  We introduce an aggregation framework to address multi-stage stochastic
programs with mixed-integer state variables and continuous local variables
(MSILPs). Our aggregation framework imposes additional structure to the integer
state variables by leveraging the information of the underlying stochastic
process, which is modeled as a Markov chain (MC). We demonstrate that the
aggregated MSILP can be solved exactly via a branch-and-cut algorithm
integrated with a variant of stochastic dual dynamic programming. To improve
tractability, we propose to use this approach to obtain dual bounds. Moreover,
we apply two-stage linear decision rule (2SLDR) approximations, in particular a
new MC-based variant that we propose, to obtain high-quality decision policies
with significantly reduced computational effort. We test the proposed
methodologies in an MSILP model for hurricane disaster relief logistics
planning. Our empirical evaluation compares the effectiveness of the various
proposed approaches and analyzes the trade-offs between policy flexibility,
solution quality, and computational effort. Specifically, the 2SLDR
approximation yields provable high-quality solutions for our test instances
supported by the proposed bounding procedure. We also extract valuable
managerial insights from the solution behaviors exhibited by the underlying
decision policies.
