  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.
