In a recent work, Schmitt and Singh propose a new quadratic facility location model to address ecological challenges faced by policymakers in Bavaria, Germany. Building on this previous work, we significantly extend our understanding of this new problem. We develop connections to traditional combinatorial optimization models and show the problem is NP-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 NP-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 naive solution method in just over a minute (on average), even when the naive solver runs for 20,000 seconds. Larger instances show an improvement of 5% (on average) compared to the naive solution method in an average of 410 seconds.
Citation
Schmidt M. & Singh, B (March, 2024). The Balanced Facility Location Problem: Complexity and Heuristics
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