Reliable location-routing design under probabilistic facility disruptions

This study considers an integer programming formulation of a reliable location routing problem in which built facilities are subject to the risk of probabilistic disruptions. In this study we identify facility locations, and outbound delivery routing and backup plans during disruptions to minimize facility setup, routing, and customer penalty costs (if no delivery is possible). A variety of approaches (e.g., Lagrangian relaxation with embedded column generation and local search) to solving the problem are assessed. We conduct numerical case studies to test the performance of the proposed model and solution algorithms. The findings offer managerial insights into how various system parameters affect the optimal solution.