{"paper":{"title":"Asymptotic optimal location of facilities in a competition between population and industries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Eugene Stepanov, Filippo Santambrogio, Giuseppe Buttazzo","submitted_at":"2013-12-19T08:38:29Z","abstract_excerpt":"We consider the problem of optimally locating a given number $k$ of points in ${\\mathbb R}^n$ for an integral cost function which takes into account two measures $\\varphi^+$ and $\\varphi^-$. The points represent for example new industrial facilities that have to be located, the measure $\\varphi^+$ representing in this case already existing industries that want to be close to the new ones, and $\\varphi^-$ representing private citizens who want to stay far away. The asymptotic analysis as $k\\to\\infty$ is performed, providing the asymptotic density of optimal locations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5437","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}