Robust inventory decision under distribution uncertainty: A CVaR-based optimization approach

We study the robust inventory decision-making problem faced by risk-averse managers with incomplete demand information in a newsvendor setting. Three basic models are developed: expected profit maximization, CVaR-based profit maximization, and a combination of the two. Each model is robustly formulated under the assumption of ellipsoid discrete distribution and again under the box discrete distribution. Each robust model can be mathematically transformed into a second-order cone program for ellipsoid uncertainty or into a general convex optimization problem for box uncertainty. Both transformed problems can be optimally solved directly. We offer propositions with proof to show the equivalence of the transformed problems with the original ones. Numerical examples are given to validate the proposed approach. We find that the performances under both ellipsoid and box uncertain distributions are robust. Finally, sensitivity analysis with respect to risk-averse levels and trade-off coefficients is conducted to validate the proposed models and solution approaches.