The research objective of this Faculty Early Career Development (CAREER) project is to advance models, theory and algorithms to solve a difficult class of optimization problems called chance-constrained mixed-integer programs (CC-MIP). Although CC-MIPs are ubiquitous in practice, operations research theory and algorithms provide limited guidance for this class of problems. CC-MIPs include quality of service or reliability constraints; they are dynamic, contain uncertain data, and involve discrete decisions. The resulting multi-stage stochastic mixed-integer programs are challenging both theoretically and computationally. The service level requirements are modeled with joint chance constraints, which are non-convex. In addition, the deterministic equivalents of CC-MIPs are very large-scale MIPs. To overcome these challenges, this research aims to develop a unified theory and computational methodology, utilizing extended formulations, polyhedral combinatorics, and decomposition algorithms. The research will be pursued in four major thrusts: (1) chance-constrained mixed-integer programs, (2) dynamic chance-constrained problems, (3) chance-constrained problems with special structures, and (4) chance-constrained problems with technology uncertainty.
The results from this research will advance decision-making tools in several sectors that operate under uncertain environments and high service level expectations, such as energy, telecommunications, finance, emergency management, and distribution systems. For example, the modeling framework and strong cutting planes for joint chance constraints may be incorporated into existing open-source MIP modeling languages and software to improve their ability to solve CC-MIPs that arise in practice. The educational goals of this award are to develop novel programs that will arm the next generation of students with skills to incorporate uncertainty into optimization theory, models and solution methods, and to attract women and other under-represented groups to pursue advanced research in this field. In pursuit of these goals, case studies will be developed from application areas to highlight the importance of incorporating uncertainty into decision-making processes, and tutorials will be given through various fora to disseminate the research results to a broader audience.
