Abstract: We study a service center location problem with ambiguous utility gains and uncertain demand. The model is motivated by the problem of deciding medical clinic/service centers, possibly in rural communities, where residents need to visit the clinics to receive health services. A resident gains his utility based on service features such as travel distance and waiting time at the facility that depend on the clinic location. The elicited location-dependent utilities are assumed to be ambiguously described by an expected value and variance constraint. We show that despite a non-convex nonlinearity, given by a constraint specified by a maximum of two second-order functions, the model admits a mixed 0-1 second-order cone (MISOCP) formulation, which leads to a two-stage-MISOCP under uncertain demand. We study the non-convex substructure of the problem, and present methods for developing its strengthened formulations by using valid tangent inequalities. We also develop a new branch-and-cut algorithm for the two-stage-MISOCP problem. Computational study shows the effectiveness of solving the strengthened formulations. Examples are used to illustrate the importance of including decision dependent ambiguity.
Biography: Sanjay Mehrotra is a Professor of Industrial Engineering and Management Sciences at Northwestern University. He is a Fellow of the Institute for Operations Research and Management Sciences (INFORMS), and the cohort leader of 2022 INFORMS Fellow Selection Committee. He is the founding director of the Center for Engineering and Health, which is a part of the Institute for Public Health and Medicine at Northwestern University. He is an expert in methodologies for decision making under uncertainty, and its applications to problems in Health Systems Engineering. He has made major contributions to the areas of Optimization Algorithms and Health Systems Engineering, for which he is known internationally. Professor Mehrotra’s current methodology research is focused on robust decision making. His health systems engineering work encompasses a wide range of topics that include predictive modeling, hospital operations modeling, and policy modeling while using and developing modern operations research tools. Professor Mehrotra has made seminal contributions to the liver and kidney distribution modeling towards reducing geographic disparity. His current healthcare systems engineering research is focusing on reducing kidney discards, improving the understanding of liver cirrhosis, and developing scalable systems for infectious disease management, and patient centered care. He has been the department editor for the Optimization department and Health Systems Engineering department for the journal IIE-Transactions. He is also the founding co-Editor of Healthcare section for the journal Naval Research Logistics. In the Optimization area Mehrotra is widely known for his predictor-corrector method for solving continuous optimization problems. He has been INFORMS Optimization Society chair and has also served on INFORMS Board of Directors. His research has been funded by NIDDK, NIA, NIBIB, NSF, ONR and DOE.