This paper discusses the variance-constrained shortest path problem. T
his problem can be used to model any application in which the travel c
osts on a link are not deterministic, but follow a distribution that h
as possible correlation with travel cost on other links. Exact solutio
n methods are proposed, and results are reported from computational ex
periments on data sets derived from a real-life routine scenario invol
ving the transportation of liquefied-gas hazardous materials.