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Solving Multi-level Problems Using Multi-Objective Optimization for Robust Solutions

Most engineering design and control system problems involve a hierarchy of sub-problems in which a lower-level sub-problem must be solved based on the setting of its upper-level sub-problems. Not only is such a hierarchical treatment necessary for an accurate evaluation of a design or a process, it also enables a systematic and computationally tractable procedure for performing the overall analysis.

In optimizing such hierarchical problems, multiple levels are generally reduced to a single level for solution. This is done mostly to be able to use an existing optimization procedure that cannot be extended to address the multi-level problem directly.

In this research project, we extend our existing bi-level evolutionary multi-objective optimization (BEMO) approach for solving multi-level problems efficiently. We shall specifically address the tri-level optimization structure representing the relationship between strategic, tactical, and operational decisions in the design and management of extended supply chains. In this context, the strategic decisions involve network design, tactical decisions involved production planning and sourcing, and the operational decisions involve production scheduling and process optimization.

The current optimization literature does not address these three decision levels in a synergistic manner, thereby leading to significant sub-optimal performance and financial losses.

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Eli Broad College of Business

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