Facility location decision under data contamination: robustness properties and performance

The facility location decision problem conventionally assumes that demand locations are known to the decision maker with certainty. However, in many practical circumstances, information on demand locations is inaccurate or involves potential errors (which we refer to as contamination). We first investigate the robustness properties of popular location estimation methods (the centre of gravity method and methods based on L1 and L2 distances) for the Weber problem. To this end, we apply two important robustness metrics from statistics to the problem: infinitesimal robustness (sensitivity to contamination) and breakdown point (amount of robustness). We then numerically compare the performances of the location estimation methods by employing a new measure called relative performance. [Received: 3 June 2024; Accepted: 3 January 2025]