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On\u2010network demand points are serviced using shortest\u2010path distances through links of the network (e.g., on\u2010road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst\u2010case distance. We solve our formulations using the \u201cBig Segment Small Segment\u201d global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi\u2010facility problems by solving a sequence of single\u2010facility problems. \u00a9 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(4), 271\u2013282 2016<\/jats:p>","DOI":"10.1002\/net.21698","type":"journal-article","created":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T16:16:44Z","timestamp":1471537004000},"page":"271-282","source":"Crossref","is-referenced-by-count":9,"title":["Mixed planar and network single\u2010facility location problems"],"prefix":"10.1002","volume":"68","author":[{"given":"Zvi","family":"Drezner","sequence":"first","affiliation":[{"name":"Steven G. 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