Reliable supply chain network design problem: Supermodularity and a cutting-plane approach

We study the reliable supply chain network design problem with the consideration of unexpected facility failures with probabilities. When such failure occurs, a facility loses its full capacity, and the customers that originally assigned to it have to be reassigned to another working facility. The goal is to minimize the initial setup costs and expected transportation costs in normal and failure scenarios. We propose a cutting-plane method based on the supermodularity of the problem. The supermodularity is general in the sense that it holds for the problem regardless the facility failures are correlated or not. Therefore, the proposed approach is capable of solving the reliable supply chain network design problem for both cases. To the best of our knowledge, the proposed approach is the first in the literature that solves the problem exactly with correlated failures. The preliminary computational studies show that this approach outperforms the best-known algorithm in the literature with uncorrelated disruptions on benchmark instances.