Mathematical modeling and optimization under uncertainty

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Mathematical models arising from application areas such as logistics, supply chain design, distribution, and transportation planning remain challenging despite the recent advances in*software and hardware capabilities. In addition to large size, variability in design parameters****leads to significant complexity both in modeling and in solution methodologies. While it*is common to assume that parameters are known and constant, variability is inherent to*all practical problems and often times, solutions generated by deterministic models turn out*to be infeasible or far from optimal when implemented. On the other hand, optimization*problems that model variability explicitly are generally more challenging due to stochasticity*and nonlinearity. The appropriate approach to model randomness depends on the amount of*information available. Under perfect information, parameters are assumed to be known and*constant during the planning horizon and the resulting models are deterministic. Under risk,*stochastic modeling assumes that parameters follow a probability distribution. Robust*optimization is an emerging framework for modeling under uncertainty where no distribution*information is available.****The focus of this research is on modeling and optimization under uncertainty. We propose*models and develop specialized optimization tools to handle uncertainty. Fortunately such*complex problems tend to exhibit special structure, which makes them suitable for decomposition methodologies such as Lagrangian relaxation/column generation, Dantzig-Wolfe decomposition, and Benders*decomposition. Two application areas will be investigated under this framework: disaster response network design and airline operations planning. In both application areas, stochastic*and robust optimization will be explored. The goal is to come up with robust designs that*optimize classical objectives like profit or cost but also remain valid or allow smooth recovery*when settings change.***The proposal provides rich research questions suitable for rigorous highly qualified personnel training.  In total, three Ph.D. and four MASc. students will have the opportunity to carry out both theoretical and applied research.  They will gain skills in analysis and modeling of quantitative decision making as well as in developing algorithms and using sophisticated optimization software. The students will apply their research work in decision making for disaster management and airline operations planning. Both areas are highly applicable and provide students the qualifications to work in academia, the airline industry, government,  aid agencies, etc.  **