DECOMPOSITION ALGORITHMS FOR TWO-STAGE STOCHASTIC INTEGER PROGRAMMING By JOHN H. PENUEL, JR. 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 DECOMPOSITION ALGORITHMS FOR TWO-STAGE STOCHASTIC INTEGER PROGRAMMING By John H. Penuel, Jr. August 2009 Chair: J. Cole Smith Major: Industrial and Systems Engineering Stochastic programming seeks to optimize decision making in uncertain conditions. This type of work is typically amenable to decomposition into firstand second-stage decisions. First-stage decisions must be made now, while second-stage decisions are made after realizing certain future conditions and are typically constrained by first-stage decisions. This work focuses on two stochastic integer programming applications. In Chapter 2, we investigate a two-stage facility location problem with integer recourse. In Chapter 3, we investigate the graph decontamination problem with mobile agents. In both problems, we develop cutting-plane algorithms that iteratively solve the first-stage problem, then solve the second-stage problem and glean information from the second-stage solution with which we refine first-stage decisions. This process is repeated until optimality is reached. If the second-stage problems are linear programs, then duality can be exploited in order to refine first-stage decisions. If the second-stage problems are mixed-integer programs, then we resort to other methods to extract information from the second-stage problem. The applications discussed in this work have mixed-integer second-stage problems, and accordingly we develop specialized cutting-plane algorithms and demonstrate the efficacy of our solution methods.