Equitable and Efficient Resource Allocation using Stochastic Fractional Optimization

使用随机分数优化实现公平且高效的资源分配

• 批准号: 1763035
• 负责人: Sanjay Mehrotra
• 金额: $ 37.81万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-09-01 至 2023-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1763035&HistoricalAwards=false
• 关键词: Equitable; Efficient; Resource; Allocation; using

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.

该奖项通过研究有限资源在参与实体之间的公平分配，为促进国家健康，繁荣和福利做出贡献。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，被称为分式规划，出现在许多设置中，并且难以解决，因为目标函数是高度非凸的。 这个项目将解决随机分式规划的有效解决方案。 该方法将被应用于提高公平性的肝移植，其中一个大的数据集的供应和需求数据，并随机数据包络分析（DEA），一种广泛使用的方法，用于评估相对生产力的决策单位。该项目将支持研究生和本科生教育，并为学生提供机会，制定解决社会重要问题的操作方法。本研究计画将发展新颖随机分式规划（SFP）的求解方法。这些问题是具有挑战性的解决，并获得最佳或接近最佳的解决方案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。本研究将利用这种结构的算法开发，并将调查技术，以产生的情况下，近似原始模型。 将开发计算效率高的算法来解决线性、凹凸和凹凸情况下的近似问题。在此基础上，将使用分布稳健的概括来促进敏感性分析，并探讨机会约束模型。所开发的方法的性能将与通用非线性和全局优化求解器硝基和BARON进行比较。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

项目成果

A Solution Approach to Distributionally Robust Joint-Chance-Constrained Assignment Problems

• DOI: 10.1287/ijoo.2021.0060
• 发表时间: 2022-02
• 期刊: INFORMS J. Optim.
• 作者: Shanshan Wang;Jinlin Li;Sanjay Mehrotra

An algorithm for stochastic convex-concave fractional programs with applications to production efficiency and equitable resource allocation

• DOI: 10.1016/j.ejor.2023.12.020
• 发表时间: 2024-06
• 期刊: European Journal of Operational Research
• 影响因子: 6.4
• 作者: Shibshankar Dey;Cheolmin Kim;Sanjay Mehrotra

Numerical Methods for Integral Equations of the Second Kind with NonSmooth Solutions of Bounded Variation

• DOI: 10.1137/22m1480422
• 发表时间: 2022-10
• 期刊: SIAM J. Numer. Anal.
• 作者: Shukai Li;Sanjay Mehrotra

Solution Approaches to Linear Fractional Programming and Its Stochastic Generalizations Using Second Order Cone Approximations

线性分式规划的求解方法及其使用二阶锥近似的随机推广

• DOI: 10.1137/19m1308165
• 发表时间: 2021
• 期刊: SIAM Journal on Optimization
• 影响因子: 3.1
• 作者: Kim, Cheolmin;Mehrotra, Sanjay
• 通讯作者: Mehrotra, Sanjay