Reliable Facility Location Design Under the Risk of Disruptions

TLDR

Reliable facility location models account for unexpected failures with site‑dependent probabilities and possible customer reassignment. This paper proposes a compact mixed‑integer program and a continuum approximation to solve the reliable uncapacitated fixed‑charge location problem, aiming to minimize initial setup and expected transportation costs under normal and failure scenarios. The authors formulate the problem as a mixed‑integer program solved via a custom Lagrangian relaxation algorithm, and use the continuum approximation to predict total system cost and generate fast near‑optimal solutions. Computational experiments demonstrate that the Lagrangian relaxation algorithm efficiently solves mid‑sized instances, while the continuum approximation yields near‑optimal solutions and serves as a practical alternative for large‑scale problems, avoiding prohibitively long runtimes.

Abstract

Reliable facility location models consider unexpected failures with site-dependent probabilities, as well as possible customer reassignment. This paper proposes a compact mixed integer program (MIP) formulation and a continuum approximation (CA) model to study the reliable uncapacitated fixed charge location problem (RUFL), which seeks to minimize initial setup costs and expected transportation costs in normal and failure scenarios. The MIP determines the optimal facility locations as well as the optimal customer assignments and is solved using a custom-designed Lagrangian relaxation (LR) algorithm. The CA model predicts the total system cost without details about facility locations and customer assignments, and it provides a fast heuristic to find near-optimum solutions. Our computational results show that the LR algorithm is efficient for mid-sized RUFL problems and that the CA solutions are close to optimal in most of the test instances. For large-scale problems, the CA method is a good alternative to the LR algorithm that avoids prohibitively long running times.