A Bi-Objective Two-Level Capacitated Facility Location Model with Primary–Backup Assignments under Depot Disruptions

Abstract

Supply chain disruptions affect the economic and delivery performance of distribution networks. This study develops a bi-objective two-level capacitated facility location model under depot disruptions, assigning customers to primary and backup depots through the same satellite to ensure service continuity. The model minimizes expected system cost and delivery time under capacity restrictions. The initial nonlinear formulation is reformulated as an equivalent mixed-integer linear programming model, and a normalized weighted-sum approach examines the objective trade-off. Experiments on 20–70-node instances reveal a clear cost–delivery-time trade-off. Both single-objective models reach proven optimality for up to 35 nodes, while larger instances exhibit increasing solution times and optimality gaps. The results demonstrate the value of balancing economic and delivery performance in disruption aware distribution network design.