Two-stage robust bilevel optimization model for facility location considering operational service level under disruption risk

Abstract: The bilevel facility location problem (BO-FLP) is one of the core optimization problems behind the design of many decentralized industrial systems, e.g., supply chain systems where a supplier constructs some critical facilities and then uses them to serve retailers in a cost-effective fashion, while retailers directly handle customers aiming to minimize the total unmet demand in a rather independent fashion. When uncertainty is considered, scenario-based stochastic approaches are commonly used, but they often become impractical due to insufficient data or an exponential number of scenarios. To address this issue, this paper adopts robust optimization and proposes a novel two-stage robust bilevel facility location model. Several structural properties are derived to improve both theoretical understanding and solution efficiency. Based on this, an enhanced column-and-constraint generation algorithm is developed for robust bilevel optimization with decision-dependent uncertainty, significantly improving exact solution capability over the standard method. Numerical results show that, compared to the centralized two-stage RO model, our model pays more attention to demand fulfillment, typically resulting in higher service efficiency and better utilization of supply capacity. Under a small-scale disruption, this new model delivers better service performance. However, under a large-scale disruption, the centralized model performs more effectively.