Mathematical modeling and optimization under uncertainty

不确定性下的数学建模与优化

• 批准号: RGPIN-2015-05063
• 负责人: Gzara, Fatma
• 金额: $ 1.46万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=613334
• 关键词: Mathematical; modeling; optimization; under; uncertainty

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.

数学模型产生的应用领域，如物流，供应链设计，分销和运输规划仍然具有挑战性，尽管最近的进展