Sanjay Mehrotra

Bio: Sanjay Mehrotra is a Professor of Industrial Engineering and Management Sciences at Northwestern University. He graduated from Columbia University with his PhD in 1987. He is a Fellow of the Institute for Operations Research and Management Sciences (INFORMS) and has served on the INFORMS board of directors. He has also been the chair of INFORMS Optimization Society. Mehrotra 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. His current optimization research is on methodologies for decision making under uncertainty, and its applications. His health systems engineering work encompasses a wide range of topics that include predictive modeling, hospital operations modeling, and policy modeling.

Title: On Chance Constrained Optimization with Gaussian Mixture Models 
Co-authors: Shibshankar Dey, Adrian Maldonado, Anirudh Subramanyam, Yi Tianyang,

Abstract: We study solutions of linear chance-constrained models specified using a Gaussian Mixture distribution. The chance constraint is approximated using a piecewise-linear approximation of the standard normal cumulative distribution to develop mixed binary quadratic formulations that provide lower and upper bounds on the original problem to a desired tolerance. A second-order cone reformulation is also provided for an inner approximation of the model. Using an off-the-shelf solver, models with hundreds of random elements with up to 15 mixture components are solved effectively (some time in minutes) to obtain solutions for problems involving 0.95, 0.99, and 0.999 chance satisfaction. A sample average approximation approach fails to obtain any meaningful solution to these problems.