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

We introduce a novel 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 present a novel branch-and-cut algorithm integrated … Read more

Modeling uncertainty processes for multi-stage optimization of strategic energy planning: An auto-regressive and Markov chain formulation

This paper deals with the modeling of stochastic processes in long-term multistage energy planning problems when little information is available on the degree of uncertainty of such processes. Starting from simple estimates of variation intervals for uncertain parameters, such as energy demands and costs, we model the temporal correlation of these parameters through autoregressive (AR) … Read more

Distributionally Robust Optimization with Markovian Data

We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with d states. We propose a data-driven distributionally robust optimization model to estimate the problem’s objective function and optimal solution. By leveraging results from … Read more