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While typically, this river exploration is done by boat, truck, helicopter, or even not at all, autonomous flying drones equipped with a camera can enhance this process. Moreover, interaction between a truck and a drone can enable the drone to be used flexibly and extend its short range. Thus, the Bavarian Red Cross equipped a truck with a drone for river coverage. Based on this real case, we introduce a truck drone arc covering problem (TD-ACP) for the application of river coverage. We formulate the TD-ACP as a mixed-integer linear program and introduce valid inequalities that strengthen the formulation and allow us to solve realistic-sized instances to optimality. In a real-world case study involving an actual river, we demonstrate that using drones for river coverage can reduce coverage time by 56.3% compared to boats and by 28.1% compared to trucks. Additionally, we propose a manual planning heuristic that is straightforward for practitioners to apply and achieves an optimality gap of 4.0% on this specific river.<\/jats:p>","DOI":"10.1007\/s10479-025-06829-9","type":"journal-article","created":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T10:01:05Z","timestamp":1757930465000},"page":"1053-1077","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Truck drone arc covering problem with an application and case study in disaster management"],"prefix":"10.1007","volume":"353","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0262-4859","authenticated-orcid":false,"given":"Alexander","family":"Rave","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pirmin","family":"Fontaine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,9,15]]},"reference":[{"key":"6829_CR1","doi-asserted-by":"publisher","unstructured":"Aljalaud, F., Kurdi, H., & Youcef-Toumi, K. 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Pirmin Fontaine declares that he has no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}