Finding a shortest path in a network is a classical problem in discrete optimization. The systems underlying the network models are subjects to a variety of sources of uncertainty. The purpose of this thesis is to model the shortest path problem with probabilistic arc failures with the aim of finding short but reliable paths through the network. This thesis proposes to use Conditional Value-at-Risk (CVaR) to find a path that is robust under probabilistic arc failures. CVaR, a quantitative risk measure, is roughly the mean excess loss associated with a decision. This thesis also develops three models of losses due to arc failures. Mixed integer linear programming models for the stochastic shortest path problem with probabilistic arc failures are formulated and implemented. The optimization models limit the CVaR of the loss due to arc failures as measured by the models of loss developed in the thesis.Industrial Engineering & Managemen
