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.
