  Parametric path problems arise independently in diverse domains, ranging from
transportation to finance, where they are studied under various assumptions. We
formulate a general path problem with relaxed assumptions, and describe how
this formulation is applicable in these domains.
  We study the complexity of the general problem, and a variant of it where
preprocessing is allowed. We show that when the parametric weights are linear
functions, algorithms remain tractable even under our relaxed assumptions.
Furthermore, we show that if the weights are allowed to be non-linear, the
problem becomes NP-hard. We also study the mutli-dimensional version of the
problem where the weight functions are parameterized by multiple parameters. We
show that even with two parameters, the problem is NP-hard.
