SBIR Phase I: Application of Valid Cuts to Optimization of Process Industry Supply Chain Management

这个小型企业创新研究（SBIR）第一阶段项目将完成评估可行性所需的初步分析，定义需求，并确定应用新的建模技术所需的额外研究，这些技术之前被证明可以在优化问题的精确求解器的性能方面取得重大改进，并应用于过程工业。具体而言，我们建议采用明尼苏达大学先前开发的方法，在生产计划和调度模型中使用基于梯队库存约束的有效切割，并扩展这些方法，使其适用于实际问题。要解决的扩展包括表达性扩展（例如，从离散库存约束移动到连续库存约束，移动到连续时间模型，添加中间产品的买卖作为解决方案的一部分），以及求解器扩展。求解器扩展是必需的，首先，将这些技术扩展到实际的问题规模（阶梯式约束建模方法的标志之一是它扩展得很好），其次，包含处理上述模型扩展所需的各种约束。这个小企业创新研究第一阶段项目将通过改善美国经济中数千亿美元部门的经济表现，产生直接的商业影响。这项工作的结果也可以通过使用改进的优化技术来最大限度地减少稀缺资源的使用或废物的产生，从而以一种将产生社会影响的方式加以应用。通过将理论结构应用于现实世界问题的过程中所获得的经验和教训，科学理解将得到提升，这一过程既可以检验理论，也可以根据观察到的现象得出新的理论。此外，Adventium Enterprises通过其附属组织Adventium Labs，建立了一个实习项目，积极参与大学理工学院的本科生指导项目，并与几家学术机构合作，包括联合提案，在学术研讨会上发表演讲，教学课程，与几个学术部门的教师交换非正式报告。并广泛参与研究界，包括发表论文，组织研讨会，并在会议计划委员会任职。这个项目延续了同样的风格，扩大了学生对行业实践和关注的接触，加深了教师和行业从业者之间的理解和联系。

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.