Two-stage robust LP with ellipsoidal right-hand side uncertainty is NP-hard

As shown in previous work, robust linear programming problems featuring polyhedral right-hand side (RHS) uncertainty (a) arise in many practical applications; (b) frequently lead to robust equivalents belonging to the class of strongly NP-hard problems. In the present paper the case of ellipsoidal RHS uncertainty is investigated and similar complexity results are shown to hold even when restricting to simplified specially structured problems related to robust production planning under uncertain customer requirements. The proof is based on a reduction which significantly differs from the one used in the case of polyhedral RHS uncertainty.