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Register a new userA Flexible Multi-Facility Capacity Expansion Problem with Risk Aversion
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This paper studies flexible multi-facility capacity expansion with risk aversion. In this setting, the decision maker can periodically expand the capacity of facilities given observations of uncertain demand. We model this situation as a multi-stage stochastic programming problem. We express risk aversion in this problem through conditional value-at-risk (CVaR), and we formulate a mean-CVaR objective. To solve the multi-stage problem, we optimize over decision rules. In particular, we approximate the full policy space of the problem with a tractable family of if-then policies. Subsequently, a decomposition algorithm is proposed to optimize the decision rule. This algorithm decomposes the model over scenarios and it updates solutions via the subgradients of the recourse function. We demonstrate that this algorithm can quickly converge to high-performance policies. To illustrate the practical effectiveness of this method, a case study on the waste-to-energy system in Singapore is presented. These simulation results show that by adjusting the weight factor of the objective function, decision makers are able to trade off between a risk-averse policy that has a higher expected cost but a lower value-at-risk, and a risk-neutral policy that has a lower expected cost but a higher value-at-risk risk.
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This paper applies the N-block PCPM algorithm to solve multi-scale multi-stage stochastic programs, with the application to electricity capacity expansion models. Numerical results show that the proposed simplified N-block PCPM algorithm, along with the hybrid decomposition method, exhibits much better scalability for solving the resulting deterministic, large-scale block-separable optimization problem when compared with the ADMM algorithm and the PHA algorithm. The superiority of the algorithms scalability is attributed to the two key features of the algorithm design: first, the proposed hybrid scenario-node-realization decomposition method with extended nonanticipativity constraints can decompose the original problem under various uncertainties of different temporal scales; second, when applying the N-block PCPM algorithm to solve the resulting deterministic, large-scale N-block convex optimization problem, the technique of orthogonal projection we exploit greatly simplifies the iteration steps and reduce the communication overhead among all computing units, which also contributes to the efficiency of the algorithm.
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