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We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then used to determine the nondominated solutions of triobjective 0\u20131 models, built to design nutritionally adequate and healthy diet plans, minimizing their environmental impact. The diet plans refer to menus for school cafeterias and we consider the carbon, water and nitrogen footprints as conflicting objectives to be minimized. Energy and nutrient contents are constrained in suitable ranges suggested by the dietary recommendation of health authorities. Results obtained on two models and on real world data are reported and discussed.<\/jats:p>","DOI":"10.1007\/s00186-024-00879-8","type":"journal-article","created":{"date-parts":[[2024,10,15]],"date-time":"2024-10-15T08:02:31Z","timestamp":1728979351000},"page":"703-721","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Designing sustainable diet plans by solving triobjective integer programs"],"prefix":"10.1007","volume":"100","author":[{"given":"Luca","family":"Benvenuti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alberto","family":"De Santis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1189-5917","authenticated-orcid":false,"given":"Marianna","family":"De Santis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniele","family":"Patria","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,10,15]]},"reference":[{"issue":"2","key":"879_CR1","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s12532-015-0093-3","volume":"8","author":"N Boland","year":"2016","unstructured":"Boland N, Charkhgard H, Savelsbergh M (2016) The L-shape search method for triobjective integer programming. 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