Equitable and Efficient Resource Allocation using Stochastic Fractional Optimization

该奖项通过研究有限资源在参与实体之间的公平分配，有助于促进国家健康、繁荣和福利。在这种情况下，公平是通过考虑每个实体的需求与其获得的供应的比率来衡量的。这些问题，被称为分数程序，出现在许多情况下，很难解决，因为目标函数是高度非凸的。本课题将研究随机分数式程序的有效解。该方法将应用于改善肝移植的公平性，其中有大量的供应和需求数据集，以及随机数据包络分析（DEA），这是一种广泛使用的评估决策单位相对生产力的方法。该项目将支持研究生和本科生教育，并为学生提供发展解决社会重要问题的操作方法的机会。本研究项目将发展新型随机分数规划（SFP）的求解方法。这些问题的解决具有挑战性，获得最优或接近最优解需要开发有效的算法。与一般的非线性优化模型相比，SFP问题具有有限的结构。该研究将在算法开发中利用这种结构，并将研究生成近似原始模型的场景的技术。将开发计算效率高的算法来解决线性、凸凹和凸凸情况下的近似问题。在此基础上，将使用分布鲁棒泛化来促进敏感性分析，并将探索机会约束模型。将所开发方法的性能与通用非线性和全局优化求解器NITRO和BARON进行比较。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award contributes to the advancement of national health, prosperity, and welfare by studying the equitable distribution of limited resources among participating entities. In this setting, equity is measured by considering the ratio of each entity's need to the supply it receives. These problems, known as fractional programs, arise in a number of settings, and are difficult to solve because the objective functions are highly non-convex. This project will address the efficient solution of stochastic fractional programs. The methodology will be applied to improve equity in liver transplantation, where a large dataset of supply and demand data are available, and to stochastic Data Envelopment Analysis (DEA), a widely used method for evaluating relative productivity of decision making units. The project will support graduate and undergraduate education and provide opportunities for students to develop operational methods to tackle societally important problems. This research project will develop solution methods for novel stochastic fractional programs (SFP). These problems are challenging to solve, and obtaining an optimal or near optimal solution requires development of efficient algorithms. SFP problems have limited structure when compared to a general nonlinear optimization model. The research will exploit this structure in algorithm development and will investigate technique to generate the scenarios to approximate the original model. Computationally efficient algorithms will be developed to solve the approximated problem for the linear, convex-concave, and convex-convex cases. Building on this, distributionaly robust generalizations will be used to facilitate sensitivity analysis, and a chance constraint model will be explored. The performance of the developed methods will be compared against general purpose nonlinear, and global optimization solvers NITRO and BARON.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.