Mixed Integer Linear and Nonlinear Optimization for Disadvantaged Populations with Accents of Fairness and Balance

Azizi, Shima

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Mixed Integer Linear and Nonlinear Optimization for Disadvantaged Populations with Accents of Fairness and Balance

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The use of mixed-integer optimization to help disadvantage populations is a relatively new area of study in operations research literature. We focus on using mixed-integer optimization to make positive societal impact and assist disadvantaged populations, rather than solely helping capitalism to maximize profits. To this end, we investigate resource allocation, team orienteering, inventory management, and network flows to help three distinct groups of disadvantaged populations: refugees, foster children, and underserved patients relying on the emergency department for their non-urgent medical needs. A common characteristic of all three studies is that scarce resources need to distributed among a large vulnerable population, while incorporating fairness and balance considerations. First, we investigate a recent healthcare innovation, community paramedicine that enables proactive visit of patients, who frequent emergency rooms and who are recently discharged from a hospital, at home. We establish the first optimization-based framework that extends concepts from the team orienteering problem with the goals of increasing patient welfare, reducing readmissions and emergency department visits, and lowering hospital costs. We ensure that critically ill patients are visited, and further extend our model to determine any supplemental resources necessary to ensure feasibility. We develop a prioritization method for patient visits based on patient health features, integrating this information into our optimization-based approach that prioritizes patients based on fairness considerations, schedules patient visits and routes healthcare providers to maximize overall patient welfare, while favoring shorter tours. We use our methods to develop managerial insights via computational experiments on a variety of test instances based on real data from a hospital system in upstate New York. In particular, we are able to find optimal and nearly optimal tours that efficiently select, route, and schedule patients in reasonable time frames. Our results lead to insights that can be used to make managerial decisions regarding establishing (or improving existing) community paramedicine programs. Second, we study allocation challenges in a refugee camp systems. Camp-based refugees seek shelter in camps, and urban refugees in nearby areas. Aid distribution to camps should prioritize camp-based refugees, yet share excess inventory with urban refugees when able. Amid uncertainty in demands and replenishments, we derive an inventory policy to govern a camp’s aid sharing with urban refugees. We use the policy to construct expected costs of referring urban refugees elsewhere, depriving camp-based refugees, and holding, and embed them in a cost-minimizing aid allocation problem. We propose two approaches to solve the resulting optimization problem, and conduct computational experiments on a real-world case study as well as on synthetic data. Our results are complemented by an extensive simulation study that reveals broad support for our optimal thresholds and allocations to generalize across varied key parameters and distributions. We conclude by presenting related discussions that reveal key managerial insights into humanitarian aid allocation under uncertainty. Finally, we study a time-space network application in a humanitarian scheduling problem. The Foster Care Visitation Scheduling Problem consists of scheduling and routing foster care workers and foster children to regular meetings with their biological parents. The purpose is to improve the quality of life for foster children and assist foster care organizations to better manage their limited resources. We construct a time-space network representation of the problem and introduce an associated integer optimization problem that appropriately captures the real-world aspects of the problem, which is motivated by a particular foster care organization in upstate New York.

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