Risk-Averse Multi-Stage Mixed-Integer Stochastic Programming Problems
Ali Irfan Mahmutoğulları
Department of Industrial Engineering, TED University
Risk-averse multi-stage mixed-integer stochastic programming problems form a class of challenging optimization problems since the problem size grows exponentially with the number of stages, they are non-convex due to integrality restrictions, and their objective functions are nonlinear in general. In this talk, we first focus on such problems with an objective of dynamic mean conditional value-at-risk. We propose a scenario tree decomposition approach to obtain lower and upper bounds for their optimal values and then use these bounds in an evaluate-and-cut procedure which serves as an exact solution algorithm for such problems with integer first-stage decisions. Later, we consider a risk-averse day-ahead scheduling of electricity generation or unit commitment problem where the objective is a dynamic coherent risk measure. We consider two different versions of the problem: adaptive and non-adaptive. In the adaptive model, the commitment decisions are updated in each stage, whereas in the non-adaptive model, the commitment decisions are fixed in the first-stage. We provide theoretical and empirical analyses on the benefit of using an adaptive multi-stage stochastic model. We also conduct computational experiments in order to verify the theoretical findings and discuss the results of these experiments.
Ali İrfan Mahmutoğulları is an assistant professor at Department of Industrial Engineering, TED University. He received his Ph.D. degree from Department of Industrial Engineering, Bilkent University in 2019. He earned his B.S. and M.S. degrees from the same department in 2011 and 2013, respectively. During his Ph.D. study, he was a visiting scholar at H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology from October 2017 to July 2018. His research interests include risk-neutral and risk-averse multi-stage stochastic optimization models and their applications to finance and energy systems.
Friday, April 26, 2019 at 4.00 pm in IE03