Column-Generation for Design of Survivable Electricity Distribution Networks

We investigate the problem of designing survivable electricity distribution networks subject to multiple, non-simultaneous link failures under a radial-network operating con…guration. We formulate this problem as a two-stage stochastic mixed-integer program in which …rst-stage decisions expand capacity; recourse decisions con…gure the network to operate as a tree and to meet demand, by opening and closing electrical switches. Dantzig-Wolfe decomposition of this formulation leads to (a) a master problem comprising binary capacity-expansion and high-level operating decisions; and (b) mixed-integer, column-generating subproblems which represent deterministic capacityexpansion models. A “super-arc representation” of the network signi…cantly reduces the number of binary variables, and provides a tighter linear-programming relaxation for the subproblems. Column generation with super-arc subproblems solves the model signi…cantly faster than CPLEX can solve the original, extensive model.