In this talk, we will cover two topics related to stochastic network optimization. In the first part, we introduce a stochastic shortest path interdiction problem where a leader interdicts a subset of arcs given a certain budget, and maximizes the worst-case objective of a follower who seeks a path with a sufficiently short distance under random traveling cost on each arc. In particular, we study the follower being risk averse, who aims to restrict the risk of traveling between origin and destination nodes for a distance that is longer than a given threshold value. We analyze two variants of the problem depending on the follower’s ability of reacting to the uncertainty. We propose branch-and-cut algorithms and meta-heuristics for solving the resulting bi-level programs.

In the second part, we consider critical infrastructure design and operations with supply, transshipment, demand nodes, and random arc disruptions with known probabilities. We analyze two types of two-stage stochastic optimization models. Model 1 focuses on a single network with small-scale failures, and repairs arcs for quick service restoration. Model 2 considers multiple interdependent infrastructures under large-scale disruptions, and mitigates cascading failures by selectively disconnecting failed components. The goal is to minimize the total cost of infrastructure design and recovery operations. We develop cutting-plane algorithms and heuristic approaches.  We test Model 1 on the IEEE 118-bus system and Model 2 on systems consisting of the 118-bus system, a 20-node network, and/or a 50-node network, with randomly generated interdependency sets in three different topological forms (i.e., chain, tree, and cycle). The results show how the optimal solutions are affected by infrastructure sizes and interdependency forms.
 
Bio:
Siqian Shen is an Assistant Professor of Industrial and Operations Engineering at the University of Michigan. She obtained a B.S. degree from Tsinghua University in China in 2007 and a Ph.D. from the University of Florida in Industrial and Systems Engineering in 2011. Her research interests are in mathematical optimization, particularly in stochastic programming, network optimization, and integer programming. Applications of her work include power system optimization, health care operations management, transportation networks, and cloud computing. She was named one of the two runners-up of the 2010 INFORMS Computing Society Best Student Paper award, was awarded the 1st Place of the 2012 IIE Pritsker Doctoral Dissertation Award, and was a recipient of 2012 IBM Smarter Planet Innovation Faculty Award.