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Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the distribution of the uncertain parameters, which is provided by: (1) sample data and (2) <jats:italic>a-priori<\/jats:italic> information on the order among the probabilities that the true data-generating distribution assigns to some regions of its support set. This type of order is enforced by means of order cone constraints and can encode a wide range of information on the shape of the probability distribution of the uncertain parameters such as information related to monotonicity or multi-modality. We seek decisions that are distributionally robust. In a number of practical cases, the resulting distributionally robust optimization (DRO) problem can be reformulated as a finite convex problem where the <jats:italic>a-priori<\/jats:italic> information translates into linear constraints. In addition, our method inherits the finite-sample performance guarantees of the Wasserstein-metric-based DRO approach proposed by Mohajerin Esfahani and Kuhn (Math Program 171(1\u20132):115\u2013166. <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"doi\" xlink:href=\"10.1007\/s10107-017-1172-1\">https:\/\/doi.org\/10.1007\/s10107-017-1172-1<\/jats:ext-link>, 2018), while generalizing this and other popular DRO approaches. Finally, we have designed numerical experiments to analyze the performance of our approach with the newsvendor problem and the problem of a strategic firm competing \u00e0 la Cournot in a market.<\/jats:p>","DOI":"10.1007\/s10288-021-00484-z","type":"journal-article","created":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T15:03:22Z","timestamp":1623423802000},"page":"465-497","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Partition-based distributionally robust optimization via optimal transport with order cone constraints"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0124-8772","authenticated-orcid":false,"given":"Adri\u00e1n","family":"Esteban-P\u00e9rez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9114-686X","authenticated-orcid":false,"given":"Juan M.","family":"Morales","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,6,11]]},"reference":[{"issue":"1","key":"484_CR1","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.ejor.2013.01.031","volume":"228","author":"J Andersson","year":"2013","unstructured":"Andersson J, J\u00f6rnsten K, Non\u00e5s SL, Sandal L, Ub\u00f8e J (2013) A maximum entropy approach to the newsvendor problem with partial information. 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