The Balanced Facility Location Problem: Complexity and Heuristics

A recent work proposes a new quadratic facility location model to address ecological challenges faced by policymakers in Bavaria, Germany. Building on this, we significantly extend our understanding of this new problem. We develop connections to traditional combinatorial optimization models and show that the problem is [Formula: see text] hard. We then develop several classes of easy-to-implement heuristics to solve this problem. These are rooted in solving special cases of the generalized quadratic assignment problem as a subproblem; this subproblem is also [Formula: see text] hard. On moderate-sized instances from Bavaria—that were previously intractable—our proposed heuristics compute feasible solutions that are 0.5% (on average) improved over the generic solution method in just over a minute (on average), even when the generic solver runs for 20,000 seconds. Larger instances show an improvement of 5% (on average) compared with the generic solution method in an average of 410 seconds. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: B. Singh was partially supported by the University of Southampton [Research Investment and Support Building Sustainable and Green Futures Program]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0693 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0693 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .