained a Ph.D. degree in Systems Engineering from the AGH University of Science and Technology in Krakow, Poland. Her research area includes theory, methodology, and applications of mathematical programming with special interest in multiobjective optimization and decision-making. Part of her work is interdisciplinary since she has introduced new multiobjective optimization concepts and methods into engineering optimization to enrich the field of automotive and structural design. She has served as the President of the MCDM Section of INFORMS. She serves as an area editor for Journal of Multi-Criteria Decision Analysis, an associate editor for Journal of Optimization Theory and Applications, and is a member of the editorial boards for International Journal of Multicriteria Decision Making, and Decision Making in Manufacturing and Services. In recognition of her lifetime contributions, she has been awarded the MCDM Gold Medal by the International Society on MCDM.

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