Strategies, models, and algorithms facilitating such models are explored
to provide transportation network managers and planners with more
flexibility under uncertainty. Network design problems with
non-stationary stochastic OD demand are formulated as real option
investment problems and dynamic programming solution methodologies are
used to obtain the value of flexibility to defer and re-design a
network. The design premium is shown to reflect the opportunity cost of
committing to a “preferred alternative” in transportation planning.
Both network option and link option design problems are proposed with
solution algorithms and tested on the classical Sioux Falls, SD network.
Results indicate that allowing individual links to be deferred can
have significant option value.
A resource relocation model using non-stationary stochastic variables as
chance constraints is proposed. The model is applied to air tanker
relocation for initial attack of wildfires in California, and results
show that the flexibility to switch locations with non-stationary
stochastic variables providing 3-day or 7-day forecasts is more
cost-effective than relocations without forecasting.
Due to the computational costs of these more complex network models, a
faster converging heuristic based on radial basis functions is evaluated
for continuous network design problems for the Anaheim, CA network with
a 31-dimensional decision variable. The algorithm is further modified
and then proven to converge for multi-objective problems. Compared to
other popular multi-objective solution algorithms in the literature such
as the genetic algorithm, the proposed multi-objective radial basis
function algorithm is shown to be most effective.
The algorithm is applied to a flexible robust toll pricing problem,
where toll pricing is proposed as a strategy to manage network
robustness over multiple regimes of link capacity uncertainty. A link
degradation simulation model is proposed that uses multivariate
Bernoulli random variables to simulate correlated link failures. The
solution to a multi-objective mean-variance toll pricing problem is
obtained for the Sioux Falls network under low and high probability
seasons, showing that the flexibility to adapt the Pareto set of toll
solutions to changes in regime – e.g. hurricane seasons, security threat
levels, etc – can increase value in terms of an epsilon indicator.
