REFORMULATION AND CUTTING-PLANE APPROACHES FOR SOLVING TWO-STAGE OPTIMIZATION AND NETWORK INTERDICTION PROBLEMS By SIQIAN SHEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy REFORMULATION AND CUTTING-PLANE APPROACHES FOR SOLVING TWO-STAGE OPTIMIZATION AND NETWORK INTERDICTION PROBLEMS By Siqian Shen August 2011 Chair: J. Cole Smith Major: Industrial and Systems Engineering This dissertation investigates models and algorithms for solving a class of two-stage optimization problems arising in a variety of practical problems, including network interdiction applications. Traditional decomposition methods for solving large-scale mixed-integer programs (MIP), such as Benders decomposition, cannot be utilized for solving the problems that we consider due to the presence of discrete variables in the second-stage problems. In the problems we study, there exist a finite set of first-stage feasible solutions and general mixed-integer variables in the second stage. We employ a decomposition strategy and apply the Reformulation-Linearization Technique (RLT) to obtain the convex hull of the formulation in terms of the second-stage variables. For some of the problems, we then describe modified Benders cuts for attaining optimality. For the others, we derive valid inequalities based on the subproblem reformulations or sub-optimal polynomial-time dynamic programming (DP) solutions. Our goal is to develop novel formulation and solution methodologies for solving several two-stage (stochastic) MIPs within practical time limits. We first consider a class of two-stage stochastic optimization problems arising in the protection of vital arcs in a critical path network. A project is completed after a series of dependent tasks are all finished. We analyze a problem in which task finishing times are uncertain, but can be insured a priori to mitigate potential delays. A decision maker must trade off costs incurred in insuring arcs with expected penalties associated