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

TL;DR

This paper introduces a two-stage robust bilevel facility location model that enhances decision-making under disruption risk by improving solution efficiency and service performance, especially in small-scale disruptions.

Contribution

It develops a novel two-stage robust bilevel optimization model with structural properties and an improved solution algorithm for decision-dependent uncertainty.

Findings

Better demand fulfillment and service efficiency in small disruptions

Enhanced solution method outperforms standard approaches

Model adapts to different scales of disruption effectively

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.