  We consider a logistics planning problem of prepositioning relief items in
preparation for an impending hurricane landfall. This problem is modeled as a
multiperiod network flow problem where the objective is to minimize the
logistics cost of operating the network and the penalty for unsatisfied demand.
We assume that the demand for relief items can be derived from the hurricane's
predicted intensity and landfall location, which evolves according to a Markov
chain. We consider this problem in two different settings, depending on whether
the time of landfall is assumed to be deterministic (and known a priori) or
random. For the former case, we introduce a fully adaptive multi-stage
stochastic programming (MSP) model that allows the decision-maker to adjust the
prepositioning decisions, sequentially, over multiple stages, as the
hurricane's characteristics become clearer. For the latter case, we extend the
MSP model with a random number of stages introduced in Guigues (2021), to the
case where the underlying stochastic process is assumed to be stage-wise
dependent. We benchmark the performance of the MSP models with other
approximation policies such as the static and rolling-horizon two-stage
stochastic programming approaches. Our numerical results provide key insight
into the value of MSP, in disaster relief logistics planning.
