Lagrangian Dual Decomposition for Two-Echelon Reliable Facility Location Problems with Facility Disruptions

This chapter considers the two-echelon supply chain network design with unreliable facilities when nodes related to facilities in both echelons fail under disruptions. A new mixed-integer programming (MIP) model is proposed for a reliable facility location with possible customer reassignment in different probabilistic scenarios. The maintaining of the materials flow between different echelons of the network is investigated under network disruptions. The performance of global optimization is investigated by comparing this approach with independent and non-integrated optimization. The objective function of the problem seeks to minimize expected costs, including fixed and service costs in the supply chain, such that maintaining the demand flow in both echelons of the network interconnects them. The medium- and large-sized problems are solved using a custom-designed Lagrangian dual decomposition algorithm. Our computational results show that the proposed algorithm is efficient for the given problems, efficiently overcomes the computational complexity of the problems, and provides good-quality solutions within an acceptable time.