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We introduce an aggregation framework to address multi-stage stochasticprograms with mixed-integer state variables and continuous local variables(MSILPs). Our aggregation framework imposes additional structure to the integerstate variables by leveraging the information of the underlying stochasticprocess, which is modeled as a Markov chain (MC). We demonstrate that theaggregated MSILP can be solved exactly via a branch-and-cut algorithmintegrated with a variant of stochastic dual dynamic programming. To improvetractability, we propose to use this approach to obtain dual bounds. Moreover,we apply two-stage linear decision rule (2SLDR) approximations, in particular anew MC-based variant that we propose, to obtain high-quality decision policieswith significantly reduced computational effort. We test the proposedmethodologies in an MSILP model for hurricane disaster relief logisticsplanning. Our empirical evaluation compares the effectiveness of the variousproposed approaches and analyzes the trade-offs between policy flexibility,solution quality, and computational effort. Specifically, the 2SLDRapproximation yields provable high-quality solutions for our test instancessupported by the proposed bounding procedure. We also extract valuablemanagerial insights from the solution behaviors exhibited by the underlyingdecision policies.

Markov Chain-based Policies for Multi-stage Stochastic Integer Linear Programming with an Application to Disaster Relief Logistics