This Small Business Innovation Research (SBIR) Phase I project will accomplish the preliminary analysis required to assess feasibility, define requirements, and determine additional research required in order to apply novel modeling techniques, previously demonstrated to deliver significant improvements in the performance of exact solvers for optimization problems, to applications in the process industries. Specifically, we propose to take methods previously developed at the University of Minnesota for using valid cuts based on echelon inventory constraints in production planning and scheduling models, and to extend those methods to make them applicable to real problems. The extensions to be addressed include expressive extensions (e.g., moving from discrete to continuous inventory constraints, moving to a continuous time model, adding buying and selling of intermediates as part of the solution), as well as solver extensions. The solver extensions are required, first, to scale these techniques up to realistic problem sizes (one of the hallmarks of the echelon constraint modeling approach is that it scales well), and second, to encompass the kinds of constraints required to address the model extensions above.
This Small Business Innovation Research Phase I project will have direct commercial impact, through improved economic performance in a multi-hundred-billion dollar sector of the U.S. economy. The results of this work may also be applied in a way that will have societal impact, through the use of improved optimization techniques to minimize the use of scarce resources, or the production of waste material. Scientific understanding will be advanced through the experience gained and lessons learned in applying theoretical constructs to real-world problems in a process that will both test the theory and elicit new theory based on observed phenomena. In addition, Adventium Enterprises, through its a_liate organization, Adventium Labs, has an established internship program, active participation in the University's Institute of Technology undergraduate mentoring program, and a record of collaboration with several academic institutions including joint proposals, presentation at academic colloquia, teaching courses, an exchange of informal presentations with faculty in several academic departments, and extensive participation in the research community, including presenting papers, organizing workshops, and serving on conference program committees. This project continues in the same vein, broadening the exposure of students to industry practices and concerns, and deepening the understanding and links between faculty and industry practitioners.
