The goal of this research is to develop a mathematical model for determining a route that attempts to reduce the risk of low probability, high consequence accidents by trying to minimize the conditional expected risk given that an accident has occurred. However, if this were the only objective of the model, then poor decisions could result. Therefore, the model formulated is a bicriterion network optimization model that considers trade-offs between the conditional expectation of a catastrophic outcome and more traditional measure of risk dealing with the expected value of the consequence. More specifically, the problem we wish to address involves finding a path that minimizes the conditional expectation of a catastrophic outcome such that the expected risk is lesser than or equal to a pre-determined value, v. The value v, is user-prescribed and is prompted by the solution to the shortest path problem which minimizes the expected risk. Two approaches are investigated. First, we apply a suitable k-shortest path algorithm to rank the extreme points for which the objective function value remains lesser than or equal to v. This enables the selection of a best path with respect to the conditional expectation objective function Second, we develop a fractional programming branch-and-bound approach that IS more robust with respect to the selected value of v. A simple numerical example is provided for the sake of illustration, and the model is also tested using real data Both data acquisition issues as well as algorithmic computational Issues are discussed. / Master of Science