Models and algorithms for reliable facility location problems and system reliability optimization

Uncertainty is one of the elements that make this world so fascinating and dynamic. However, the existence of uncertainty also poses a great challenge to reliable system design. Our study uses various models and algorithms to address reliability issues in the context of (1) the uncapacitated facility location problem where facilities are vulnerable, and (2) the system reliability problem where components are subject to fail.; We first study the uncapacitated reliable facility location problem in which the failure probabilities are site-specific. The problem is formulated as a two-stage stochastic program and then a nonlinear integer program. Several heuristics that can produce near-optimal solutions are proposed for this computationally difficult problem. The effectiveness of the heuristics is tested through extensive computational studies. The computational results also lead to some managerial insights. For the special case where the failure probability at each facility is a constant (independent of the facility), we provide an approximation algorithm with a worst-case bound of 2.674.; Another part of our research is related to the development and application of a monotonic branch-reduce-bound algorithm, a powerful tool to obtain globally optimal solution to problems in which both the objective function and constraints possess monotonicity. We tailor the algorithm to solve a mixed integer nonlinear programming problem. Its convergence analysis and acceleration techniques are also discussed. The algorithm is then successfully applied to solve system reliability optimization problems in complex systems, including the redundancy allocation optimization problem and the reliability-redundancy allocation optimization problem. Compared to the existing techniques, the monotonic branch-reduce-bound algorithm is not only versatile but also very efficient in dealing with different types of problems in system reliability.; We also develop several models that can be used to fortify the reliability of the existing facilities. They are the extensions to the models in the first part of the dissertation and offer insights on which facility to choose and to what extent it should be fortified. The properties and solution methodologies of the models are discussed. In particular, a monotonic branch-reduce-bound algorithm is used to solve one of these models. The efficiency of the algorithm is demonstrated in the computational results.