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It produces the extreme points (i.e., the vertices) as well as the facets of the Edgeworth\u2013Pareto hull. We note that these extreme points are the extreme supported non-dominated points of a MOMILP. We also show how to extend the concept of geometric duality for multi-objective linear programming problems to the Edgeworth\u2013Pareto hull of MOMILPs and use this extension to develop the algorithm. The algorithm relies on a novel oracle that solves single-objective weighted-sum problems and we show that the required number of oracle calls is polynomial in the number of facets of the convex hull of the extreme supported non-dominated points in the case of MOMILPs. Thus, for MOMILPs for which the weighted-sum problem is solvable in polynomial time, the facets can be computed with incremental-polynomial delay\u2014a result that was formerly only known for the computation of extreme supported non-dominated points. Our algorithm can be an attractive option to compute lower bound sets within multi-objective branch-and-bound algorithms for solving MOMILPs. This is for several reasons as (i) the algorithm starts from a trivial valid lower bound set then iteratively improves it, thus at any iteration of the algorithm a lower bound set is available; (ii) the algorithm also produces efficient solutions (i.e., solutions in the decision space); (iii) in any iteration of the algorithm, a relaxation of the MOMILP can be solved, and the obtained points and facets still provide a valid lower bound set. Moreover, for the special case of multi-objective linear programming problems, the algorithm solves the problem to global optimality. A computational study on a set of benchmark instances from the literature is provided.<\/jats:p>","DOI":"10.1007\/s00186-023-00847-8","type":"journal-article","created":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T10:02:37Z","timestamp":1704362557000},"page":"263-290","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An outer approximation algorithm for generating the Edgeworth\u2013Pareto hull of multi-objective mixed-integer linear programming problems"],"prefix":"10.1007","volume":"100","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7950-6965","authenticated-orcid":false,"given":"Fritz","family":"B\u00f6kler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7428-9770","authenticated-orcid":false,"given":"Sophie N.","family":"Parragh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1439-8702","authenticated-orcid":false,"given":"Markus","family":"Sinnl","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3700-5134","authenticated-orcid":false,"given":"Fabien","family":"Tricoire","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,1,4]]},"reference":[{"issue":"2","key":"847_CR1","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1287\/ijoc.2021.1092","volume":"34","author":"N Adelgren","year":"2022","unstructured":"Adelgren N, Gupte A (2022) Branch-and-bound for biobjective mixed-integer linear programming. 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