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We consider the robust single-source capacitated facility location problemwith uncertainty in customer demands. A cardinality-constrained uncertainty setis assumed for the robust problem. To solve it efficiently, we propose anallocation-based formulation derived by Dantzig-Wolfe decomposition and abranch-and-price algorithm. The computational experiments show that ourbranch-and-price algorithm outperforms CPLEX in many cases, which solves theordinary robust reformulation. We also examine the trade-off relationshipbetween the empirical probability of infeasibility and the additional costsincurred and observe that the robustness of solutions can be improvedsignificantly with small additional costs.

A branch-and-price algorithm for the robust single-source capacitated facility location problem under demand uncertainty