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Value of randomization in stochastic facility location problems under distributional ambiguity

​Distributionally-robust optimization (DRO) is a new paradigm for decision-making under uncertainty that offers a unifying framework for stochastic programming and robust optimization while avoiding some of their shortfalls. In DRO, the expected value of a probabilistic cost function is minimized, where the expectation is taken with respect to the worst-case probability distribution from a distributional ambiguity set that is constructed based on sample data or information about the "true" distribution of the uncertain parameters. I will start by providing a general overview of DRO and shedding light on some recent advances in the modelling and resolution of DRO problems. I will then show how to tractably reformulate and solve stochastic versions of two classical facility location problems (a single-stage UFLP and a two-stage CFLP) with uncertain demand distributions that belong to distributional ambiguity sets defined based on the Wasserstein statistical metric. Next, I will introduce and discuss the idea of "randomization" in the context of DRO problems and show how and when it can reduce risk. Finally, I will present a two-layer column-generation algorithm for a class of randomized DRO problems and apply it to solve the two facility location problems stated earlier. An illustrative example and some computational results will be presented to demonstrate the value of randomization.​]


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