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Xian Yu(yuxianumich.edu) Abstract: We study the capacitated facility location problem over a finite time horizon with uncertain demand at each stage. We model a multistage stochastic integer program based on a scenario tree representation of the multiperiod uncertainty, as opposed to a twostage approach that does not have the flexibility of dynamically locating facilities but has to decide multiperiod facilitylocation plans at the beginning of the horizon. At each stage, after realizing the demand, we optimize facility locations and recourse flows from built facilities to demand sites, with the goal of minimizing certain measure of the total cost of locating facilities and transportation. We quantify the lower bounds for the gaps between optimal objective values of the multistage models and their twostage counterparts, under riskneutral and riskaverse (coherent risk) measures. We also show that the bound with risk aversion is at least as large as the riskneutral bound. We employ Stochastic Dual Dynamic integer Programming (SDDiP) for solving the riskneutral multistage model, and extend the method for the riskaverse case using expected conditional risk measures (ECRMs). We conduct computational studies on diverse instances to empirically demonstrate the bounds, as well as to show the computational efficacy of SDDiP for solving both riskneutral and riskaverse multistage models. Keywords: Multistage stochastic integer programming; riskaverse optimization; Stochastic Dual Dynamic integer Programming (SDDiP) Category 1: Stochastic Programming Category 2: Integer Programming ((Mixed) Integer Linear Programming ) Category 3: Applications  Science and Engineering (Facility Planning and Design ) Citation: Download: [PDF] Entry Submitted: 09/16/2018 Modify/Update this entry  
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