Reliable facility location design under disruptions

Distribution networks have been facing an increased exposure to risk of unpredicted disruptions causing significant economic forfeitures. At the same time, the existing literature features very few studies which examine the impact of facility fortification for improving network reliability. In this paper, we present two related models for design of reliable distribution networks: a reliable P-median problem (RPMP) and a reliable uncapacitated fixed-charge location problem (RUFL). Both models consider heterogenous facility failure probabilities, one layer of supplier backup, and facility fortification within a finite budget. Both RPMP and RUFL are formulated as nonlinear integer programming models and proved to be NP-hard. We develop Lagrangian relaxation-based (LR) solution algorithms and demonstrate their computational efficiency. We compare the effectiveness of the LR-based solutions to that of the solutions obtained by a myopic policy which aims to fortify most reliable facilities regardless of the demand topology. Finally, we discuss an alternative way to assess the effectiveness of the design solutions by using the rate of return on fortification investment.