  We consider the robust single-source capacitated facility location problem
with uncertainty in customer demands. A cardinality-constrained uncertainty set
is assumed for the robust problem. To solve it efficiently, we propose an
allocation-based formulation derived by Dantzig-Wolfe decomposition and a
branch-and-price algorithm. The computational experiments show that our
branch-and-price algorithm outperforms CPLEX in many cases, which solves the
ordinary robust reformulation. We also examine the trade-off relationship
between the empirical probability of infeasibility and the additional costs
incurred and observe that the robustness of solutions can be improved
significantly with small additional costs.
